Add files via upload

Sierpinski.ipynb

@@ -20,27 +20,29 @@
     "import matplotlib.pyplot as plt\n",
     "import random\n",
     "\n",
-    "triangle = ((0, 0), (0.5, (3**0.5)/2), (1, 0))\n",
-    "\n",
-    "def random_points(vertexes, N=4000):\n",
-    "    \"Create N points by repeatedly moving halfway towards a random vertex.\"\n",
+    "def random_walk(vertexes, N):\n",
+    "    \"Repeatedly moving 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",
     "        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",
+    "    Xv, Yv = transpose(vertexes)\n",
+    "    plt.plot(X, Y, 'r.')\n",
+    "    plt.plot(Xv, Yv, 'bs')\n",
+    "    plt.gca().set_aspect('equal')\n",
+    "    plt.gcf().set_size_inches(9, 9)\n",
+    "    plt.axis('off')\n",
+    "    plt.show()\n",
+    "    \n",
     "def midpoint(p, q): return ((p[0] + q[0])/2, (p[1] + q[1])/2)\n",
     "\n",
     "def transpose(matrix): return zip(*matrix)\n",
     "\n",
-    "def show(points):\n",
-    "    \"Display points in a scatter plot.\"\n",
-    "    X, Y = transpose(points)\n",
-    "    plt.scatter(X, Y, marker='.', color='r')\n",
-    "    plt.gca().set_aspect('equal')\n",
-    "    plt.gcf().set_size_inches(9, 9)\n",
-    "    plt.axis('off')\n",
-    "    plt.show()"
+    "triangle = ((0, 0), (0.5, (3**0.5)/2), (1, 0))"
    ]
   },
   {
@@ -50,9 +52,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiAAAAHlCAYAAADMREeGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQACAOgECANQJEACgToAAAHUCBACo+w+5qYLFmW2r/wAAAABJRU5ErkJggg==\n",
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x10bff2748>"
+       "<matplotlib.figure.Figure at 0x10ada1748>"
       ]
      },
      "metadata": {},
@@ -60,14 +62,14 @@
     }
    ],
    "source": [
-    "show(random_points(triangle))"
+    "show_walk(triangle, 20)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Wow! The [Sierpinski Triangle](https://en.wikipedia.org/wiki/Sierpinski_triangle)! Let's try with more points:"
+    "OK, the first 20 points don't tell me much. What if I try 20,000 points?"
    ]
   },
   {
@@ -77,9 +79,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiAAAAHlCAYAAADMREeGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x10bff2d30>"
+       "<matplotlib.figure.Figure at 0x10ada1a90>"
       ]
      },
      "metadata": {},
@@ -87,13 +89,14 @@
     }
    ],
    "source": [
-    "show(random_points(triangle, 20000))"
+    "show_walk(triangle, 20000)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
+    "Wow! The [Sierpinski Triangle](https://en.wikipedia.org/wiki/Sierpinski_triangle)! \n",
     "What happens if we start with a different set of vertexes, like a square?"
    ]
   },
@@ -104,9 +107,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x114a56438>"
+       "<matplotlib.figure.Figure at 0x10ada1c18>"
       ]
      },
      "metadata": {},
@@ -116,14 +119,14 @@
    "source": [
     "square = ((0, 0), (0, 1), (1, 0), (1, 1))\n",
     "\n",
-    "show(random_points(square))"
+    "show_walk(square)"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "There doesn't seem to be any structure there. Let's try again and compare the two:"
+    "There doesn't seem to be any structure there. Let's try again to make sure:"
    ]
   },
   {
@@ -133,9 +136,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAigAAAIXCAYAAAC2IaX9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvV2OXbvOLbbsOl24cflDOhC4TgcSYB8kHUiamVYk3rgo\nP2wDSRqRp/tkf0CebFh5WHueKVH8GaSkqWWbAgi7qtaak/olOTgkvSml3LJkyZIlS5YsWR6pvN2t\nQJYsWbJkyZIlCy3poGTJkiVLlixZHq6kg5IlS5YsWbJkebiSDkqWLFmyZMmS5eFKOihZsmTJkiVL\nlocr6aBkyZIlS5YsWR6upIOSJUuWLFmyZHm4kg5KlixZsmTJkuXhSjooWbJkyZIlS5aHK+mgZMmS\nJUuWLFkerqSDkiVLlixZsmR5uJIOSpYsWbJkyZLl4Uo6KFmyZMmSJUuWhyvpoGTJkiVLlixZHq6k\ng5IlS5YsWbJkebiSDkqWLFmyZMmS5eFKOihZsmTJkiVLlocr6aBkyZIlS5YsWR6upIOSJUuWLFmy\nZHm4kg5KlixZsmTJkuXhSjooWbJkyZIlS5aHK+mgZMmSJUuWLFkerqSDkiVLlixZsmR5uJIOSpYs\nWbJkyZLl4Uo6KFmyZMmSJUuWhyvpoGTJkiVLlixZHq6kg5IlS5YsWbJkebiSDkqWLFmyZMmS5eFK\nOihZsmTJkiVLlocr6aBkyZIlS5YsWR6upIOSJUuWLFmyZHm4kg5KlixZsmTJkuXhSjooWbJkyZIl\nS5aHK+mgZMmSJUuWLFkerqSDkiVLlixZsmR5uJIOSpYsWbJkyZLl4Uo6KFmyZMmSJUuWhyvpoGTJ\nkiVLlixZHq6kg5IlS5YsWbJkebiSDkqWLFmyZMmS5eFKOihZsmTJkiVLlocr6aBkyZIlS5YsWR6u\npIOSJUuWLFmyZHm4kg5KlixZsmTJkuXhSjooWbJkyZIlS5aHK+mgZMmSJUuWLFkerqSDkiVLlixZ\nsmR5uJIOSpYsWbJkyZLl4Uo6KFmyZMmSJUuWhyvpoGTJkiVLlixZHq6kg5IlS5YsWbJkebiSDkqW\nLFmyZMmS5eFKOihZsmTJkiVLlocr6aBkyZIlS5YsWR6upIOSJUuWLFmyZHm4kg5KlixZsmTJkuXh\nSjooWbJkyZIlS5aHK+mgZMmSJUuWLFkerqSDkiVLlixZsmR5uJIOSpYsWbJkyZLl4Uo6KFmyZMmS\nJUuWhyvpoGTJkiVLlixZHq6kg5IlS5YsWbJkebiSDkqWLFmyZMmS5eFKOihZsmTJkiVLlocr6aBk\nyZIlS5YsWR6upIOSJUuWLFmyZHm4kg5KlixZsmTJkuXhSjooWbJkyZIlS5aHK+mgZMmSJUuWLFke\nrqSDkiVLlixZsmR5uJIOSpYsWbJkyZLl4Uo6KFmyZMmSJUuWhyvpoGTJkiVLlixZHq6kg5IlS5Ys\nWbJkebiSDkqWLFmyZMmS5eFKOihZsmTJkiVLlocr6aBkyZIlS5YsWR6upIOSJUuWLFmyZHm4kg5K\nlixZsmTJkuXhSjooWX6u8ubN29ubN+9ub9682a1KlixZsmRZV9JByfLzlDdv3t5ut//jdrv9v7fb\n7f/8++ffrzySk/ZIuvyOJdt/Xsm2fLjyey7wWX7W8l9ut9v/dLvd/vH3v/9lrzobypVOmrVge3VJ\nA4AXpK3SYedLZJxlWz5kyU7I8jOV/3a73V5vt9v3v//9b3vVCZRxI32Nk4Yt2P8drMvPZAB2O1J4\nW9Gx8D8s1TnaLle255s3T7fb7b/e/OMMm1e7x8ZvVh53kciytuyaaPV7vTqUUm632/9yu93++9vt\n9j///fPPU+YY6biT5mtvfcG+6/6/3263p9vtVgBdfI7VXddnE8GZPYZXOVIz2/4s9Vj4/2632/9z\nW+X8RdvF873R/rw/+7/ebrf/8eZ34O159TM52b9KKaWk/G5yu70tt9vHcrt9+/vft5veO6bD/Xnv\nyu32Zupn19X/3d/1LX//+26gHX118fb57faGfP4N+TutywdVH+t5vK4//pZe31VjeFYfrWz7/tkf\npus8o108uvVt9Oyeq62Opdxur4E5Is+rFWMjRZXtCqQ4ZJaR3TXR+vfGdfAsaLscsl4P3PDgY4H+\nO29xpc+sf27r8gVqW0nH/j3U0PT6rhrDaB/5nOPxtl81rtD3eN/Rzrkv7Pfa8VS30Y/QXG11/DRp\nfr0Rnj82f1Mg2a5ACiizjOw58epnIQvUuHPUT/D4ZPcsaKsdshlIjv8ZdPHvnQTZoYi0Nx1/T+Xu\nFNII+bl6p10nblyfutYICm2vNcZCm2etMzgXERkdQ/ffPcPPsOo6Ps51hI3v9+PnH6G5OrpGIv37\nCEjsbyTbFUgBZYaR7Sfee2hC88aJWyB9jo4d9ct/bxd9fUFbGfkgbeN/hmUoKMJQyzdxkR1ZXPvx\n91o9W3I67UVeGteIwV1hLHR96uh8HiLi6X/ps94UCZ9+sR0cux6yQ2z1Ox88eeZRfI0c7d+UJbJd\ngRRQZhjZ+wJ0GPMf5XZ7gSaibpzeFq+BxXS1n+lZ0OK8DWsxpm3z2d0O3oWVT6/UCAqn19gi28Pn\nnGGzU3h65DzXeZw5z/Q5EEGjpJSW3leyA+VBFKX0CzLfNKdTdog9/R51PPu+w9Kfs/s3ZZpsVyDF\nIffoXCcj6t9/V1oHBTXumnGabwxPXdFFe0Uk7VmMj/9/LRpvQn6X3/nkOSjPgl5jiyy30PNG3E7h\n6ZHzYxgCOYXyqfTGbzRV9pZpNz/ZWEMUbYfoAzTftM9Y31/Z7zwqKzlhEkosOTePMSZ/U9muQAoo\nEoQbI9PVuX0sJaEZpxUplN2ENH1BfSZ/o1yMUmbvIIjp/Fy8vAR73PX8FnmcrCcaXmFI2jZ4FY3c\n2Lh6LojR1j57BjB0nbAdIownI3/GTulcyxni06DXBzopQ7JdgRRQZAhXh2X751DjGuWyxDgonmfP\nXDC8z+IjqjoiawmcPcp0/SKn64yND33czULHMB4D9pyx+iHvttGBkR03EhrX10f/7BP5ueaX1YjK\nB3FuYakQlIMylwPVv0NKsb5j2pmmP9MB+UlkuwIpoMgQrs94jEYyK6MMO61iOy7ywosbMj6lYUdk\nV0Zgcj2fBZ2jzqjf8ZqZ/tA/TzlVz2E99LGnIQd+J0kni3rSJDRNI/18BDTYdvA543OVY8s5Hcfv\n/iLrg5b+9J+zknK5bFcgxSE8KVR2NiSS2BwD8kld5CJRshwNYVEmBvciMG9fxz4iaw8Ru9454aJT\n+rs5sPo9Om+J0R7d8Pd4ycI9pyqqRxQlQXWWv49vvbc+q/9sH5g2F7FckfaVgoT/KCf/60u53f40\n1gCeRJwpnoeT7QqkBKSPDCQuAI02dKfCfi9dIP5in2cjIb5IVY8cbcTg/k6Mld/X8eQc6ByUmFGW\n+9az40CDuldwW/y7TLD3eA8D05ANr7MTM6jymNXTHVKfW0R4DUns/1bPDetk4BHH0uYjRcee3NY1\ngvKhtE7Ld2Ye6McSROufTs1S2a5ASlCsHC8fbZQyQvK7P/cTeV7v9GjGIRKp6pEjbQMaReKoD19H\nTkeqzxw4u9efJzBHSY7xsTZjlwm2kMfSd9LvLIPseRbOy+gRJ4z3NYtTIyOJWtvGxvBsHhD2Po74\n+6WcCIrktMrjIlL/q+v+G8p2BVKC0k8obtIeP8e2v/LvfVvuyIn8PC/bH38vjRy1nTajC4+OuLT6\nzEqlUF3ltAqHnq3nB3n4HDSSxxZyPRpHUAj6uZ5rgBoWGwns0cv773sHFxkf8xxd+zn9POGcbqSv\nZ/CcvAR2bt6fyJP1PNkRrZ2cazYcpKiyXYGUoPQTqp8s7aJND1eLG7JzEcYMuOdvPj1Gt0aO69i2\n8WgqRT9vpn/v/OhtLg+h1tE+vlx3CDRUjqJk9ee4I9bRC+wsTlR/mSGfIkSP/Z/l6MbSOV5nEp+D\nVirKN47X81uQlCA3BjLNM1m2K5ASFD6KsBYlGmGOpHseI/cageDP31HEyRvJzXcS2sVbjmhnRdsr\n69PqWBMT/QiCj29yOOPtrpW2fsfn5WgZ40S1uvZO5p5dctF0TgxxlNELPm1Z/6yjEHv4LbazsWL+\npXSyXYEUp8gGDI3S6OI6Spz1w6mP0X52isx+1tpFSotoHyGKtJ+HpQ20MY2Mpf57PErC87L0euqc\nKD563jnmo0gN2gf8++rP036gY4rrF8nx9DnMo4ioL4259yDJ30S2K5DiED4a8RL43pR7hFnChuh8\n5lOhx3/r+u4lkemLaSRyXL9I2amNec4hb+hH01YyvB8d09yzbU4F5QqNHd4lcVBW9U1sfGNcn/57\n/yjolRr9+KTOh7X9WU6PeuakzReiqI1vfF3VhymNbFcgxSF81K9NIP78CoRDIuuAk28fDQbV2i/q\nbKxepPhoXdraXdcnktvXo2GkzvbfrAgbyf1zZFjtMkkO3fDzLWJz5DrHPTrf+u/JQQdfV+lma80p\ntdveMyfxtJV+kaLVR+mUXCrbFUhxSD9htUXwqdxv1i3CpI1NNB4mL4XLt++EQXVo3pdCuFJH/nNI\nnp46Mf4dBlY03L4LiVTt7ec+I0T5U2PO70wHukUk9OeuctzjTvYbqF119OtT8fC4rFOA/XNERv/a\nv9lkbXmsPhYi/BvIdgVSHNJGyRb0X6dxSvFeXifrUE/24/1fxcm6I+Kwjahnd844FOzVUW9zzrHi\nSZsI/0N/T//9EYKlTDqVUzVyPWmk7x9fsxxoHhnS+mvlmTXRwINyULiTkjkHIOZo3b/LnwI8XneN\nAI86w1xq6rEQ4d9AtiuQAopnEewN1ucFiyC2VfP8/Ip8u3+XQrStZ3x2REe9vjxpULine truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiAAAAIXCAYAAACl9uUJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x114a56f28>"
+       "<matplotlib.figure.Figure at 0x10aa16080>"
       ]
      },
      "metadata": {},
@@ -143,7 +146,7 @@
     }
    ],
    "source": [
-    "show(random_points(square))"
+    "show_walk(square, 20000)"
    ]
   },
   {
@@ -160,9 +163,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x114168f98>"
+       "<matplotlib.figure.Figure at 0x112dac8d0>"
       ]
      },
      "metadata": {},
@@ -172,7 +175,7 @@
    "source": [
     "right_triangle = ((0, 0), (0, 1), (1, 0))\n",
     "\n",
-    "show(random_points(right_triangle, 10000))"
+    "show_walk(right_triangle)"
    ]
   },
   {
@@ -189,9 +192,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x111d27ba8>"
+       "<matplotlib.figure.Figure at 0x113619278>"
       ]
      },
      "metadata": {},
@@ -201,7 +204,7 @@
    "source": [
     "pentagon = ((0.5, -0.688), (0.809, 0.262), (0., 0.850), (-0.809, 0.262), (-0.5, -0.688))\n",
     "\n",
-    "show(random_points(pentagon))"
+    "show_walk(pentagon)"
    ]
   },
   {
@@ -218,9 +221,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAigAAAHlCAYAAADfkwdyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x111d1ce80>"
+       "<matplotlib.figure.Figure at 0x112d80cc0>"
       ]
      },
      "metadata": {},
@@ -228,7 +231,7 @@
     }
    ],
    "source": [
-    "show(random_points(pentagon, 7000))"
+    "show_walk(pentagon, 10000)"
    ]
   },
   {
@@ -238,9 +241,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAigAAAHlCAYAAADfkwdyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAigAAAHlCAYAAADfkwdyAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x111138630>"
+       "<matplotlib.figure.Figure at 0x113575f28>"
       ]
      },
      "metadata": {},
@@ -248,7 +251,7 @@
     }
    ],
    "source": [
-    "show(random_points(pentagon, 10000))"
+    "show_walk(pentagon, 20000)"
    ]
   },
   {
@@ -265,9 +268,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAigAAAIXCAYAAAC2IaX9AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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 truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1148fa860>"
+       "<matplotlib.figure.Figure at 0x1133e1fd0>"
       ]
      },
      "metadata": {},
@@ -277,7 +280,7 @@
    "source": [
     "hexagon = ((0.5, -0.866), (1, 0), (0.5, 0.866), (-0.5, 0.866), (-1, 0), (-0.5, -0.866))\n",
     "\n",
-    "show(random_points(hexagon))"
+    "show_walk(hexagon)"
    ]
   },
   {
@@ -287,9 +290,9 @@
    "outputs": [
     {
      "data": {
-      "image/png": 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truncated
+      "image/png": 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truncated
       "text/plain": [
-       "<matplotlib.figure.Figure at 0x1148fada0>"
+       "<matplotlib.figure.Figure at 0x1135ff198>"
       ]
      },
      "metadata": {},
@@ -297,7 +300,7 @@
     }
    ],
    "source": [
-    "show(random_points(hexagon, 20000))"
+    "show_walk(hexagon, 20000)"
    ]
   },
   {