Add figures, make a Bezier
[matches/FYP2014.git] / ipython_notebooks / fractals_basic.ipynb
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2  "metadata": {
3   "name": ""
4  },
5  "nbformat": 3,
6  "nbformat_minor": 0,
7  "worksheets": [
8   {
9    "cells": [
10     {
11      "cell_type": "heading",
12      "level": 1,
13      "metadata": {},
14      "source": [
15       "Basic Fractals Stuff"
16      ]
17     },
18     {
19      "cell_type": "raw",
20      "metadata": {},
21      "source": [
22       "Main reference:\n",
23       "The Fractal Nature of Bezier Curves, Ron Goldman, Year?\n",
24       "\n",
25       "Also, wikipedia."
26      ]
27     },
28     {
29      "cell_type": "heading",
30      "level": 2,
31      "metadata": {},
32      "source": [
33       "Definitions"
34      ]
35     },
36     {
37      "cell_type": "markdown",
38      "metadata": {},
39      "source": [
40       "Fractals are *attractors* Fixed points of *iterated function systems*. <cite data-cite=\"barnsley1993\"</cite>"
41      ]
42     },
43     {
44      "cell_type": "markdown",
45      "metadata": {},
46      "source": [
47       "An iterated function system: $W = \\left\\{w_1, ... w_n\\right\\}$ (collection of *maps* w_i)"
48      ]
49     },
50     {
51      "cell_type": "heading",
52      "level": 2,
53      "metadata": {},
54      "source": [
55       "Stierpinski Triangle Generation"
56      ]
57     },
58     {
59      "cell_type": "code",
60      "collapsed": false,
61      "input": [
62       "import random"
63      ],
64      "language": "python",
65      "metadata": {},
66      "outputs": [],
67      "prompt_number": 192
68     },
69     {
70      "cell_type": "code",
71      "collapsed": false,
72      "input": [
73       "def stierpinski(n, x0 = (0,0)):\n",
74       "    \"\"\" Generates the Stierpinski Triangles using Iterated Function System \"\"\"\n",
75       "    # Define the maps in the iterated function system W\n",
76       "    W = [lambda p : (0.5*p[0], 0.5*p[1])] # scale\n",
77       "    W += [lambda p : (0.5*p[0]+0.25, 0.5*p[1] + 0.25*sqrt(3))] # scale & shift up&right\n",
78       "    W += [lambda p : (0.5*p[0]+0.5, 0.5*p[1])] # scale & shift right\n",
79       "    x = [x0]\n",
80       "    # Repeatedly randomly select one of the maps in W\n",
81       "    # As the number of iterations approaches infinity this becomes equivelant to the definition\n",
82       "    # (I think. I mean, it seems to work)\n",
83       "    for i in xrange(n):\n",
84       "        x.append(random.choice(W)(x[i]))\n",
85       "    return x\n",
86       "    "
87      ],
88      "language": "python",
89      "metadata": {},
90      "outputs": [],
91      "prompt_number": 436
92     },
93     {
94      "cell_type": "code",
95      "collapsed": false,
96      "input": [
97       "points = stierpinski(10000, (0.5, 0.5))"
98      ],
99      "language": "python",
100      "metadata": {},
101      "outputs": [],
102      "prompt_number": 437
103     },
104     {
105      "cell_type": "code",
106      "collapsed": false,
107      "input": [
108       "# Silly matplotlib needs x and y as seperate lists\n",
109       "x = [p[0] for p in points]\n",
110       "y = [p[1] for p in points]"
111      ],
112      "language": "python",
113      "metadata": {},
114      "outputs": [],
115      "prompt_number": 438
116     },
117     {
118      "cell_type": "code",
119      "collapsed": false,
120      "input": [
121       "title(\"Stierpinski Triangles (10000 points)\")\n",
122       "scatter(x, y, marker=',', s = 1e-3)"
123      ],
124      "language": "python",
125      "metadata": {},
126      "outputs": [
127       {
128        "metadata": {},
129        "output_type": "pyout",
130        "prompt_number": 440,
131        "text": [
132         "<matplotlib.collections.PathCollection at 0x11957d50>"
133        ]
134       },
135       {
136        "metadata": {},
137        "output_type": "display_data",
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nD8+HFaW1tpbGzkiSeeoKioCGdnZwIDA6/I197ezmeffYZKpaJ79+5kZGSgp6fH5MmT2bVrF8nJ\nybz99tt4e3tfkVelUnHixAlSUlJobW2lqqoKS0tLvL29KSwsJD4+nokTJzJp0qRbep2E+5fo4xce\nKIcOHSIhIYGxY8cyevRotLW1USqVtLS0YGlpSXh4OGvXrmX+/PlX9K8XFRURHx+Pg4MDw4YNw8fH\nBz09PTIyMnB3dyciIoKysrKrBv7c3FwaGxuxs7NjzJgxBAYGoqOjQ7du3ViwYAFpaWn8+OOPLFy4\nECsrqw55z58/z+HDhxk6dCg+Pj4olUpMTEwwMDDAwsICLy8v2tvbOXXqFEOGDLmt108QRFePcM9x\nc3Pj0UcfJSIigqqqKiwsLLCxscHZ2ZmCggL69etHc3MzxcXFHfLV1taSmJiIpaUlZWVlnD9/Hhsb\nGywsLOjfvz8///wzZWVltLS08PHHH3e4myooKODLL7+kvb2dsrIyLly4gKOjI3Z2dmhra/Ppp5/S\n0tLCc889R1FRUYfhoZGRkbz99tt4eXkRExODSqXCw8MDOzs7LCwsOHDgABcuXGDPnj2sWrXqjl1H\n4cElAr9wz1Cr1aSlpeHh4cGwYcN49913+fXXXzUbpMTHx5OUlIStrS1PPPEEe/bs4ddff9XkT05O\nxsTEBHd3dxQKBUePHiUjIwOAXbt2UV5eztKlS7G3t0epVNLU1AT8PnTzf//7H1ZWVsyePZvAwEDi\n4uLIzc3V5M3Pz8fHxwe1Wk1MTIxmGeaSkhLi4uLw8PBAR0cHa2trzp49S3t7OwCpqam0trbi6+vL\n7NmzcXV1FTN7hdtOBH7hnpGSkkJUVBSHDx/GwMBA8zozM5OysjJSU1PZt28fK1eu5NSpU5w7d47c\n3FzKy8v54osv2LVrF9HR0bi7u3Px4kUKCgr46KOPUKvV7Nixg6amJuRyOUOGDKF79+689dZbNDY2\nsm3bNqqqqkhNTUVHR4egoCAqKioICwujrq6On376icrKSiIjI9HT02PDhg3Mnz+f+Ph49uzZQ0pK\nCmfOnGHYsGEEBgYSEhLCP/7xD2JiYvjmm2/IyspixIgRODo64uzsTGRkJOfOnevqyy3cx8TDXeGe\noFKpWLhwIb169eLAgQO8//77REVF0atXL+RyOceOHdPcqe/cuROlUom3tzdVVVXI5XIkSeLll18m\nPDwcV1dXIiIiqKiowM/Pj6effpoLFy7Q0tKCo6Mjvr6+pKWlkZKSwkMPPURTUxMxMTF4e3tTXFyM\ntbU1LS09Uj3yAAAgAElEQVQtnDp1iqFDh1JZWYmPjw+7du0CwMbGhvr6eiwtLenVqxdxcXGUl5fT\n0tLCwIEDsbe3Jy4ujhEjRlBUVMSpU6cICgrC1taWd955B09PT/z9/VmwYIFmMpog/NnNxE4R+IW7\n3uXZr0ZGRlRWVlJXV4eHhweXLl1CLpcjl8spLi7GysoKHR0d2tvbSU1NxdfXl9OnT2NnZ4eNjQ3t\n7e1UVVVhYmKCrq4uSUlJdO/eHUtLSxoaGjAwMMDY2BhdXV2amprIzs7Gw8MDfX194uPjGTBggKaL\npqamhra2NszMzKipqcHW1pYLFy7Q1taGh4eH5kFwQEAAbW1tqNVqSkpK6NatG6ampuTk5GBnZ0db\nWxsNDQ1UVlbi5eVFaWkpsbGx1NXVYWpqyuOPP97FV1+4W4nAL9y3mpub+eCDD/D396dfv37ExcUx\nderUDrNz7yeVlZW899572NjY0NDQwLBhwxg7dmxXV0u4C4nN1oX7VkREBC0tLajVapRKJZGRkZpN\n0+83SqWSsLAwdHV1mTx5MgqFgh9++IHY2NiurppwnxHj+IW72pgxY+jZsye6urp8//336OrqUlRU\nhK+vL9ra2l1dvVvqk08+4cSJE9jZ2aGnp8elS5fQ09MjPT2dgQMHdnX1hPuICPzCXSs2NpYvv/yS\nwsJCLCwsmDRpEtHR0VRXV2s2U7lfZGdnk5CQgLm5OdXV1dTV1fH4448TGRkpgr5wy91U4A8PD+eV\nV16hvb2duXPn8sYbb1xxTFRUFK+++ioqlQpra2uioqJupkjhAVFeXs65c+cYOXIkCoUCV1dXFAoF\nvr6+NDc388orr7B48WI8PDy6uqq3RF5eHubm5sydOxeVSqVZIrqhoYFLly6RlpbGmDFjNMs9C8LN\nuOE+/vb2ds3wuNTUVHbs2EFaWlqHY2pqali4cCH79+8nOTmZH3/88aYrLNz/kpKSiI6ORk9PD1tb\nW4KDg3F0dEQmk+Hj40NzczMTJkxg3rx5bN68uaure9NKS0vZvn07zs7OODg4dLjDl8lk/PTTT5SU\nlHDs2DGqq6u7sKbC/eKGA39sbCweHh64urqiq6vLjBkzCA0N7XDM999/z2OPPYajoyPw+6bXgnA9\nDQ0NqNVqampqKC4uJiIigvDwcNRqNc3NzRw+fJiysjIeffRRAgMD2bx5M2fOnOnqat+wffv2sX//\nfhYuXIi3t3eHJZpzcnL47rvvUKlUODk5YWpqSnV1tRgFJ9y0G+7qKSws7LDxhKOj4xX/AS9evIhK\npWLEiBHU19ezaNEinnnmmSvOtWzZMs3vw4cPZ/jw4TdaLeEe9+2336Krq8vcuXORJIklS5Zw6dIl\nCgoK+P7777l06RJTpkzh0qVL6OrqolAo2LBhAwMHDkQmk3V19f+W5ORktLS0iIqKIigoCE9PT9LS\n0tiyZQtyuRxjY2P09fXx9fXF1dWVJUuW4ObmRlBQEI899tg9117h5kRFRd2yrvIbDvydedOpVCrO\nnTtHZGQkTU1NDB48mEGDBuHp6dnhuD8GfuHBVVlZibOzM9XV1fzyyy/ExMQAEBYWhre3N9XV1fTo\n0YPffvuNjRs3kpCQwOjRozExMdHMfr1XVFVVsW/fPoYMGcKIESOwt7fH3Nycuro6fvjhB6qqqnB0\ndMTd3R0tLS2++uor7O3tCQ4OpqSkhKKiIhQKRVc3Q7iD/nxTvHz58hs+1w0HfoVCQX5+vuZ1fn6+\npkvnMicnJ6ytrTE0NMTQ0JChQ4eSkJBwReAXBPh9QTNDQ0P8/PxQKpUEBARQWVmJjY0NNTU1rFix\nQrOPbvfu3dHT00OhUBAWFkZ5eXlXV/9vqaqqIjc3lylTpuDn56dZmsHb25uVK1eSnp5Ov379qK6u\nplevXpoZywqFgrVr17Jw4UKWLl36t/YJFoTLbnjmbltbGz179iQyMlLzQGrHjh306tVLc8xvv/3G\nyy+/TEREBK2trQQGBvLDDz902KhCzNwV6urqCAsLw8LCgoMHDzJ16lQefvjhTuWNjo5m5cqVTJ8+\nnRkzZtDa2nrFWvh3mx9//JG4uDgaGxupqqriyy+/xMjIqFN5o6KiUCqVxMTE4ODgwHPPPXffzmIW\nrq9LZu7q6Ojw2WefMWbMGLy9vXniiSfo1asXISEhhISEAODl5cXYsWPp3bs3gYGBzJs376q7EwkP\ntgsXLpCenk5tbS36+vqkpKRo1sS5nrq6Ovbs2YOfnx/19fXs2LGDL7/8ktra2jtQ6xvXr18/5s6d\ny4QJE9DS0uKzzz7rVHuzsrLYu3cvLS0tFBYWEhYWxqhRo2hubr4DtRbuJ2KtHqFLpaWl8fPPP+Pn\n58ekSZP49NNPOX/+PCYmJnzyySfXfZa0fv16UlNTCQ4O5umnn+bTTz/FyMgIIyMjnnzyyTvYis6p\nrq4mOjqa5uZmMjMzmTVrFufPnyc9PZ0FCxZgZmZ23fwbNmzgyJEj+Pj48Prrr3P06FHmzZvH3Llz\nWbNmzR1qhXC3EGv1CPes9vZ25HI5u3btIjw8nOeffx4PDw9SU1PZu3fvNfOFh4dTV1fHiBEjMDAw\n4OjRo/j7+2NiYkJ6ejp5eXl3sBWdk5yczNGjRzlw4ADnzp0jJyeHuLg4UlNT+fbbbyktLb1m3ra2\nNoYOHcrixYuxsLBg9uzZfPvtt0ybNg09PT2USuUdbIlwrxN3/EKXaG9vR1tbm0uXLqGtrU1VVRX+\n/v5oaWlRWFjIJ598Qm1tLcuWLcPe3r5D3pqaGj7++GNsbGzw8/PDx8cHY2NjtLS0SEhIICYmBrlc\njr+/P76+vl3Uwo5yc3OZP38+ixcvxsXFBS0tLUxMTFCpVPz222+afQJeeOGFK/rsCwsL+frrr5kx\nYwbu7u7U1NRw7tw5VCoVSqWSlJQUnnjiCbp3795FrRO6gthsXbinKJVKVqxYQWBgIEeOHOHxxx8n\nODhYk15RUYFCocDCwgKVStUhb3FxMWfOnGHgwIE4Ozvj6uraYc2e6upqdHV1KSsr45dffrkrAn9y\ncjI7duzg0UcfxcnJCRsbG4yNjTXpx48fx9TUlD59+pCfn4+Li4smraKiguzsbAYNGkRSUpJmn97L\nD7/Xr19PdHQ0OTk5vP766/fNEhbC7SW6eoQ7LjQ0FGNjY5qamqirq+PkyZNkZ2cDsG3bNhYvXqy5\nkwkLC9MsBdLS0sKRI0fIzc0lKSkJmUxGSUmJ5rwRERF8+eWXjBo1Ci8vL1xdXcnKyrrzDfwTtVqN\nu7s7Pj4+nD17lu3bt2vSsrOz0dXV5R//+AcVFRWsWbOG1NRU4PfN4d9//32OHj2KmZkZiYmJLFiw\nQHNt4uPjUavVFBcXk5+fT2FhIRUVFV3SRuHeIgK/cEfFxsaSkZFBr169GDp0KAqFgtDQUDZu3AiA\nJEk4Ozsjl8t58sknOXToED/88AOVlZUcO3aM8vJyxo8fz6uvvkp1dTW7d+9m+/btSJLEqVOnqK6u\nRqVSYWtry6lTp0hMTKS1tbXL2ltdXY2Hhwd2dnb07t2b3NxcqqqqKCsro7i4mPDwcCIiItDW1mbg\nwIGYmJiQkpKCWq1mz549JCQkoFKp8Pb2xtraGjc3NxISEjh//jzLli3Dzc2NY8eOsX79ek6dOsUP\nP/zQZW0V7h2ij1+4ozZt2kRMTAyLFy8G0GxkPmnSJMzMzGhra+PgwYNkZmYyduxYsrOzqa2t5aGH\nHsLX15f29nYiIyMZPny4Zh/b4uJizMzM0NPTIzk5GR0dHaysrDh58iTGxsakpqZy4MCBO75/bVlZ\nGXPnziUwMBB7e3sUCgVNTU24urqyatUqxo8fz5AhQ9ixYwdTp07F3NycjIwM+vbty86dOzW/l5WV\n4e3tTVRUFAEBAfz6669YWVlRX19Pr169MDY2Jj8/X9PuwsJCFi1a9JejhIR7m9h6Ubjr1dTUcOLE\nCXR0dHB2dsbb25v6+nqysrKQyWT06tWLoqIiTE1NSUxMREdHB1tbW3R1dSktLUWpVOLn54dcLicu\nLg43Nzfkcjm1tbWaLg53d3dOnTqleQCqra1NQ0MDn376KSYmJuzevRsdnTvzWKu4uJgRI0Ywb948\npk2bRktLC87Ozpq5CqGhofTr1w97e3u0tLSwtLTskD8vLw9tbW3NwoZVVVU0NDRgYmJCTU0NJSUl\nBAQEIEkSycnJmJiYYGFhQVZWFhEREfTp04dp06aJyV33MRH4hbuaSqVi/fr1tLa2Eh0dTd++fXnv\nvffQ1dW9reWq1WoiIyM1a/4MGzaMhx566LYvbqZWq9myZQvbt29n2rRp9OvXj0GDBt3WMuH3kVJv\nvPEGw4cPJy4ujqFDhzJy5MjbXq7QNcSoHuGu1tTURGlpKUZGRlhaWmJqakp2djY9evS4reXu3r2b\nyspKnn76aRwdHZk8eTLa2tq3fTG3kJAQYmNjGTduHNra2hQXF1NeXk63bt1ua7n19fWaCWyzZ8/m\n8ccfZ/Xq1YwZM+a2livce8T3QOG2q6qqYurUqYwaNYoNGzbg7+9Penr6bS2zrKwMuVyOq6srzs7O\n7N27l0mTJrFt27YOiwvearW1tZibm+Pl5cXDDz/MvHnz6NGjB8uXL6etre22lbt//34mTpzI8ePH\nGTRoEKdPn8bd3Z2zZ89ed2KY8GASgV+4rSIjIykqKmLVqlXExsaSnZ1NbGwsJiYm5OTkUFdXd8vL\nrKurY8mSJTQ2NuLu7s4333zD+fPnaWlpwdTUlLVr196Wma719fVER0eTnJzM4MGD8fLyYunSpaxa\ntYrz58+zdevW2xL8c3NzCQsLw83Njfnz5/Pjjz9y8uRJHn74YQoKCigrK7vlZQr3NtHVI9w2eXl5\nVFVV4e7uzuLFi/Hx8cHCwoKysjIUCgWzZs1i9erVt7zrJTo6Gh0dHfr27YuJiQnTpk1DpVLR0NCA\nUqnkyJEjNDY2oqend8vKbGlpISQkhLNnzzJ06FDN8hGjRo3CysqKDRs28OWXX+Lg4MCECRNuWbnw\n+3pHhoaGvP7660iSpHkw3rdvX6ZMmcLq1auZPHkyo0aNuqXlCvcuEfiF2yI3N5ft27ejpaVFTk4O\n8+bN0wynHDt2LLGxsbz00ktcvHgRd3d37Ozsbkm5OTk5HD9+nD59+nDs2DHmzJmjSbO0tKSyspK5\nc+cSFRWFu7v7LVvmIDs7GwMDA3R0dJg+fTrm5uYAmoerK1asoLy8XLMU859H8dyoxMREtLS0SE1N\npbW1VbP6raurK7W1tWzZsgU9PT0MDAxuSXnC/UEEfuGWKygo4JdffqGpqYmJEydiamoKoFl6eO/e\nvTg4OODo6IhSqaSoqAgdHZ2b3pM5OTmZ6upq5syZg7W1NRUVFTQ1NWFkZERTUxOff/45KpWKF198\nEVNT005N7EpOTsbIyAg3N7drHtPc3My2bdsYNWoUZmZmV+wH0NbWRnl5OZGRkbS2trJ69Wq2bdum\n+XC4UV9//TXnz5/ntdde45VXXtGM53dycqK9vZ3k5GRaW1spKSmhoKCA9PR0evbseVNlCvcHEfiF\nW0qtViNJEkqlkj59+uDs7ExERATt7e0MGjSI0tJSTExMOHfuHOPGjSMyMpLq6mocHR2ZOHHiDU86\nUqvVhIaGYm1tjb+/P21tbSQlJbF69WoWLlxIc3Mzu3btwsnJCZlMRr9+/cjJyfnL83p6el532GlN\nTQ2VlZUEBASgUCgYOXIkzz33HAYGBrzyyis0NzdTXFyMrq4uL7zwAufPn8fHx4eGhoabCvwqlYrm\n5mYcHBxobGwkICBA88HSv39/DAwM+Omnn9DR0eHjjz8mNDQUlUqFWq0WY/sFMY5fuLWWL1+OUqnU\n7A1rYGBAQkICCoWCCxcuMHbsWHx8fNi7dy+1tbU0NDRoFhabOHHiDW3LKUkSixcv5siRI/Tu3RtL\nS0vMzMyQy+Wkp6cjl8uZNGkS3377rWYGrbGxMWq1mj59+lBUVMSIESP+drlqtZpXX30Ve3t7mpub\nqa6u5oknnqC4uJiff/6ZxMREZs6ciY2NDSUlJQQHB5OWlkZ6ejqenp489dRTNxT829rauHDhAvn5\n+dTX12NpaUlOTg6VlZWcOHGCkSNHMm3aNHbv3q3Z+e63335jzJgxfP311wQEBDBt2rS/Xa5wdxET\nuIS7QkFBAdHR0YwcOZLy8nL09PTQ09OjqakJfX19UlNTcXFxwdbWFm1tbUpLS7GyssLAwIDU1FTN\n2vx/d0XN9evXc+HCBWbPnk1jYyMODg6YmprS0NBAeXk5dXV1DBs2jO+++45+/fqhr6+Pubk5+vr6\n7N69m82bN7Nq1aq/HQxzc3M5dOgQQUFB6OnpUVJSgp+fH62trSQnJxMbG8vs2bNpb2+nqqpK070U\nGxuLq6ur5pvCH1fj7IyEhAROnz7NvHnzqKiooLW1ldbWVrKysqirq8Pa2hpPT0/S0tLo1asXhYWF\nODs709LSwpkzZ8jJyWHRokWd3u5RuDuJwC90uczMTNatW8fkyZPx8fHB0dGx0zNkU1JSOHfunGZd\n+sWLF3c6CJeXl7Nw4UJcXV1paGhg5cqVnX5wWlpaysyZMzE3N6dPnz68/fbbncp3OW9paSlHjx4l\nISGBdevWIZfLO5X39OnTHDx4kKqqKhwcHFiyZEmnu1+++eYb4uPjqampYfDgwbz00kudrnN7eztb\nt27FwcGBlJQUXnvtNdHtcw8TO3AJXa6iooIePXpQU1NDaGhopwOSWq3m7NmzFBYWcuLECUxNTamo\nqKC8vPwv8zY1NZGfn88//vEPfHx8cHZ27vRkpfb2dvbt28fbb7+Nq6srBQUFFBQUdCpvU1MTkZGR\nREZGalbSTE1N7dQYfaVSyfnz5+nZsyejR48mODi40x+QkZGRmu6qoqIiYmJiaGpq6lRepVJJWFgY\nPj4+KBQKTp8+zYsvvihuuh5QIvALNy0uLo5PP/0UtVrN1KlTUalUODk5ERER8Zd5IyIiaGtrw83N\njQMHDjBkyBDOnz/Ppk2b/jIopaamsn37dnr27MnMmTPR19fn4MGDnQr+b731Ft9++y3nzp1j9erV\nvPjii5SUlJCQkPCXeX/55RfCwsKwtbXlv//9L2PHjiU1NZULFy5cN19rayuvvfYa1tbW+Pr6Ehwc\nTHh4OIcOHfrLtpaXl7Nr1y6ampp45JFH2Lt3L5MnT2b37t1/Gfybmpo0awfp6Ojg7+/PlClTyM7O\n1uyDIDxYxKge4aYUFxeTlJSEt7c3JSUlbNy4kYqKCqZOnUpERAQ9e/bE1dX1qnlramqIiYkhLy+P\nnj17UlZWhpaWFl5eXujq6lJYWIijo+NV827atIn09HSCgoJITEykqqqKnJwc7O3tSUpKoqysDD8/\nv6vm3bZtG7m5uZiamnLgwAFSU1PR09OjtbWVcePG4e/vf832nj59mn379tGjRw/Ky8uJjY2lsLCQ\nyZMnc+zYMbp3737FcM7LmpubSUpKQltbm8zMTM2/ZWRkoFarGTlyJIaGhlfNe/DgQZqamrCwsGDF\nihUEBwdjZmbG119/ja6uLk899dQ161xRUUFtbS1DhgxhxYoVvPXWW/j4+GBjY0Nubu51h6oK9ycR\n+IWbUlBQQExMDK+//jr5+fl4enpqxu0XFRWxePFiXnvtNQICAjrkO3PmDKdOneLJJ58kKioKNzc3\nzMzMGDFiBN27d+f06dOcPHmSkSNHXjG+X6lUkpubi42NDaNGjSIjIwM7Oztefvll2tvb+e2330hP\nT79q4K+srOTs2bP079+fgIAADA0NSU5Opra2Fi8vL+zs7AgNDWXUqFEdtkeE3z+oQkJCmD17tmYr\nRCsrK8aNGwf8vsnMtUbpnDlzhtTUVM3mKdbW1ly6dImLFy+ip6eHs7MzlZWVV/2ga2pqwsXFhblz\n55KYmIiNjQ2TJ0+mpaUFR0dHqqqqaGxsvKK+l+u8f/9+evTowcCBAwkKCsLR0REtLS3mz59PZmYm\n586do2/fvrd91VLh7iG6eoQblpSUxMWLF5HJZFhaWjJy5EjN7lltbW0EBwfj7u5OYmIiarW6Q96M\njAwaGhrQ09Nj3LhxjB49GhsbG0aOHElGRgb79u2joqJCs+3iH+Xm5mrKaWpqYsCAATg6OuLp6UlJ\nSQkxMTH07NmT/fv3d8inVqtZtWoVdnZ2NDc3Y25uTkBAAHPmzOGVV17B09OTr776CoCGhoYOeSVJ\n4pdffsHd3Z3vv/+e0tJSBg4ciLu7O/D7A2oLCwv2799PaGjoFXWOi4tj7969rFu3DhMTE4yMjPD1\n9WXq1KkoFAoOHDjAypUr2bJlS4d8BQUFzJgxg7S0NM0GNE888QSGhobI5XJ69+5NXV0d2dnZmgly\nl1VXV7N161bMzMzIyclBR0eH/v37Y2trS7du3TRdVq2trZw5c6aTf3XhfiACv3BDLgeSdevW0adP\nH0JCQjQTosrLy/n8888pLS1l+PDhmge4l4WFhTF48GCmT5/OunXr+M9//qPZG1eSJEpKSujevTuV\nlZX88ssvREZGavJmZGTw1VdfYWRkxOHDh9myZYumT7+iooJz587R2tpKRUUFenp6pKSkaPKuWbOG\nxMRETExMqK2tZefOnZq+9aKiIhISEpg7dy4pKSksWLCgQwD//PPPNd00fn5+REVFaQJtZmYmpaWl\n2Nvbk5eX12H1z+bmZrZu3UpUVBRTpkyhe/fuvP/++1RWVgK/L/WwYcMGoqOjuXjxItu3b+fw4cOa\n/Je7rNLT00lISGDDhg2atMrKSl577TXkcjmhoaHMmzdP02cvSRKffPIJMTExyOVytLW1Wbt2bYcP\nh379+uHi4oJKpWLTpk2iv/8Bor1s2bJlXVmB5cuX08VVEP6m+Ph43nzzTeLj49mxYwdhYWEUFxdz\n4cIFHnroIaKjo7G2tmbOnDkYGhoSGxuLUqkkOzsbLy8vPv30UyRJYujQoZr+7qKiIpydnfniiy+I\niYnBysqKf//735q76549e1JSUsLBgwd55ZVXCAgIYMiQITg7O9Pe3o6JiQnr16/n9OnTKBQKFixY\nwOnTpwkPD2fUqFFUV1ejo6NDYGAgTz75JPn5+bi4uHDixAl8fX354IMPqK2tRVtbm4CAABobG6mr\nq2Pw4MFs2bKFpKQkpk+fzowZM9DR0aFHjx7IZDKUSiV79uzh5MmT+Pr68uijj/Ljjz/SrVs3tLS0\n2Lx5M5mZmQQEBPD000+jVqvJzMzE398fuVzO0qVLqa+v53//+x8ODg4YGBjQ1NREYGAgubm5rFix\ngrFjx/LCCy9o9i9obW3FycmJbdu2MXToUAYMGIClpSVpaWnExcURHBzMjh070NLSIigoiPHjx9Pa\n2kplZSUPPfQQeXl5FBcXU1RUxJNPPsmxY8c4c+YMarWawYMHd/G7S+ism4mdYhy/8LfFx8dz5MgR\n2tvbkclkREREMG7cOFQqFQMGDGDIkCHs3r0bV1dXbG1taWhoQFtbm59//pm+ffuSn59Pbm4uPXr0\n4MSJEwQFBXHw4EF8fHwoLCwkKCiItLQ0zMzMkCSJrKwsAgMDKSoqolevXkiShJubG7m5uZrRQ+7u\n7ri5ubFt2zba2tqYMWMGxcXF1NfX4+rqioGBgWYPWzc3N5YsWcIjjzxCUVGRpo/e1taWjz76iIsX\nL5KXl8crr7xCWVkZBQUFeHp68ttvv+Hm5kZtbS0+Pj7U19cjk8nIyMjAxsaGAQMGcOTIEezt7cnK\nyqK5uZnW1lYef/xxfv31V5566ikaGhqoqKggPj6eHj16aB5EOzk5cezYMYKDg7G0tKS1tZXs7GzK\nysoYN24cQUFBVFRUUFlZybp165g9ezb19fXo6Oho1ubZuHEjy5Ytw8jIiPXr19O/f39UKhVpaWmM\nGTOG2tpaJElCT0+P0tJSiouLyc/P1wyd9fPzY8aMGQwfPrwL311CZ4kJXMIdc+bMGc6dO8egQYOQ\nJAmVSkVrayv29vZYWFiQm5tL3759+eWXX7C0tMTKygodHR2MjY1pa2ujsrKSuro6evfuTVtbG7Gx\nsfTu3ZuWlhZKS0tRqVQ4OjqSnZ1Nfn4+VlZWWFlZ4eHhwZ49e5g+fTrnz5/HwsICe3t76urqyMnJ\nwdXVFSMjI0JDQ7GxscHZ2Rl9fX0kSUJXV5eSkhIqKytxcXFh0KBB5ObmUltbi729PfX19ZqHspmZ\nmWzdupXg4GCCgoI4efIk/v7+mJubk5qailKpxMDAAB8fH3R0dNDW1qa6ulpzN56cnExSUhIDBw4k\nNzeXxsZGhg8fzq5du3jkkUewsrKivLycxMREzM3NNSOXysvL8fLyIjMzk/r6erS1tRk4cCDm5ua0\ntrZiYWGBsbExRUVFxMbGMnDgQJKSktDV1aVbt264uLiwbds2HnnkEWQyGdra2hgZGVFSUkJoaCgv\nvvgi+fn55OXlMWjQIKytrcnJyeHYsWM4OjrS1tZGTk4OiYmJTJ06lYkTJ3bl20zoBBH4hTuiuLiY\ns2fPkpeXh4WFxXWHEAr3npqaGjZs2EBmZiZvvPEGXl5eXV0l4Tq6bOZueHg4Xl5eeHp6smbNmmse\nFxcXh87/x955R0V1rQ/7QXqv0qWKYhcEezd2McaYaGJMTIxJvMnP6E25aTeJNzeWxMQUTSxRI0YF\nG3YFFRBQKUoTcOhShjJDZxjalO8PF+cLNzHBgljmWcu1wD173r3PObxn73e/RUeHw4cP3404DV2I\nSqVi/fr1bNy4EUNDQyoqKhCLxV09LA33ALVazdGjR7l+/Tqenp7MnTuXX375hdra2q4emoZO4o4V\nv1Kp5K233uLMmTNkZGSwb9++P3W9UyqV/Otf/2LatGmalf1DSn19PWvXrqW1tZXFixcza9Ys1Go1\nWlpanVI6UcP9JT09nby8PORyOQEBAWzatImysjLWrFnT1UPT0EncseKPj4+nZ8+euLm5oaury4IF\nC5LBSb0AACAASURBVP7Uf/nHH39k3rx5dO/e/a4GqqHr2LRpEwqFAgcHB65fv05QUJBgY16xYgWt\nra1dPUQNd4hcLic4OBhPT08yMjLIy8sDYPLkycjlclJTU7t4hBo6gzuO3BWLxfTo0UP43dnZ+Q9B\nIGKxmKNHjxIeHk5CQsItIwN/75I0fvx4jVfBA8ShQ4c4cuQIy5Ytw8HBASMjI1xcXAAwMDBAoVBw\n4MABjb3/IUStVlNYWIijoyNGRkbMnz8fgOPHjwseRZs3b+aTTz7B0dGxi0erITIyksjIyHvyXXes\n+DsS3r1ixQrWrl0rHELcytSj8eN/cPH19WXkyJH079+fIUOGtGurr68nICCA8vJyKioq7rp0oob7\nh1qtZsmSJRgYGGBubo6Hhwe2trZCe2trK+np6YwfP57MzEyN4n8A+N9F8apVq+74u+7Y1OPk5NQu\nQrGoqOgPeUauXr3KggULcHd359ChQ/zjH//g2LFjdzxYDfePuro6AgMDKSkp4dtvv8XAwKBdqcJj\nx47xyy+/0LNnTwYMGCCkOtDwcHDw4EHy8/OZNm0ac+bMITU1lTNnzgA3z+WioqIYP348Y8eOJSoq\nitjY2C4esYZ7yR2v+P38/MjOzubGjRs4OjoSHBzMvn372n2mzV4I8PLLLxMQEMDs2bPvfLQa7gsK\nhYKNGzeSlZUlFDXJy8sjIyODGTNmIBaLycnJwczMDGNjY8rKyujfvz/Z2dk4OTlpKjs94DQ3N9PQ\n0MCMGTPo2bMnVVVVaGtr09jYCNxMM9FWu9jDw4Px48cTFhZGQ0MDkyZN6uLRa7gX3LHi19HRYePG\njUydOhWlUsmSJUvo06cPW7ZsAeD111+/Z4PUcH+prq6mpqaGXr16sWPHDiIiIggICODq1avI5XLy\n8/MZO3YshYWFrFu3jt69e+Pt7U1xcTGGhoYaxf8Ao1QqCQ8Px9raGrlcTlRUFNHR0Tg6OuLq6opI\nJOLKlSt069YNqVRKbGwsGRkZGBsbs3XrVrp3787AgQO7ehoa7hJNAJeGdrSF8V+7do1Ro0YREhKC\nvr4+U6ZMQSaTYWBgQElJCVOmTCEkJIT09HQ++ugjampqiIyMxNjYmJkzZ3b1NDTcgn379nHp0iV+\n+OEHcnJyqKmpITc3l+7du+Pr64uFhQWZmZkoFArq6uooLS2lX79+1NbWkp6ejkwmY/ny5V09DQ1o\nInc13CPkcrlQFERXVxcXF5db5pf/M1asWCHUcP3qq6/Q0dGUe3iQUCqVXL16lYsXLyKXy3nvvffQ\n09PrUN9r164RHBxMcnIyb775ppDfSEPXoam5q+GecfToUb788ktCQ0OJjo7+Q176WxEXF8fzzz+P\nlpYWKSkpnDhxopNHquF2aCtAk5iYSG1tLTExMVy8eLHDfffv34+1tTW5ubn89NNPmtiNhxyN4tcA\nQHl5OefPn2flypUEBgYybNgw5HJ5hyNztbW1aW5u5quvvuL111/nl19+QSKRdPKoNXQEhUJBRkYG\nP/zwA9XV1bzxxhv4+flx8eJFoQTkrSgqKuLLL7/k8uXLjB49mqioKJ5//nmmTp1KTEzMfZqBhnuN\nZi+ugeTkZL766ivMzc2JjY0Vsk66uLiQlZWFVCq9ZR1aiURCTEwM+vr6ODk5UVNTw/nz55HJZCxZ\nsoSlS5dqPLm6mIKCAlJSUhgwYACNjY1UVlYyfvx4PvnkE7S0tFi5cuUtD+SzsrKor6/Hz8+PnTt3\nMmrUKOrq6vDw8ODy5csMHz5cY9J7CNHY+DWwd+9ekpKS8Pb2Rk9Pj6amJkxNTZFIJNTX15Odnc3m\nzZsxMDBo10+hULBt2zZMTEzo27cvXl5eNDU1ce7cOdzc3Ni0aRNFRUUEBgbesuC6hs7l4sWLRERE\nsHTpUiwsLDh9+jQ9evSgsbFRONy1s7Nj/vz5wvlMG7t37+bSpUtMnjyZpqYmHB0dcXBwoKmpCQMD\nA7Zv346Ojg6rV6/uotk93tyN7tS8qh9z2vK/v/zyy/Tt27ddW2ZmJlu2bGHMmDHs3LmTpUuXtlvd\nnThxAm9vb6ytrWlubsbMzAwzMzOh4MjEiRM5ceIE1dXVGsXfRVhZWdGtWzcSExMZO3Ysc+bMEdoc\nHBxQq9Vs2LABQ0PDdm1lZWXs2LEDR0dHtm/fzqFDh4QXv1qtZv/+/VhZWZGamsrx48cJCAi473PT\ncOdobPyPMaWlpRw8eJD4+Hhu3LhBTU1Nu1S8CQkJKJVK/P396dmzJ9ra2kJbU1MTIpEIuVxOdnY2\nFy5cEOrm1tbWsmHDBgBeeeUVdu7cydatW+/v5B5z6uvrWbZsGVZWVowYMQKRSNQuz0tubi6nT5+m\ntrYWJycnjh49SlpaGnDTu0ssFjN//nwWLFjAkiVLCA0NFVaXNTU1nDlzhtLSUuzs7FCpVDQ1NXXF\nNDXcIRrF/xijVCoZM2YMn376KTNmzCAxMZGIiAjgpm1XLpfz5JNP4uzsjEgkEpLwVVdXs2rVKjIz\nM/Hw8CA7O5vW1lZhN/DFF1+Ql5dHz549GT58OIsWLcLJyYnS0tIum+vjRtv9u3HjBv369cPY2JiK\nigqKi4sBEIlEWFpaYmtry8SJE5HJZGzbtg2As2fPEhkZyZgxY5g0aZJQBjIhIYGioiI++OAD/Pz8\nePvtt5k5cyYxMTG89tprXTldDbeJxsb/mFJcXExiYiJVVVVYWlpSU1NDVFQUTU1NDBkyhOzsbPz9\n/dm1axdjxoxBoVCwfPlyTpw4QUBAABKJhNDQUKqqqoiKiqJ79+60tLQwbtw49u3bh5eXF+Xl5Sxc\nuJDq6mrUajX6+vq8/fbbmsPATiYmJoajR4/SvXt36uvrmThxIrt378bPzw8tLS169eqFra0tv/76\nK0OHDkWpVKJWq/n111/5v//7Pz777DMmTpyIvr4+xsbGGBgYoKenh0qlwsTEhA0bNrBy5UoSEhLo\n378/tra2FBYWMmjQICZPntzV039s0Nj4NXQYlUqFRCKhubmZlpYWPDw88PDwIDExEScnJ3R1dVEo\nFKxYsYKWlhaSk5N55plnUKlU2NraMmjQIOzt7XFwcMDMzIzo6GhcXFyoqamhubmZAQMGoKuri5aW\nFtbW1vj4+CAWi6moqODAgQOUlJSwevVq9PX1u/pSPLLo6OhgZWWFn58fUqkUR0dH5s6dS01NDSNH\njqSmpobW1laGDh2Kt7c3tbW1Qr0MZ2dn3n33Xdzc3LC3t6exsZE+ffrQ2tqKWCzG0NAQNzc3zM3N\n6dWrF5aWlri6urJnzx6Ki4upqqoS8jtpeHDRrPgfM6qqqoiMjKS6upoRI0b84UC3s9i2bRuxsbHY\n2dkxevRoZsyYcV/kPm5cvnwZR0dHVq5cyf79++/L7kqpVLJx40YaGhqorq5m5cqVmjTO9wFN5K6G\nDmNubo6NjQ01NTWUl5cLB3qdiUwmY/369WRlZeHh4cGAAQM6XebjSFJSEitWrGDhwoV4e3uTnp5+\nX+Q2NjZiZGREQEAAhoaGVFdX3xe5Gu4czYr/MaKiooKvvvqKpUuXYm1tze7duzly5Ag//vgj/fv3\n7xSZlZWVREREEB8fzzvvvIOWlhYSiQRXV1dMTU07RebjSGlpKbt370Ymk7FgwQIqKytJTEzE0NCw\nUw9eMzMzycjI4KmnnkKlUrF9+3acnJzo27evxoW3k9HY+DX8LcHBweTl5VFSUsJnn33GtGnTuHz5\nMjo6Ohw5cqRTFL9CoSAlJQWpVMrMmTNZvXo1AQEB6OnpER0djYeHB1OnTr3nch9HTp06hbOzMxKJ\nhIqKCkQiEUqlklOnTjFixIhO22Xt2LEDHR0d1Go1MpmMy5cv4+XlRWpqKi+99BIODg6dIlfD3aFR\n/I8BarUaHR0dhg4dio+PD9ra2vTo0YOmpibi4uJIT09HLBbj5OR0T+UWFhayb98+5s6di4uLCw4O\nDnh6euLu7k51dTXh4eGYmZkxYsSIeyr3ccTW1hZLS0t8fX2xtrbG0tKSgwcPYm9vT3Fx8T1X/IWF\nhURHRzN+/HgGDx5MbW0t169fp3///vTs2ZO8vDzmz5/P3r17/1CZT0PXo1H8jzgKhYI1a9YglUoZ\nO3Ys8+bNE9q8vb1xc3MjMDCQ8vJyrK2t/5CW4U6pr6+nurqa5uZmpFIp06dP54MPPgBuvoiuX7+O\nhYUFa9eu5YUXXuCZZ565J3IfV0QiEYaGhrz11lsAdO/enR49evDhhx+yZ88erly5wjvvvHNPiuSo\nVCpSU1PJzc2lqKgId3d3vL298fb2Fj6TmZnJ/v37mTNnDpcuXepw+mcN9wfN4e4jjlKpxMzMjCee\neIKQkBASExOFtmvXrrF3716mTZtGeHg4//rXv8jIyLhrmSqVitOnTxMREcF//vMfampqOHfunNDe\nFvGpUCiYP3++YCrQcPvU1tayceNGnnjiCQ4dOsSVK1eAmy/XrVu34uXlxfz58+nZsycKheKeyExL\nS+PMmTOYm5uTl5fHjh07qKqqAm4+b5GRkdTX12NhYUFBQQFhYWH3RK6Ge4dG8T+iqNVqEhISOH/+\nPAsWLGDkyJEYGxtz4MABGhoayM7OJjIykqlTpzJr1iymTZuGp6cnUVFRdy07Ojqa2NhY+vbti4uL\nCzKZjJiYGMG88/XXXyOTyfj3v//N2LFjuXr1KklJSfdg1o8XO3bs4Pnnn8fPzw89PT08PDyEF7dU\nKiUxMREfHx/hGv/6668dzsF/K1pbW4mOjmbOnDk899xzQkBeZmYmjY2NlJSUUF9fj7GxMevWrWPC\nhAkcOnSow+m9NdwfNF49jyiJiYmEhoYyZswYKisrycvLY9euXRgZGeHn50dLSwt2dnb06NEDIyMj\nsrKy6N27N2lpafTr14/nn3/+juSmpaWRn5+Pvr4+hYWFSKVS7O3tqaysxMXFhf3796Ovr88rr7xC\n7969uXz5MiUlJQwdOhQbGxu8vLzu8ZV4NElNTUVbW5tXX30Va2trpk+fTlJSEosWLcLR0REXFxd+\n/vlnxo0bh0wmY8WKFaxdu5bm5mYGDx58x3b3pKQkKisrSU9PZ/jw4ejp6VFYWMiVK1fw9PRk//79\n+Pr6olKpyM3Npbm5mf79+zNmzBhGjRqFiYnJPb4Sjy+a0osa2iGXy4mPj0cqlfL0009TWFhISkoK\nFy5cYMyYMUKIfv/+/fHw8KC5uZnU1FRSUlJIT08XCqpYW1vfltz09HTefPNNXnzxRaZMmSKYd3x8\nfDA3N6e6upqsrCyefvppcnNzaWhowMLCAqlUSlNTEzt27GDVqlUaN8C/IS0tjfXr17N8+XKSkpLo\n3bs3JiYmXLhwgcWLF2NiYiKk1HZ1daWoqIgDBw4wYMAAcnJyKC8v54svvrjt4K6mpiYuXLiAu7s7\njo6OGBsbI5FIaG1tpaGhAZFIRGNjIy0tLdTW1pKSkkKfPn0YOnQora2teHl50aNHj066Ko8fGsWv\noR2NjY2kpaWRl5fHs88+i5aWVof6qVQqTp48iYWFBaGhoTz33HP069evQ33VajWJiYls2rSJRYsW\nMWHChA6Pt6SkhE8//VRI/fDZZ5/dVq3fx4mGhgb279/Pt99+yzfffMOUKVM63LegoIDU1FTOnz+P\nk5MT7733Xof7xsTEsGnTJmbMmEFVVRVvv/12h/tKJBJ+++035s2bh56eHvb29h3uq+HWaCJ3NQhE\nREQQGhpKY2Mjtra2fPXVVx1+OE6cOEFSUhJnz56lpaWFhISEDstNS0vj4MGDbN++HS0tLdavX9+h\nfmq1mj179pCens6ECRNwcXFh165dqFSqDst+nKivrycsLIw33niDuLg4Idvm31FXV0d0dDS2trYs\nWrQIc3NzxGJxh/pWV1dTUVHBnDlzOHnyJMePHyc7O7vDY46IiEBbW5tffvmFTZs2aRZ6DwAad85H\niIaGBlJSUujZsyejRo0iIyODnJwcamtrsbCw+Mu+RUVFaGtr4+npyRNPPIFUKv1Te3tlZSUqlUpI\n6gU3V+wNDQ2MHDkSLS0t9PX1MTAwIC8vDw8Pj7+V2717d9asWYOfnx/Gxsb897//Zc6cObi4uNzZ\nhXgEaat2lpyczPjx4xkxYgT5+fkEBgby5ptv/u0OKTMzEx0dHTw9PdHW1qawsLDDLpbh4eFERkay\nbt06XF1dycrKIjIyku7du//lc1VXV0dwcDBHjhxh79695ObmcvbsWSoqKto9PxruP5oV/yNCY2Mj\nVVVVaGtr061bN/bv309qaio9evQgPz//L/sWFhayZMkSzp8/T3JyMl9++SUvvfQSP//8MwqFQnDV\ng5sK6PdugVlZWRw5cgS5XM6uXbtYvHgxxcXFjB8//m9ztpSVlZGYmMiIESNwd3dHW1ub1atXCzZh\nzcrw/3P9+nWioqIYOnQoxcXFqFQqampqqKmp4fvvv6ehoeGWfXfu3Mnx48dRKpXs27ePs2fPEhYW\nRnZ2NuXl5X8pNz8/n6NHj2Jra8sPP/xAXl4eV65cQSwWc/bs2b+8Ry0tLRQVFeHj48PcuXORSqWk\np6dz/fp1GhsbNbu6LkSz4n8EaGpqIjc3FwMDA9zc3HB2diY+Ph5fX19MTU3Jzc3lwIEDjBw5klmz\nZrXrq1arWb58uVBwo7KyEqVSybJly3B0dGTNmjVIJBK+/vprDAwMsLOza9dfIpFQUFCAj48PCxYs\nID4+Hk9PT4yMjMjIyKChoYExY8b84ZyhvLycvXv3YmlpiYWFBbW1tTQ1NfHcc8/R0tIirDIXLVqk\nCf4BbGxsWLhwId26daOlpYX+/ftjZGSEnp4eIpGICxcuMG3atD/UzU1KSiIwMJABAwbg5+eHp6cn\nOjo6gg/+nj17kMvl7Ny58w8yS0tLSUhIYPbs2djY2BATEyN4g40bN46TJ0/St2/fPz0HioqKwsTE\nhIkTJ6JUKikuLqayspJp06bh7OxMXFwcJSUld+w9puHu0Cj+R4Do6Gjq6+vR19enX79+eHh4MHDg\nQOBmYrZ169YRFhZGZGQkEydObBe9mZ+fj7+/v/AC+P3WvaSkhIiICCQSCTExMYwbNw5dXV2hfceO\nHaSlpeHi4iKkXWiLDC4rKyMjI4OamhrBhfT37NixgyNHjmBtbc3ixYuFF8rTTz9NcXExQUFBFBcX\ns2PHDt54443OuXAPAQ0NDWzYsAFbW1v69etHr169hJTWvXr1Am4q2R9//BFXV9d2Sri5uZldu3Yx\nZcoUBg0aRO/evYW2qVOnEhISgrOzM9evX6elpeUPL9iUlBROnDhB3759efLJJxk/frzQJhKJyMjI\nEJT/71/seXl5/Pe//6Vv376sXLkSV1dXJk2aJLRfvnyZuro6odbD758pDfcHjannIef69et88cUX\nREdHExERQVVVlRAs09jYSGBgIAUFBcybNw+ZTNbuMDA2NpZt27bh5uZGc3MzISEh7Wrufv/99xw5\ncgRDQ0OkUilXr14V2q5du8bRo0fx9vbmtddeaxcRLJPJOH36NI6Ojly8eJFDhw61G3NBQQFnzpzB\nxsaGfv36cenSJaFNpVLxyy+/UFpaysSJE3F2dkYul9/z6/awIJPJkEqlyGQywsPD+eijj9qZSPbu\n3YuOjg7Lly9n//79Qt1jpVLJ+vXrsbCwEFxpc3JyhH5paWkEBQURFxeHnZ0dOTk57YKs8vPzyc/P\np1evXujo6LTbSSiVSr799luam5upra0lOzu7ncnn+vXr9OzZk9mzZ/PZZ5+1ezbg5m6vrYBPSEgI\nMpnsnl83DX+NZsX/ENPa2sru3bupra1l5MiReHl5UVlZyU8//cT7779PSUkJWlpaDBkyhHnz5mFu\nbk5ycjI6Ojq4ubmRn5+PiYkJ06ZN4+LFi5w6dYrp06djbm5OdnY2MpmMd955h8mTJ/PDDz8QHx+P\ni4sLjo6OSCQSnn76aSZOnEhNTQ1ws4B3WzUvOzs7Bg8eTO/evSkrK2P//v0MHDgQfX19Lly4wIYN\nG+jWrRtFRUVUV1ejUqno1q0b0dHRlJeX06dPH8aMGcP7779PcXExc+bMeSzdAOPj41m4cCE+Pj6s\nW7eO2tpa6urqMDAwICQkBD8/P7S1tZk6dSqJiYnExMRga2tLU1MT5eXlTJ48mXHjxiEWi6msrKRn\nz55IpVJ2796NkZERc+fOxcDAQMjoOWPGDM6cOcOlS5cYPXo0U6dOJSkpifT0dAYOHEhjYyMbNmwg\nPj6ekJAQCgoK+PLLL/Hy8uKjjz7i+vXrbN26lSeeeIKRI0eSlpYmHORKJBIiIiLQ19cnICAAExMT\nkpOTiYiIICAgoIuv9OPFXfvxnzlzhhUrVqBUKnn11Vf517/+1a59z549gkuhqakpP//8s2CGAI0f\n/90QFBTEuXPnKCkpYcqUKQwcOBAHBwf279/P6NGjyczMxNjYmF27djFhwgQcHBwQi8XI5XLefvtt\nDh06hJ+fH+Xl5aSnp6OtrY2pqSlqtZqGhgaMjIwwNzenqKiIhoYGrly5gp2dHd26dcPb25unnnoK\nExMTgoKCkMvlmJqa0rt3b1JTUxk9ejTV1dUkJCSQk5NDZWUlQ4cOFbxKnnjiCY4fP05tbS1WVlak\npqZiZWWFUqnExsaG9PR0vL29qays5OjRo/j7+7Njx46uvuT3jaqqKj799FNKSkrQ19dn8uTJuLq6\nolAoKCoqQqlUkpOTg6+vL8899xxbt24lKCgIKysrxowZw5QpU0hISEBbWxs7OzsOHz7MvHnzcHd3\nJzs7m9TUVNLT07G2tmbJkiWEhYURHx/PvHnziI2NxdbWFisrK6RSKaWlpUyePJn6+nqOHj2KWq1G\nS0uLl19+mcjISCoqKrC0tMTZ2ZnY2Fj69++PlpYWTz75JJGRkdTU1ODv749EIuH06dOMGTOG4cOH\no62tTVJSEpGRkaxYsaLDMSMabtJl+fiVSiVvvfUW586dw8nJCX9/f2bPnk2fPn2Ez3h4eBAVFYW5\nuTlnzpzhtddeIzY29m7EauCmjbWyspLZs2eTnp7OrFmz6NmzJwCffvoparWaiooKysvLGTt2LFZW\nVlhbW+Pn54dSqUQulwupkmUyGRYWFri4uFBZWUl5eTk2NjYMHjwYuVxObW0trq6uXLlyBV9fX27c\nuIGTkxPe3t6IRCL8/f0pKSnB0tKSgoICbG1tcXR0xMDAgLFjx+Lg4MCVK1fw8/PDyMiIPn36oKur\nS21tLRKJBENDQ6ZPn05eXh6FhYWUlZUxY8YMMjIy6N+/P2KxmKFDhyKVSh8LN0CVSsWlS5cwNjbm\nww8/pK6ujvLyclpbW2lqakKpVOLk5CTcM4A5c+YIppmamhoyMzMxMzPD2tqa+vp6XFxcsLS0xN7e\nnpqaGp544gmcnJwwNzfH0tISPT09rK2taWpqYtKkScTExFBXV4e/v7/goVVaWsqwYcNwcXHB2NgY\nHR0devXqhZWVFZMmTeLs2bM4ODiwdOlSpFIpVlZWvPDCC/zyyy+0tLQwfPhwHBwc8PDwwMXFheTk\nZIyNjXFycmL58uWsWrWK0aNHd/HVfzy4qxX/5cuXWbVqFWfOnAFg7dq1AEL63f+lurqaAQMGtLMz\na1b8d8a7776Lrq4ub7zxBq6url09nE6lpKSEbdu24e7uTr9+/RgyZEhXD6nTUKvVrFu3jlOnTuHg\n4MCmTZuwsbHp6mF1Op988gnx8fEEBgY+lia9O6HLVvxisbhd7o02N61bsX379j8tsv35558LP48f\nP76d94CG9sjlcl555RU+//xzkpKSKC8vp6Gh4b4VTe8KCgsL0dHRISkpiby8PHx9fTuchuJh48aN\nGxQUFGBjY8OsWbPYvHkzH3/88SM736CgICwsLPD09KSsrIzz58+zcOHCrh7WA0lkZCSRkZH35Lvu\nSvHfzsMYERHBjh07/jQt7O8Vv4a/pri4WIjEHThwIOfPnyctLY2vv/76kctvo1AoCAoKonv37owc\nORIbGxu++eYbWlpa0NfX7+rh3XPEYjGRkZEEBATg5eWFpaUlWVlZQubUR43du3cTGRnJggULWLx4\nMYsWLSIoKIiMjIxHeiFzp/zvonjVqlV3/F13pfidnJwoKioSfi8qKvrTdK+pqaksXbqUM2fOYGlp\neTciH2u2bNnC5cuXWbFiBZmZmeTm5lJaWsro0aPJzs5m0KBBj4xPdFs9ASMjIy5evIi5uTnPPPMM\ny5YtY+/evVRUVPDuu+8+MithtVrNN998Q1NTE3379iU3N1f4OSkpSSit+CjRFnfSFktQVVWFgYEB\nX375JWvWrNGk7OhE7sqP38/Pj+zsbG7cuEFLSwvBwcHMnj273WcKCwuZO3cuv/32m3D4qOHOGDVq\nFIsWLUKpVFJVVUVOTg42Njb07t2b3bt3t/OHf9gpLS2lpKSEPn36MGzYMGbOnImDgwN9+vRBJBJx\n5MiR20oi9yCjVqsJDQ3F0NAQX19fhg0bxrBhw3BychLcM+Pj4ykrK+vqod4zAgMD8fT0xMnJSTjU\nT05Oxt7enqeeeoqffvpJU7ylE7mrFb+Ojg4bN25k6tSpKJVKlixZQp8+fdiyZQsAr7/+Ov/5z3+o\nrq5m2bJlAOjq6hIfH3/3I3/MEIlEaGtrY29vT69evdDV1eWpp54CbiZOUygUhIaGYm9v/9CbBdry\nz1hZWeHj48PMmTOFNh0dHVxcXHB3d+fYsWPU19e3iwp9GCkuLubXX39FoVCwcOFCwcwxdOhQ4TPL\nly8nNjaWzz77rKuGec/IzMyktbWVjz76iA8++KBdCm+FQsGnn37Kzp07sbe3Z8WKFV040kcXTT7+\nh4DNmzdja2vL4MGDqa2tRU9PT/B5vn79OhcvXsTS0pLjx4/j5OTEypUrH1pPkLY0zcXFxXh5eXHm\nzBkWLFggKPcDBw5w7NgxVq9ezbp160hOTubw4cPY2tp28cjvjMLCQlasWEFNTQ09evTAxcWF7WpJ\nqQAAIABJREFUxYsX4+npCdyMcu7WrRtXrlzh3LlzDB48mKVLl3bxqO+cyspKvv76a1QqFXV1ddTX\n17NlyxZMTExoaGigqqqK119/HYAJEyYwZ84cTVW2W6DJx/8Ik5ubS0ZGBnZ2dhgZGZGXl8fq1auF\n8Pu2cPfBgwfzz3/+E3Nzcy5evEhzc3NXDvuOUCqVnDhxArVazZIlS5g0aRLDhw/n559/JiMjg7Ky\nMn799VdkMhlOTk6sWrUKGxube1InuCtobW2lvr6esWPH8vnnn/P0009TVVWFqakpcDNtQkFBATk5\nOfTs2RNPT0/i4uIe2oVSW1zJ4sWLGTx4MKtWraJv376EhIQAEBcXx759+1i+fDlr167FwsKCt99+\nm4qKii4e+aOHZsX/AKNSqYRgt+bmZlpbW1m/fj2vvPIKQ4cOxd3dnV27dpGcnMzQoUOFQKy2qMvf\nR0g/DGRnZwv+66ampjQ1NREREUFxcTGjR4+mtraWHj16oKOjg46ODrm5uejp6VFSUsK0adPamYQe\nBq5du0ZcXByZmZnIZDIWLFiAlpYWUqkUT09PKisr2bdvH6WlpcyYMYP4+HgCAgJQKpUEBAS0S7b3\noKNQKFizZg3Nzc3o6elhampKr169MDExobCwEIlEAiCU3XRwcOCnn37CxcUFGxsbXnvtNU293v9B\ns+J/RGn7gzA3Nyc6OpqzZ8/i5OREdnY29vb2aGlp0a1bN5qamoRoWj09PUxMTPjuu+/+1HX2QaWi\nooLDhw8D4O7ujlqtxtbWlgEDBvDjjz/y8ssv4+zszKBBg/D29kahUODm5iakBS4oKECpVHbxLDpO\neno6CQkJODs7Y2NjQ21tLZWVlZiamtKtWzf09PSws7PDzMwMPT095HI5RkZGlJaWcujQIRYvXkxr\na2tXT6PDaGlpYW5uTmNjo3CvYmNjkUgkqFQqzMzMsLW1xdzcHDs7O4yNjRkyZIgQ+V1YWNjVU3ik\n0Kz4H1AkEgkHDhxArVbz7LPP3pYN+8svv+TSpUusWbPmoVn1r1y5krKyMp577jnGjRvX4ZiElpYW\nTp8+jampKRMmTHho3DtDQkIoKyvDzc2N6dOnd7ifXC5n/vz5KBQKvv/+eyE184NO24v7vffew8zM\n7Lb6SqVS1q1bx/vvv//QnuV0BpoV/yNGW8pjhULB7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6R///68++67qNVq4fBNKpVy6NAh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139        "text": [
140         "<matplotlib.figure.Figure at 0x110c8590>"
141        ]
142       }
143      ],
144      "prompt_number": 440
145     },
146     {
147      "cell_type": "heading",
148      "level": 2,
149      "metadata": {},
150      "source": [
151       "Koch Snowflake Generation"
152      ]
153     },
154     {
155      "cell_type": "markdown",
156      "metadata": {},
157      "source": [
158       "I worked this one out myself. You might say I'm a special *snowflake*."
159      ]
160     },
161     {
162      "cell_type": "code",
163      "collapsed": false,
164      "input": [
165       "def koch1(n, x0 = (0,0), x1 = (1,0)):\n",
166       "    \"\"\" Recursively generates a Koch Curve between two points \"\"\"\n",
167       "    s = asarray([x1[0] - x0[0], x1[1] - x0[1]]) # Get displacement from x0 to x1\n",
168       "    # Calculate normal vector\n",
169       "    normal = asarray([-s[1], s[0]])\n",
170       "    normal = normal / sum(normal*normal)**0.5\n",
171       "    # Calculate the three points \n",
172       "    # Are these are the maps that form the iterated function system?\n",
173       "    # \"Notice that in each case the entire fractal can be recovered from a single point.\" Goldman\n",
174       "    # But for this I need *two* points :S\n",
175       "    \n",
176       "    a = asarray(x0) + s/3. # 1/3 from x0 to x1\n",
177       "    b = asarray(x0) + 2.*s/3. # 2/3 from x0 to x1\n",
178       "    c = asarray(x0) + 0.5*s + ((sum(s*s)**0.5)/3.)*normal # Form an equilateral triangle with a & b\n",
179       "    \n",
180       "    # Make first generation of points\n",
181       "    p = [x0, tuple(a), tuple(c), tuple(b), x1]\n",
182       "    \n",
183       "    if (n <= 1):\n",
184       "        return p\n",
185       "    \n",
186       "    result = []\n",
187       "    for i in xrange(len(p)-1):\n",
188       "        result +=  koch1(n-1, p[i], p[i+1])[:-1]\n",
189       "        \n",
190       "    return result + [p[-1]]\n",
191       "\n",
192       "def koch(n, p):\n",
193       "    \"\"\" Generate Koch Curves between every two points in p, including between the last and first \"\"\"\n",
194       "    result = []\n",
195       "    for i in xrange(len(p)-1):\n",
196       "        result += koch1(n, p[i], p[i+1])[:-1]\n",
197       "    return result + koch1(n, p[-1], p[0])"
198      ],
199      "language": "python",
200      "metadata": {},
201      "outputs": [],
202      "prompt_number": 351
203     },
204     {
205      "cell_type": "code",
206      "collapsed": false,
207      "input": [
208       "# Plot some iterations of it.\n",
209       "for n in xrange(5):\n",
210       "    points = koch(n, [(0,0),(0.5, 0.75), (1,0)])\n",
211       "    x = [p[0] for p in points]\n",
212       "    y = [p[1] for p in points]\n",
213       "    plot(x, y, ',-')\n",
214       "title(\"Koch Snowflake (first 5 iterations)\")"
215      ],
216      "language": "python",
217      "metadata": {},
218      "outputs": [
219       {
220        "metadata": {},
221        "output_type": "pyout",
222        "prompt_number": 434,
223        "text": [
224         "<matplotlib.text.Text at 0x17e28a50>"
225        ]
226       },
227       {
228        "metadata": {},
229        "output_type": "display_data",
230        "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEICAYAAABYoZ8gAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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LFcbPfYLo6PPC5ix8TWOLdj4Taxmc0i8cCZi9K9s2qjkF7wFL/vPXWjXK03ZrNFhPx7nPB9ZoSo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\nAJ6DXIkfG4+p1NTE0UvthUz80mWhKionZp/AsY8jlcty+eQbR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231        "text": [
232         "<matplotlib.figure.Figure at 0x110e3310>"
233        ]
234       }
235      ],
236      "prompt_number": 434
237     },
238     {
239      "cell_type": "code",
240      "collapsed": false,
241      "input": [
242       "# Plot performance\n",
243       "# Python doesn't have an actual (good) profiler because apparently we don't care about efficiency :P\n",
244       "# (It has profilers but they all just print to stdout and don't actually return values)\n",
245       "from time import time\n",
246       "\n",
247       "nAverages = 5\n",
248       "nMax = 10\n",
249       "\n",
250       "costs = []\n",
251       "stddevs = []\n",
252       "for n in xrange(nMax):\n",
253       "    cost = []\n",
254       "    for i in xrange(nAverages):\n",
255       "        t0 = time()\n",
256       "        koch(n, [(0,0),(0.5, 0.75), (1,0)])\n",
257       "        cost += [time() - t0]\n",
258       "    costs += [mean(cost)]\n",
259       "    stddevs += [var(cost)**0.5]\n",
260       "    \n",
261       "figure()\n",
262       "errorbar(range(nMax), costs, xerr=0, yerr=stddevs)\n",
263       "title(\"Avg Time (s) vs n\")\n",
264       "\n"
265      ],
266      "language": "python",
267      "metadata": {},
268      "outputs": [
269       {
270        "metadata": {},
271        "output_type": "pyout",
272        "prompt_number": 432,
273        "text": [
274         "<matplotlib.text.Text at 0x10cc01d0>"
275        ]
276       },
277       {
278        "metadata": {},
279        "output_type": "display_data",
280 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281        "text": [
282         "<matplotlib.figure.Figure at 0xd431a50>"
283        ]
284       }
285      ],
286      "prompt_number": 432
287     },
288     {
289      "cell_type": "markdown",
290      "metadata": {},
291      "source": [
292       "So I worked it out, but I didn't work it out very efficiently..."
293      ]
294     },
295     {
296      "cell_type": "code",
297      "collapsed": false,
298      "input": [
299       "# It might be O(n^4) if I remember DSA right which I might not...\n",
300       "plot(range(nMax), costs)\n",
301       "fit = numpy.polynomial.polynomial.polyfit(range(nMax), costs, 4)\n",
302       "plot(linspace(0, nMax), map(lambda x : sum([fit[i]*x**i for i in xrange(len(fit))]), linspace(0, nMax)))"
303      ],
304      "language": "python",
305      "metadata": {},
306      "outputs": [
307       {
308        "metadata": {},
309        "output_type": "pyout",
310        "prompt_number": 447,
311        "text": [
312         "[<matplotlib.lines.Line2D at 0x12142190>]"
313        ]
314       },
315       {
316        "metadata": {},
317        "output_type": "display_data",
318        "png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAD9CAYAAABZVQdHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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+aiiVd3mjUMg5O1JymqKqKosogjlUcoqiriZO3J864WOXdpsjdhYDgnBc9uGxjOqzxCA1smF0MC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\nPkwhLyLiwxTyIiI+TCEvIuLD/j8UvjWJpFx3SAAAAABJRU5ErkJggg==\n",
319        "text": [
320         "<matplotlib.figure.Figure at 0x121a9310>"
321        ]
322       }
323      ],
324      "prompt_number": 447
325     },
326     {
327      "cell_type": "code",
328      "collapsed": false,
329      "input": [],
330      "language": "python",
331      "metadata": {},
332      "outputs": []
333     }
334    ],
335    "metadata": {}
336   }
337  ]
338 }

UCC git Repository :: git.ucc.asn.au