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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Conway's life and games\n",
"\n",
"![](data:image/jpeg;base64,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)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Conway's Life"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"Some of his achievements:\n",
" \n",
"* Game of Life\n",
"* Surreal numbers\n",
"* Free Will Theorem"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Game of Life\n",
"\n",
"\n",
"<img style=\"height: 600px\" src=\"https://raw.githubusercontent.com/marcoemrich/game-of-life-rules/master/gol_rules.png\">"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"from pylab import rc\n",
"\n",
"import numpy as np\n",
"import scipy\n",
"from IPython.display import HTML\n",
"from matplotlib import animation\n",
"\n",
"rc('animation', html='html5')"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [],
"source": [
"def life_step(X):\n",
" \"\"\"Game of life step using scipy tools\"\"\"\n",
" from scipy.signal import convolve2d\n",
" nbrs_count = convolve2d(X, np.ones((3, 3)), mode='same', boundary='wrap') - X\n",
" return (nbrs_count == 3) | (X & (nbrs_count == 2))"
]
},
{
"cell_type": "code",
"execution_count": 175,
"metadata": {
"scrolled": false,
"slideshow": {
"slide_type": "skip"
}
},
"outputs": [],
"source": [
"def life_animation(X, dpi=120, fps=30, frames=10, interval=300, mode='loop', save=None):\n",
" \"\"\"Produce a Game of Life Animation\n",
" \n",
" Parameters\n",
" ----------\n",
" X : array_like\n",
" a two-dimensional numpy array showing the game board\n",
" dpi : integer\n",
" the number of dots per inch in the resulting animation.\n",
" This controls the size of the game board on the screen\n",
" frames : integer\n",
" The number of frames to compute for the animation\n",
" interval : float\n",
" The time interval (in milliseconds) between frames\n",
" mode : string\n",
" The default mode of the animation. Options are ['loop'|'once'|'reflect']\n",
" \"\"\"\n",
" X = np.asarray(X)\n",
" assert X.ndim == 2\n",
" X = X.astype(bool)\n",
" \n",
" X_blank = np.zeros_like(X)\n",
"# figsize = (X.shape[1] * 1. / dpi, X.shape[0] * 1. / dpi)\n",
"# print(figsize, dpi)\n",
"\n",
" fig = plt.figure(dpi=dpi);\n",
" plt.close()\n",
" ax = fig.add_axes([0, 0, 1, 1], xticks=[], yticks=[], frameon=False)\n",
" im = ax.imshow(X, cmap=plt.cm.binary, interpolation='nearest')\n",
" im.set_clim(-0.05, 1) # Make background gray\n",
" orig = X.copy()\n",
" # initialization function: plot the background of each frame\n",
" def init():\n",
" im.set_data(orig)\n",
" animate.X = orig\n",
" return (im,)\n",
"\n",
" # animation function. This is called sequentially\n",
" def animate(i):\n",
" im.set_data(animate.X)\n",
" animate.X = life_step(animate.X)\n",
" return (im,)\n",
"\n",
" anim = animation.FuncAnimation(fig, animate, init_func=init,\n",
" frames=frames, interval=interval,\n",
" blit=True)\n",
" \n",
" #print anim_to_html(anim)\n",
" htmlcode = anim.to_jshtml(default_mode=mode)\n",
" if save:\n",
" anim.save(save+'.gif', writer='imagemagick', fps=fps)\n",
" return HTML(htmlcode)\n",
"\n",
"\n",
"def pattern(*figs, height=50, width=70):\n",
" '''Concatenate different patterns into a single board'''\n",
" X = np.zeros((height, width)) \n",
" for patt, x0, y0 in figs:\n",
" X[y0:y0+len(patt), x0:x0+len(patt[0])] = patt\n",
" return X"
]
},
{
"cell_type": "code",
"execution_count": 110,
"metadata": {
"scrolled": false,
"slideshow": {
"slide_type": "slide"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_imgac1f9f10fb434e7ab1fea8cb743cdad2\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_sliderac1f9f10fb434e7ab1fea8cb743cdad2\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"animac1f9f10fb434e7ab1fea8cb743cdad2.set_frame(parseInt(this.value));\"></input>\n",
" <div class=\"anim-buttons\">\n",
" <button onclick=\"animac1f9f10fb434e7ab1fea8cb743cdad2.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"animac1f9f10fb434e7ab1fea8cb743cdad2.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"animac1f9f10fb434e7ab1fea8cb743cdad2.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"animac1f9f10fb434e7ab1fea8cb743cdad2.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"animac1f9f10fb434e7ab1fea8cb743cdad2.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"animac1f9f10fb434e7ab1fea8cb743cdad2.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"animac1f9f10fb434e7ab1fea8cb743cdad2.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"animac1f9f10fb434e7ab1fea8cb743cdad2.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"animac1f9f10fb434e7ab1fea8cb743cdad2.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form action=\"#n\" name=\"_anim_loop_selectac1f9f10fb434e7ab1fea8cb743cdad2\" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_ac1f9f10fb434e7ab1fea8cb743cdad2\"\n",
" checked>\n",
" <label for=\"_anim_radio1_ac1f9f10fb434e7ab1fea8cb743cdad2\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_ac1f9f10fb434e7ab1fea8cb743cdad2\"\n",
" >\n",
" <label for=\"_anim_radio2_ac1f9f10fb434e7ab1fea8cb743cdad2\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_ac1f9f10fb434e7ab1fea8cb743cdad2\"\n",
" >\n",
" <label for=\"_anim_radio3_ac1f9f10fb434e7ab1fea8cb743cdad2\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_imgac1f9f10fb434e7ab1fea8cb743cdad2\";\n",
" var slider_id = \"_anim_sliderac1f9f10fb434e7ab1fea8cb743cdad2\";\n",
" var loop_select_id = \"_anim_loop_selectac1f9f10fb434e7ab1fea8cb743cdad2\";\n",
" var frames = new Array(40);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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"BAIaAACCOywkFnTLSG3mAAAAAElFTkSuQmCC\\\n",
"\"\n",
" frames[39] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
"AAASdAAAEnQB3mYfeAAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0\\\n",
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"AIDAQAMAQGCgAQAgMNAAABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAAABAY\\\n",
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"gYEGAIDAQAMAQGCgAQAgMNAAABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAA\\\n",
"ABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAAABAYaAAACAw0AAAEBhoAAAID\\\n",
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"MNAAABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAAABAYaAAACAw0AAAEBhoA\\\n",
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"AQAgMNAAABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAAABAYaAAACAw0AAAE\\\n",
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"MNAAABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAAABAYaAAACAw0AAAEBhoA\\\n",
"AAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAAABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDAQAMAQGCg\\\n",
"AQAgMNAAABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAAABAYaAAACAw0AAAE\\\n",
"BhoAAAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAAABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDAQAMA\\\n",
"QGCgAQAgMNAAABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAAABAYaAAACAw0\\\n",
"AAAEBhoAAAIDDQAAgYEGAIDAQAMAQGCgAQAgMNAAABAYaAAACAw0AAAEBhoAAAIDDQAAgYEGAIDA\\\n",
"QAMAQGCgAQAgMNAAABAYaAAACG70LQq8OKqFaAAAAABJRU5ErkJggg==\\\n",
"\"\n",
"\n",
"\n",
" /* set a timeout to make sure all the above elements are created before\n",
" the object is initialized. */\n",
" setTimeout(function() {\n",
" animac1f9f10fb434e7ab1fea8cb743cdad2 = new Animation(frames, img_id, slider_id, 299.0,\n",
" loop_select_id);\n",
" }, 0);\n",
" })()\n",
"</script>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 110,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.random.seed(0)\n",
"X = np.zeros((30, 40), dtype=bool)\n",
"r = np.random.random((10, 20))\n",
"X[10:20, 10:30] = (r > 0.75)\n",
"life_animation(X, dpi=120, frames=40, mode='once')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Static configurations"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_imgab4f54e7a3de460884d4af8a345be8d4\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_sliderab4f54e7a3de460884d4af8a345be8d4\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"animab4f54e7a3de460884d4af8a345be8d4.set_frame(parseInt(this.value));\"></input>\n",
" <div class=\"anim-buttons\">\n",
" <button onclick=\"animab4f54e7a3de460884d4af8a345be8d4.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"animab4f54e7a3de460884d4af8a345be8d4.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"animab4f54e7a3de460884d4af8a345be8d4.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"animab4f54e7a3de460884d4af8a345be8d4.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"animab4f54e7a3de460884d4af8a345be8d4.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"animab4f54e7a3de460884d4af8a345be8d4.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"animab4f54e7a3de460884d4af8a345be8d4.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"animab4f54e7a3de460884d4af8a345be8d4.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"animab4f54e7a3de460884d4af8a345be8d4.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form action=\"#n\" name=\"_anim_loop_selectab4f54e7a3de460884d4af8a345be8d4\" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_ab4f54e7a3de460884d4af8a345be8d4\"\n",
" >\n",
" <label for=\"_anim_radio1_ab4f54e7a3de460884d4af8a345be8d4\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_ab4f54e7a3de460884d4af8a345be8d4\"\n",
" checked>\n",
" <label for=\"_anim_radio2_ab4f54e7a3de460884d4af8a345be8d4\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_ab4f54e7a3de460884d4af8a345be8d4\"\n",
" >\n",
" <label for=\"_anim_radio3_ab4f54e7a3de460884d4af8a345be8d4\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_imgab4f54e7a3de460884d4af8a345be8d4\";\n",
" var slider_id = \"_anim_sliderab4f54e7a3de460884d4af8a345be8d4\";\n",
" var loop_select_id = \"_anim_loop_selectab4f54e7a3de460884d4af8a345be8d4\";\n",
" var frames = new Array(3);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
"AAASdAAAEnQB3mYfeAAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0\\\n",
"dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAJ20lEQVR4nO3YQYobMRRF0XLwVPtfqHpeGSVgPEjf\\\n",
"DFrfcM4KHiUVXPS47/u+AACAb/l1egAAAHwSAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgE\\\n",
"NAAABAIaAAACAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIaAAACAQ0AAIGABgCA\\\n",
"QEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIaAAACAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgA\\\n",
"AAgENAAABAIaAAACAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIaAAACAQ0AAIGA\\\n",
"BgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIaAAACAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQ\\\n",
"CGgAAAgENAAABAIaAAACAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIaAAACAQ0A\\\n",
"AIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIaAAACAQ0AAIGABgCAQEADAEAgoAEAIBDQ\\\n",
"AAAQCGgAAAgENAAABAIaAAACAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIaAAAC\\\n",
"AQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIaAAACAQ0AAIGABgCAQEADAEAgoAEA\\\n",
"IBDQAAAQCGgAAAgENAAABAIaAAACAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIa\\\n",
"AAACAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIaAAACAQ0AAIGABgCAQEADAEAg\\\n",
"oAEAIBDQAAAQCGgAAAgENAAABAIaAAACAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAA\\\n",
"BM+vr6/TGwAA4GN4gQYAgEBAAwBAIKABACAQ0AAAEAhoAAAIBDQAAAQCGgAAAgENAACBgAYAgEBA\\\n",
"AwBAIKABACAQ0AAAEAhoAAAIBDQAAAQCGgAAAgENAACBgAYAgEBAAwBAIKABACAQ0AAAEAhoAAAI\\\n",
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"\"\n",
"\n",
"\n",
" /* set a timeout to make sure all the above elements are created before\n",
" the object is initialized. */\n",
" setTimeout(function() {\n",
" animab4f54e7a3de460884d4af8a345be8d4 = new Animation(frames, img_id, slider_id, 299.0,\n",
" loop_select_id);\n",
" }, 0);\n",
" })()\n",
"</script>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 111,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X = np.zeros((6, 21))\n",
"X[2:4, 1:3] = 1\n",
"X[1:4, 5:9] = [[0, 1, 1, 0],\n",
" [1, 0, 0, 1],\n",
" [0, 1, 1, 0]]\n",
"X[1:5, 11:15] = [[0, 1, 1, 0],\n",
" [1, 0, 0, 1],\n",
" [0, 1, 0, 1],\n",
" [0, 0, 1, 0]]\n",
"X[1:4, 17:20] = [[1, 1, 0],\n",
" [1, 0, 1],\n",
" [0, 1, 0]]\n",
"\n",
"life_animation(X, dpi=120, frames=3)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### The \"Blinker\" and the \"Toad\" (Period-2 oscillators)\n"
]
},
{
"cell_type": "code",
"execution_count": 112,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_imga8717f1208794cb2a0400c38e379ed64\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_slidera8717f1208794cb2a0400c38e379ed64\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"anima8717f1208794cb2a0400c38e379ed64.set_frame(parseInt(this.value));\"></input>\n",
" <div class=\"anim-buttons\">\n",
" <button onclick=\"anima8717f1208794cb2a0400c38e379ed64.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"anima8717f1208794cb2a0400c38e379ed64.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"anima8717f1208794cb2a0400c38e379ed64.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"anima8717f1208794cb2a0400c38e379ed64.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"anima8717f1208794cb2a0400c38e379ed64.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"anima8717f1208794cb2a0400c38e379ed64.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"anima8717f1208794cb2a0400c38e379ed64.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"anima8717f1208794cb2a0400c38e379ed64.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"anima8717f1208794cb2a0400c38e379ed64.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form action=\"#n\" name=\"_anim_loop_selecta8717f1208794cb2a0400c38e379ed64\" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_a8717f1208794cb2a0400c38e379ed64\"\n",
" >\n",
" <label for=\"_anim_radio1_a8717f1208794cb2a0400c38e379ed64\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_a8717f1208794cb2a0400c38e379ed64\"\n",
" checked>\n",
" <label for=\"_anim_radio2_a8717f1208794cb2a0400c38e379ed64\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_a8717f1208794cb2a0400c38e379ed64\"\n",
" >\n",
" <label for=\"_anim_radio3_a8717f1208794cb2a0400c38e379ed64\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_imga8717f1208794cb2a0400c38e379ed64\";\n",
" var slider_id = \"_anim_slidera8717f1208794cb2a0400c38e379ed64\";\n",
" var loop_select_id = \"_anim_loop_selecta8717f1208794cb2a0400c38e379ed64\";\n",
" var frames = new Array(4);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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"\"\n",
" frames[1] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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"\"\n",
" frames[3] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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"\"\n",
"\n",
"\n",
" /* set a timeout to make sure all the above elements are created before\n",
" the object is initialized. */\n",
" setTimeout(function() {\n",
" anima8717f1208794cb2a0400c38e379ed64 = new Animation(frames, img_id, slider_id, 299.0,\n",
" loop_select_id);\n",
" }, 0);\n",
" })()\n",
"</script>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 112,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"blinker = [[1, 1, 1]]\n",
"toad = [[1, 1, 1, 0],\n",
" [0, 1, 1, 1]]\n",
"\n",
"\n",
"X = pattern((blinker, 1, 1),\n",
" (toad, 6, 1), width=10, height=4)\n",
"\n",
"life_animation(X, frames=4)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### The pulsar (period-3)"
]
},
{
"cell_type": "code",
"execution_count": 113,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_img453f3961ff6d4444951d57947d723311\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_slider453f3961ff6d4444951d57947d723311\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"anim453f3961ff6d4444951d57947d723311.set_frame(parseInt(this.value));\"></input>\n",
" <div class=\"anim-buttons\">\n",
" <button onclick=\"anim453f3961ff6d4444951d57947d723311.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"anim453f3961ff6d4444951d57947d723311.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"anim453f3961ff6d4444951d57947d723311.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"anim453f3961ff6d4444951d57947d723311.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"anim453f3961ff6d4444951d57947d723311.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"anim453f3961ff6d4444951d57947d723311.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"anim453f3961ff6d4444951d57947d723311.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim453f3961ff6d4444951d57947d723311.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim453f3961ff6d4444951d57947d723311.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form action=\"#n\" name=\"_anim_loop_select453f3961ff6d4444951d57947d723311\" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_453f3961ff6d4444951d57947d723311\"\n",
" >\n",
" <label for=\"_anim_radio1_453f3961ff6d4444951d57947d723311\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_453f3961ff6d4444951d57947d723311\"\n",
" checked>\n",
" <label for=\"_anim_radio2_453f3961ff6d4444951d57947d723311\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_453f3961ff6d4444951d57947d723311\"\n",
" >\n",
" <label for=\"_anim_radio3_453f3961ff6d4444951d57947d723311\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_img453f3961ff6d4444951d57947d723311\";\n",
" var slider_id = \"_anim_slider453f3961ff6d4444951d57947d723311\";\n",
" var loop_select_id = \"_anim_loop_select453f3961ff6d4444951d57947d723311\";\n",
" var frames = new Array(6);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
"AAASdAAAEnQB3mYfeAAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0\\\n",
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"CAQ0AAAEAhoAAAIBDQAAgYAGAIBAQAMAQCCgAQAgENAAABAIaAAACAQ0AAAEAhoAAAIBDQAAgYAG\\\n",
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"\"\n",
"\n",
"\n",
" /* set a timeout to make sure all the above elements are created before\n",
" the object is initialized. */\n",
" setTimeout(function() {\n",
" anim453f3961ff6d4444951d57947d723311 = new Animation(frames, img_id, slider_id, 299.0,\n",
" loop_select_id);\n",
" }, 0);\n",
" })()\n",
"</script>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 113,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"X = np.zeros((17, 17))\n",
"X[2, 4:7] = 1\n",
"X[4:7, 7] = 1\n",
"X += X.T\n",
"X += X[:, ::-1]\n",
"X += X[::-1, :]\n",
"pulsar = X.copy()\n",
"life_animation(X, frames=6)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### The glider (period-4 oscillator that moves)"
]
},
{
"cell_type": "code",
"execution_count": 176,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_img7f4d15038ebf4ed68cb07ea5f652cff8\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_slider7f4d15038ebf4ed68cb07ea5f652cff8\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"anim7f4d15038ebf4ed68cb07ea5f652cff8.set_frame(parseInt(this.value));\"></input>\n",
" <div class=\"anim-buttons\">\n",
" <button onclick=\"anim7f4d15038ebf4ed68cb07ea5f652cff8.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"anim7f4d15038ebf4ed68cb07ea5f652cff8.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"anim7f4d15038ebf4ed68cb07ea5f652cff8.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"anim7f4d15038ebf4ed68cb07ea5f652cff8.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"anim7f4d15038ebf4ed68cb07ea5f652cff8.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"anim7f4d15038ebf4ed68cb07ea5f652cff8.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"anim7f4d15038ebf4ed68cb07ea5f652cff8.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim7f4d15038ebf4ed68cb07ea5f652cff8.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim7f4d15038ebf4ed68cb07ea5f652cff8.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form action=\"#n\" name=\"_anim_loop_select7f4d15038ebf4ed68cb07ea5f652cff8\" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_7f4d15038ebf4ed68cb07ea5f652cff8\"\n",
" >\n",
" <label for=\"_anim_radio1_7f4d15038ebf4ed68cb07ea5f652cff8\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_7f4d15038ebf4ed68cb07ea5f652cff8\"\n",
" checked>\n",
" <label for=\"_anim_radio2_7f4d15038ebf4ed68cb07ea5f652cff8\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_7f4d15038ebf4ed68cb07ea5f652cff8\"\n",
" >\n",
" <label for=\"_anim_radio3_7f4d15038ebf4ed68cb07ea5f652cff8\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_img7f4d15038ebf4ed68cb07ea5f652cff8\";\n",
" var slider_id = \"_anim_slider7f4d15038ebf4ed68cb07ea5f652cff8\";\n",
" var loop_select_id = \"_anim_loop_select7f4d15038ebf4ed68cb07ea5f652cff8\";\n",
" var frames = new Array(32);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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"\"\n",
" frames[1] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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"\"\n",
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"\"\n",
"\n",
"\n",
" /* set a timeout to make sure all the above elements are created before\n",
" the object is initialized. */\n",
" setTimeout(function() {\n",
" anim7f4d15038ebf4ed68cb07ea5f652cff8 = new Animation(frames, img_id, slider_id, 100.0,\n",
" loop_select_id);\n",
" }, 0);\n",
" })()\n",
"</script>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 176,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"glider = [[1, 0, 0],\n",
" [0, 1, 1],\n",
" [1, 1, 0]]\n",
"life_animation(pattern((glider, 0,0), width=8, height=8), frames=32, interval=100)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### The Glider Gun (Unbounded growth)"
]
},
{
"cell_type": "code",
"execution_count": 177,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_img5c6c7c07d51044889cc7bf52ae0ec7ee\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_slider5c6c7c07d51044889cc7bf52ae0ec7ee\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"anim5c6c7c07d51044889cc7bf52ae0ec7ee.set_frame(parseInt(this.value));\"></input>\n",
" <div class=\"anim-buttons\">\n",
" <button onclick=\"anim5c6c7c07d51044889cc7bf52ae0ec7ee.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"anim5c6c7c07d51044889cc7bf52ae0ec7ee.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"anim5c6c7c07d51044889cc7bf52ae0ec7ee.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"anim5c6c7c07d51044889cc7bf52ae0ec7ee.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"anim5c6c7c07d51044889cc7bf52ae0ec7ee.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"anim5c6c7c07d51044889cc7bf52ae0ec7ee.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"anim5c6c7c07d51044889cc7bf52ae0ec7ee.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim5c6c7c07d51044889cc7bf52ae0ec7ee.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim5c6c7c07d51044889cc7bf52ae0ec7ee.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form action=\"#n\" name=\"_anim_loop_select5c6c7c07d51044889cc7bf52ae0ec7ee\" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_5c6c7c07d51044889cc7bf52ae0ec7ee\"\n",
" checked>\n",
" <label for=\"_anim_radio1_5c6c7c07d51044889cc7bf52ae0ec7ee\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_5c6c7c07d51044889cc7bf52ae0ec7ee\"\n",
" >\n",
" <label for=\"_anim_radio2_5c6c7c07d51044889cc7bf52ae0ec7ee\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_5c6c7c07d51044889cc7bf52ae0ec7ee\"\n",
" >\n",
" <label for=\"_anim_radio3_5c6c7c07d51044889cc7bf52ae0ec7ee\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_img5c6c7c07d51044889cc7bf52ae0ec7ee\";\n",
" var slider_id = \"_anim_slider5c6c7c07d51044889cc7bf52ae0ec7ee\";\n",
" var loop_select_id = \"_anim_loop_select5c6c7c07d51044889cc7bf52ae0ec7ee\";\n",
" var frames = new Array(180);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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"\"\n",
"\n",
"\n",
" /* set a timeout to make sure all the above elements are created before\n",
" the object is initialized. */\n",
" setTimeout(function() {\n",
" anim5c6c7c07d51044889cc7bf52ae0ec7ee = new Animation(frames, img_id, slider_id, 50.0,\n",
" loop_select_id);\n",
" }, 0);\n",
" })()\n",
"</script>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 177,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"glider_gun =\\\n",
"[[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],\n",
" [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0],\n",
" [0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1],\n",
" [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,1,1],\n",
" [1,1,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\n",
" [1,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,1,1,0,0,0,0,1,0,1,0,0,0,0,0,0,0,0,0,0,0],\n",
" [0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0],\n",
" [0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\n",
" [0,0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0]]\n",
"\n",
"life_animation(pattern((glider_gun, 1, 1)), frames=180, interval=50, mode='once')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Logic"
]
},
{
"cell_type": "code",
"execution_count": 164,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [],
"source": [
"reverse_gun = [i[::-1] for i in glider_gun]"
]
},
{
"cell_type": "code",
"execution_count": 165,
"metadata": {
"slideshow": {
"slide_type": "fragment"
}
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_img84562aa8682d4bde84c6335f023a82cf\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_slider84562aa8682d4bde84c6335f023a82cf\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"anim84562aa8682d4bde84c6335f023a82cf.set_frame(parseInt(this.value));\"></input>\n",
" <div class=\"anim-buttons\">\n",
" <button onclick=\"anim84562aa8682d4bde84c6335f023a82cf.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"anim84562aa8682d4bde84c6335f023a82cf.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"anim84562aa8682d4bde84c6335f023a82cf.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"anim84562aa8682d4bde84c6335f023a82cf.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"anim84562aa8682d4bde84c6335f023a82cf.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"anim84562aa8682d4bde84c6335f023a82cf.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"anim84562aa8682d4bde84c6335f023a82cf.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim84562aa8682d4bde84c6335f023a82cf.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim84562aa8682d4bde84c6335f023a82cf.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form action=\"#n\" name=\"_anim_loop_select84562aa8682d4bde84c6335f023a82cf\" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_84562aa8682d4bde84c6335f023a82cf\"\n",
" checked>\n",
" <label for=\"_anim_radio1_84562aa8682d4bde84c6335f023a82cf\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_84562aa8682d4bde84c6335f023a82cf\"\n",
" >\n",
" <label for=\"_anim_radio2_84562aa8682d4bde84c6335f023a82cf\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_84562aa8682d4bde84c6335f023a82cf\"\n",
" >\n",
" <label for=\"_anim_radio3_84562aa8682d4bde84c6335f023a82cf\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_img84562aa8682d4bde84c6335f023a82cf\";\n",
" var slider_id = \"_anim_slider84562aa8682d4bde84c6335f023a82cf\";\n",
" var loop_select_id = \"_anim_loop_select84562aa8682d4bde84c6335f023a82cf\";\n",
" var frames = new Array(180);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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"\"\n",
"\n",
"\n",
" /* set a timeout to make sure all the above elements are created before\n",
" the object is initialized. */\n",
" setTimeout(function() {\n",
" anim84562aa8682d4bde84c6335f023a82cf = new Animation(frames, img_id, slider_id, 50.0,\n",
" loop_select_id);\n",
" }, 0);\n",
" })()\n",
"</script>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 165,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"life_animation(pattern((glider_gun, 1, 1), (reverse_gun, 46, 1), width=100, height=100), frames=180, interval=50, mode='once')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Other patterns"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [],
"source": [
"diehard = [[0, 0, 0, 0, 0, 0, 1, 0],\n",
" [1, 1, 0, 0, 0, 0, 0, 0],\n",
" [0, 1, 0, 0, 0, 1, 1, 1]]\n",
"\n",
"boat = [[1, 1, 0],\n",
" [1, 0, 1],\n",
" [0, 1, 0]]\n",
"\n",
"r_pentomino = [[0, 1, 1],\n",
" [1, 1, 0],\n",
" [0, 1, 0]]\n",
"\n",
"beacon = [[0, 0, 1, 1],\n",
" [0, 0, 1, 1],\n",
" [1, 1, 0, 0],\n",
" [1, 1, 0, 0]]\n",
"\n",
"acorn = [[0, 1, 0, 0, 0, 0, 0],\n",
" [0, 0, 0, 1, 0, 0, 0],\n",
" [1, 1, 0, 0, 1, 1, 1]]\n",
"\n",
"spaceship = [[0, 0, 1, 1, 0],\n",
" [1, 1, 0, 1, 1],\n",
" [1, 1, 1, 1, 0],\n",
" [0, 1, 1, 0, 0]]\n",
"\n",
"block_switch_engine = [[0, 0, 0, 0, 0, 0, 1, 0],\n",
" [0, 0, 0, 0, 1, 0, 1, 1],\n",
" [0, 0, 0, 0, 1, 0, 1, 0],\n",
" [0, 0, 0, 0, 1, 0, 0, 0],\n",
" [0, 0, 1, 0, 0, 0, 0, 0],\n",
" [1, 0, 1, 0, 0, 0, 0, 0]]"
]
},
{
"cell_type": "code",
"execution_count": 178,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_imgb5db5ad2dc4742d187a38c4d4b5819e0\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_sliderb5db5ad2dc4742d187a38c4d4b5819e0\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"animb5db5ad2dc4742d187a38c4d4b5819e0.set_frame(parseInt(this.value));\"></input>\n",
" <div class=\"anim-buttons\">\n",
" <button onclick=\"animb5db5ad2dc4742d187a38c4d4b5819e0.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"animb5db5ad2dc4742d187a38c4d4b5819e0.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"animb5db5ad2dc4742d187a38c4d4b5819e0.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"animb5db5ad2dc4742d187a38c4d4b5819e0.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"animb5db5ad2dc4742d187a38c4d4b5819e0.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"animb5db5ad2dc4742d187a38c4d4b5819e0.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"animb5db5ad2dc4742d187a38c4d4b5819e0.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"animb5db5ad2dc4742d187a38c4d4b5819e0.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"animb5db5ad2dc4742d187a38c4d4b5819e0.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form action=\"#n\" name=\"_anim_loop_selectb5db5ad2dc4742d187a38c4d4b5819e0\" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_b5db5ad2dc4742d187a38c4d4b5819e0\"\n",
" checked>\n",
" <label for=\"_anim_radio1_b5db5ad2dc4742d187a38c4d4b5819e0\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_b5db5ad2dc4742d187a38c4d4b5819e0\"\n",
" >\n",
" <label for=\"_anim_radio2_b5db5ad2dc4742d187a38c4d4b5819e0\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_b5db5ad2dc4742d187a38c4d4b5819e0\"\n",
" >\n",
" <label for=\"_anim_radio3_b5db5ad2dc4742d187a38c4d4b5819e0\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_imgb5db5ad2dc4742d187a38c4d4b5819e0\";\n",
" var slider_id = \"_anim_sliderb5db5ad2dc4742d187a38c4d4b5819e0\";\n",
" var loop_select_id = \"_anim_loop_selectb5db5ad2dc4742d187a38c4d4b5819e0\";\n",
" var frames = new Array(100);\n",
" \n",
" frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAHgCAYAAACMxVqsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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"BAIaAAACAQ0AAIGABgCAQEADAEAgoAEAIBDQAAAQCGgAAAgENAAABAIaAAACAQ0AAIGABgCAQEAD\\\n",
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"\"\n",
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"\"\n",
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"\"\n",
"\n",
"\n",
" /* set a timeout to make sure all the above elements are created before\n",
" the object is initialized. */\n",
" setTimeout(function() {\n",
" animb5db5ad2dc4742d187a38c4d4b5819e0 = new Animation(frames, img_id, slider_id, 50.0,\n",
" loop_select_id);\n",
" }, 0);\n",
" })()\n",
"</script>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 178,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"life_animation(pattern((block_switch_engine, 10, 10)), frames=100, interval=50, mode='once')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"### Fun and art"
]
},
{
"cell_type": "code",
"execution_count": 179,
"metadata": {},
"outputs": [],
"source": [
"from PIL import Image\n",
"import numpy as np\n",
"\n",
"im = Image.open('conwaycabify.png')\n",
"a = 0+~np.array(im.convert('1'))"
]
},
{
"cell_type": "code",
"execution_count": 180,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"<link rel=\"stylesheet\"\n",
"href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/\n",
"css/font-awesome.min.css\">\n",
"<script language=\"javascript\">\n",
" function isInternetExplorer() {\n",
" ua = navigator.userAgent;\n",
" /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
" return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
" }\n",
"\n",
" /* Define the Animation class */\n",
" function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
" this.img_id = img_id;\n",
" this.slider_id = slider_id;\n",
" this.loop_select_id = loop_select_id;\n",
" this.interval = interval;\n",
" this.current_frame = 0;\n",
" this.direction = 0;\n",
" this.timer = null;\n",
" this.frames = new Array(frames.length);\n",
"\n",
" for (var i=0; i<frames.length; i++)\n",
" {\n",
" this.frames[i] = new Image();\n",
" this.frames[i].src = frames[i];\n",
" }\n",
" var slider = document.getElementById(this.slider_id);\n",
" slider.max = this.frames.length - 1;\n",
" if (isInternetExplorer()) {\n",
" // switch from oninput to onchange because IE <= 11 does not conform\n",
" // with W3C specification. It ignores oninput and onchange behaves\n",
" // like oninput. In contrast, Mircosoft Edge behaves correctly.\n",
" slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
" slider.setAttribute('oninput', null);\n",
" }\n",
" this.set_frame(this.current_frame);\n",
" }\n",
"\n",
" Animation.prototype.get_loop_state = function(){\n",
" var button_group = document[this.loop_select_id].state;\n",
" for (var i = 0; i < button_group.length; i++) {\n",
" var button = button_group[i];\n",
" if (button.checked) {\n",
" return button.value;\n",
" }\n",
" }\n",
" return undefined;\n",
" }\n",
"\n",
" Animation.prototype.set_frame = function(frame){\n",
" this.current_frame = frame;\n",
" document.getElementById(this.img_id).src =\n",
" this.frames[this.current_frame].src;\n",
" document.getElementById(this.slider_id).value = this.current_frame;\n",
" }\n",
"\n",
" Animation.prototype.next_frame = function()\n",
" {\n",
" this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
" }\n",
"\n",
" Animation.prototype.previous_frame = function()\n",
" {\n",
" this.set_frame(Math.max(0, this.current_frame - 1));\n",
" }\n",
"\n",
" Animation.prototype.first_frame = function()\n",
" {\n",
" this.set_frame(0);\n",
" }\n",
"\n",
" Animation.prototype.last_frame = function()\n",
" {\n",
" this.set_frame(this.frames.length - 1);\n",
" }\n",
"\n",
" Animation.prototype.slower = function()\n",
" {\n",
" this.interval /= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.faster = function()\n",
" {\n",
" this.interval *= 0.7;\n",
" if(this.direction > 0){this.play_animation();}\n",
" else if(this.direction < 0){this.reverse_animation();}\n",
" }\n",
"\n",
" Animation.prototype.anim_step_forward = function()\n",
" {\n",
" this.current_frame += 1;\n",
" if(this.current_frame < this.frames.length){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.first_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.last_frame();\n",
" this.reverse_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.last_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.anim_step_reverse = function()\n",
" {\n",
" this.current_frame -= 1;\n",
" if(this.current_frame >= 0){\n",
" this.set_frame(this.current_frame);\n",
" }else{\n",
" var loop_state = this.get_loop_state();\n",
" if(loop_state == \"loop\"){\n",
" this.last_frame();\n",
" }else if(loop_state == \"reflect\"){\n",
" this.first_frame();\n",
" this.play_animation();\n",
" }else{\n",
" this.pause_animation();\n",
" this.first_frame();\n",
" }\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.pause_animation = function()\n",
" {\n",
" this.direction = 0;\n",
" if (this.timer){\n",
" clearInterval(this.timer);\n",
" this.timer = null;\n",
" }\n",
" }\n",
"\n",
" Animation.prototype.play_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = 1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_forward();\n",
" }, this.interval);\n",
" }\n",
"\n",
" Animation.prototype.reverse_animation = function()\n",
" {\n",
" this.pause_animation();\n",
" this.direction = -1;\n",
" var t = this;\n",
" if (!this.timer) this.timer = setInterval(function() {\n",
" t.anim_step_reverse();\n",
" }, this.interval);\n",
" }\n",
"</script>\n",
"\n",
"<style>\n",
".animation {\n",
" display: inline-block;\n",
" text-align: center;\n",
"}\n",
"input[type=range].anim-slider {\n",
" width: 374px;\n",
" margin-left: auto;\n",
" margin-right: auto;\n",
"}\n",
".anim-buttons {\n",
" margin: 8px 0px;\n",
"}\n",
".anim-buttons button {\n",
" padding: 0;\n",
" width: 36px;\n",
"}\n",
".anim-state label {\n",
" margin-right: 8px;\n",
"}\n",
".anim-state input {\n",
" margin: 0;\n",
" vertical-align: middle;\n",
"}\n",
"</style>\n",
"\n",
"<div class=\"animation\">\n",
" <img id=\"_anim_img8bb55a5e14d74d8fa87ab712f53f1fb3\">\n",
" <div class=\"anim-controls\">\n",
" <input id=\"_anim_slider8bb55a5e14d74d8fa87ab712f53f1fb3\" type=\"range\" class=\"anim-slider\"\n",
" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
" oninput=\"anim8bb55a5e14d74d8fa87ab712f53f1fb3.set_frame(parseInt(this.value));\"></input>\n",
" <div class=\"anim-buttons\">\n",
" <button onclick=\"anim8bb55a5e14d74d8fa87ab712f53f1fb3.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
" <button onclick=\"anim8bb55a5e14d74d8fa87ab712f53f1fb3.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
" </i></button>\n",
" <button onclick=\"anim8bb55a5e14d74d8fa87ab712f53f1fb3.previous_frame()\">\n",
" <i class=\"fa fa-step-backward\"></i></button>\n",
" <button onclick=\"anim8bb55a5e14d74d8fa87ab712f53f1fb3.reverse_animation()\">\n",
" <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
" <button onclick=\"anim8bb55a5e14d74d8fa87ab712f53f1fb3.pause_animation()\"><i class=\"fa fa-pause\">\n",
" </i></button>\n",
" <button onclick=\"anim8bb55a5e14d74d8fa87ab712f53f1fb3.play_animation()\"><i class=\"fa fa-play\"></i>\n",
" </button>\n",
" <button onclick=\"anim8bb55a5e14d74d8fa87ab712f53f1fb3.next_frame()\"><i class=\"fa fa-step-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim8bb55a5e14d74d8fa87ab712f53f1fb3.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
" </i></button>\n",
" <button onclick=\"anim8bb55a5e14d74d8fa87ab712f53f1fb3.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
" </div>\n",
" <form action=\"#n\" name=\"_anim_loop_select8bb55a5e14d74d8fa87ab712f53f1fb3\" class=\"anim-state\">\n",
" <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_8bb55a5e14d74d8fa87ab712f53f1fb3\"\n",
" >\n",
" <label for=\"_anim_radio1_8bb55a5e14d74d8fa87ab712f53f1fb3\">Once</label>\n",
" <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_8bb55a5e14d74d8fa87ab712f53f1fb3\"\n",
" >\n",
" <label for=\"_anim_radio2_8bb55a5e14d74d8fa87ab712f53f1fb3\">Loop</label>\n",
" <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_8bb55a5e14d74d8fa87ab712f53f1fb3\"\n",
" checked>\n",
" <label for=\"_anim_radio3_8bb55a5e14d74d8fa87ab712f53f1fb3\">Reflect</label>\n",
" </form>\n",
" </div>\n",
"</div>\n",
"\n",
"\n",
"<script language=\"javascript\">\n",
" /* Instantiate the Animation class. */\n",
" /* The IDs given should match those used in the template above. */\n",
" (function() {\n",
" var img_id = \"_anim_img8bb55a5e14d74d8fa87ab712f53f1fb3\";\n",
" var slider_id = \"_anim_slider8bb55a5e14d74d8fa87ab712f53f1fb3\";\n",
" var loop_select_id = \"_anim_loop_select8bb55a5e14d74d8fa87ab712f53f1fb3\";\n",
" var frames = new Array(500);\n",
" \n",
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"gg==\\\n",
"\"\n",
"\n",
"\n",
" /* set a timeout to make sure all the above elements are created before\n",
" the object is initialized. */\n",
" setTimeout(function() {\n",
" anim8bb55a5e14d74d8fa87ab712f53f1fb3 = new Animation(frames, img_id, slider_id, 299.0,\n",
" loop_select_id);\n",
" }, 0);\n",
" })()\n",
"</script>\n"
],
"text/plain": [
"<IPython.core.display.HTML object>"
]
},
"execution_count": 180,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"life_animation(a[::5,::5], dpi=120, fps=30,frames=500, mode='reflect')"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Surreal numbers\n",
"\n",
"The achievement for which Conway himself was most proud, according to Kochen, was his invention of a new system of numbers, the surreal numbers. This continuum of numbers includes not only real numbers such as integers, fractions and irrational numbers such as pi, but also the infinitesimal and infinite numbers. \n",
"\n",
"Mathematician John Horton Conway first invented surreal numbers, and Donald Knuth (TAOCP) introduced them to the public in 1974 in his mathematical novelette \"Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness\".\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"![](https://www.researchgate.net/profile/Mickael_Matusinski/publication/306186762/figure/fig1/AS:395755064971265@1471366768199/The-tree-of-surreal-numbers.png)"
]
},
{
"cell_type": "code",
"execution_count": 181,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
" <iframe\n",
" width=\"560\"\n",
" height=\"315\"\n",
" src=\"https://www.youtube.com/embed/mPn2AdMH7UQ\"\n",
" frameborder=\"0\"\n",
" allowfullscreen\n",
" ></iframe>\n",
" "
],
"text/plain": [
"<IPython.lib.display.IFrame at 0x7f46601b07f0>"
]
},
"execution_count": 181,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from IPython.display import IFrame\n",
"IFrame('https://www.youtube.com/embed/mPn2AdMH7UQ', 560, 315)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"How can surreal numbers represent irrational numbers such as $\\pi$?\n",
"\n",
"\n",
"One intuitive way to go around this is that you start with the closest integer:\n",
"\n",
"$3 = \\{0,1,2 | 4\\} = \\{ L | R\\}$.\n",
"\n",
"And then continue getting closer to $\\pi$ by adding rationals to either $L$ or $R$.\n",
"A strategy to calculate each rational ($a_n$) could be:\n",
"\n",
"$a_(n) = a_{n-1} + 2^{-n} * sign(\\pi-a_{n-1})$\n",
"\n",
"\n",
"If $a_n < \\pi$, $a_n$ is added to $L$, otherwise it goes to $R$. \n",
"\n",
"$3 = \\{0,1,2, 3 | \\} $\n",
"\n",
"$3.5 = \\{0,1,2, 3 | 4\\} $ # Adding 4\n",
"\n",
"$3.25 = \\{0,1,2, 3 | 3.5 4\\}$ # Adding 3.5\n",
"...\n",
"\n",
"\n",
"$ \\pi = \\{ 3.14150... | 3.141509...\\}\n"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Free Will Theorem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"if we have a free will in the sense that our choices are not a function of the past, then, subject to certain assumptions, so must some elementary particles."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# References"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"* [Code for game of life](https://jakevdp.github.io/blog/2013/08/07/conways-game-of-life/)\n",
"* [A Turing machine made in Life](http://www.rendell-attic.org/gol/tm.htm)\n",
"* John Horton Conway, a ‘Magical Genius’ in Math, Dies at 82 [NY Times](https://www.nytimes.com/2020/04/15/technology/john-horton-conway-dead-coronavirus.html)\n",
"* [Implementation of logical functions in the Game of Life](https://www.rennard.org/alife/CollisionBasedRennard.pdf)\n",
"* [Surreal Numbers: How two ex-students turned on to pure mathematics and found total happiness ](https://www-cs-faculty.stanford.edu/~knuth/sn.html)"
]
}
],
"metadata": {
"celltoolbar": "Slideshow",
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.2"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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