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Sierpinski.ipynb

@@ -6,7 +6,7 @@
    "source": [
     "# A Chaos Game with Triangles\n",
     "\n",
-    "John D. Cook [proposed](https://www.johndcook.com/blog/2017/07/08/the-chaos-game-and-the-sierpinski-triangle/) an interesting \"game\" from the book *[Chaos and Fractals](https://smile.amazon.com/Chaos-Fractals-New-Frontiers-Science/dp/0387202293)*: start at a vertex of an equilateral triangle. Then move to a new point halfway between the current point and one of the three vertexes, chosen at random. Repeat to create *N* points, and plot them. What do you get? \n",
+    "John D. Cook [proposed](https://www.johndcook.com/blog/2017/07/08/the-chaos-game-and-the-sierpinski-triangle/) an interesting \"game\" from the book *[Chaos and Fractals](https://smile.amazon.com/Chaos-Fractals-New-Frontiers-Science/dp/0387202293)*: start at a vertex of an equilateral triangle. Then move to a new point halfway between the current point and one of the three vertexes of the triangle, chosen at random. Repeat to create *N* points, and plot them. What do you get? \n",
     "\n",
     "I'll refactor Cook's code a bit and then we'll see:"
    ]
@@ -21,17 +21,17 @@
     "import random\n",
     "\n",
     "def random_walk(vertexes, N):\n",
-    "    \"Repeatedly moving halfway from current point towards a random vertex; repeat for N points.\"\n",
+    "    \"Walk halfway from current point towards a random vertex; repeat for N points.\"\n",
     "    points = [random.choice(vertexes)]\n",
-    "    for i in range(N-1):\n",
+    "    for _ in range(N-1):\n",
     "        points.append(midpoint(points[-1], random.choice(vertexes)))\n",
     "    return points\n",
     "\n",
     "def show_walk(vertexes, N=5000):\n",
-    "    \"Randomly walk between vertexes for N poibnts; show reults.\"\n",
-    "    X, Y = transpose(random_walk(vertexes, N))\n",
+    "    \"Walk halfway towards a random vertex for N points; show reults.\"\n",
+    "    Xs, Ys = transpose(random_walk(vertexes, N))\n",
     "    Xv, Yv = transpose(vertexes)\n",
-    "    plt.plot(X, Y, 'r.')\n",
+    "    plt.plot(Xs, Ys, 'r.')\n",
     "    plt.plot(Xv, Yv, 'bs')\n",
     "    plt.gca().set_aspect('equal')\n",
     "    plt.gcf().set_size_inches(9, 9)\n",
@@ -52,9 +52,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiAAAAHlCAYAAADMREeGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQACAOgECANQJEACgToAAAHUCBACo+w+5qYLFmW2r/wAAAABJRU5ErkJggg==\n",
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiAAAAHlCAYAAADMREeGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x10ada1748>"
+       "<matplotlib.figure.Figure at 0x1087f3748>"
       ]
      },
      "metadata": {},
@@ -79,9 +79,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x10ada1a90>"
+       "<matplotlib.figure.Figure at 0x10879e710>"
       ]
      },
      "metadata": {},
@@ -107,9 +107,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x10ada1c18>"
+       "<matplotlib.figure.Figure at 0x111077438>"
       ]
      },
      "metadata": {},
@@ -136,9 +136,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x10aa16080>"
+       "<matplotlib.figure.Figure at 0x10d934320>"
       ]
      },
      "metadata": {},
@@ -163,9 +163,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x112dac8d0>"
+       "<matplotlib.figure.Figure at 0x110e3e048>"
       ]
      },
      "metadata": {},
@@ -175,7 +175,7 @@
    "source": [
     "right_triangle = ((0, 0), (0, 1), (1, 0))\n",
     "\n",
-    "show_walk(right_triangle)"
+    "show_walk(right_triangle, 20000)"
    ]
   },
   {
@@ -192,9 +192,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x113619278>"
+       "<matplotlib.figure.Figure at 0x110f7e588>"
       ]
      },
      "metadata": {},
@@ -221,9 +221,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x112d80cc0>"
+       "<matplotlib.figure.Figure at 0x111093048>"
       ]
      },
      "metadata": {},
@@ -241,9 +241,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x113575f28>"
+       "<matplotlib.figure.Figure at 0x111001160>"
       ]
      },
      "metadata": {},
@@ -268,9 +268,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1133e1fd0>"
+       "<matplotlib.figure.Figure at 0x1111368d0>"
       ]
      },
      "metadata": {},
@@ -290,9 +290,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1135ff198>"
+       "<matplotlib.figure.Figure at 0x1087f3630>"
       ]
      },
      "metadata": {},