{ "metadata": { "name": "", "signature": "sha256:75ff2eba72835d13c709eb98712eaa3c2fd13e188279ce15158eb38f6d91cbfc" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Fractal de Barnsley\n", "==================\n", "\u00c9 o conjunto produzido por um sistema de fun\u00e7\u00f5es interativos [IFS](http://en.wikipedia.org/wiki/Iterated_function_system). Neste caso o sistema tem quatro fun\u00e7\u00f5es afins,\n", "que s\u00e3o contra\u00e7\u00f5es. O algoritmo para o esbo\u00e7o da figura \u00e9 o *Jogo Aleat\u00f3rio*" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from pylab import random_integers\n", "from matplotlib.pyplot import plot\n", "\n", "def IFS(n,x):\n", " ''' Define o sistema de quatro tranformacoes de R2, n um inteiro entre 1 e 4\n", " e x um vetor de R2 '''\n", " if (n==1):\n", " return [0.85*x[0] +0.04*x[1] , -0.04*x[0] + 0.85*x[1] +1.6]\n", " elif (n==2):\n", " return [-0.15*x[0]+0.28*x[1], 0.26*x[0] + 0.24*x[1] + 0.44]\n", " elif (n==3):\n", " return [0.20*x[0] -0.26*x[1], 0.23*x[0]+0.22*x[1] + 1.6]\n", " else:\n", " return [0,0.16*x[1]]\n", " \n", "x0=[0,0]\n", "\n", "a=[]\n", "b=[] \n", "for j in range(200000) :\n", " x0=IFS(random_integers(1,4), x0)\n", " a.append(x0[0])\n", " b.append(x0[1])\n", " \n", "plot(a,b,'.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 1, "text": [ "[]" ] }, { "metadata": {}, 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MLld6VyiSZelI8iBdi7B4VwmnCz3qpEqiOaGLBPUjDE6oJdMmJoKLcNwzPLWf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\nNYXZtKlENft3G/wqrVSv23c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"text": [ "" ] } ], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Jogo do tri\u00e2ngulo\n", "Neste segundo exemplo escolhemos tr\u00eas pontos A, B e C, formando um tri\u00e2ngulo. Iniciamos com um ponto qualquer P, sorteamos um dos tr\u00eas\n", "pontos e marcamos o ponto no meio do segmento entre P e o ponto sorteado. Este ser\u00e1 o novo P, e repetimos o experimento." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from pylab import random_integers\n", "from matplotlib import *\n", "#Escolhemos (ou fixamos) tres pontos\n", "A=[-1,-1.]\n", "B=[0,2] \n", "C=[2,0]\n", "\n", "def Jogo(n,x):\n", " ''' Escolhe um ponto e anda ate a metade do caminho deste ponto'''\n", " if (n==1):\n", " return [0.5*x[0]+0.5*A[0], 0.5*x[1]+0.5*A[1]]\n", " elif (n==2):\n", " return [0.5*x[0] +0.5*B[0], 0.5*x[1] +0.5*B[1]]\n", " else:\n", " return [0.5*x[0] + 0.5*C[0], 0.5*x[1] + 0.5*C[1]]\n", "P=[0,0] \n", "a=[0]\n", "b=[0]\n", "for j in range(20000):\n", " P = Jogo(random_integers(1,3),P)\n", " a.append(P[0])\n", " b.append(P[1])\n", "plot(a,b,'.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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RpVqSTxg5Mhngxz8u3rzebRE2L8mEsRgVRVuwwJ82nY2NQF0dcPHFVCwwEqH9\nyBYO9NqQphxNr1ydMySkUvI2VBEy9lWmOhCVXgaAVauAp5923o5XwWixejU5gXVgGBSiqaPzlw6l\nC6Cqny+8UB7PHwv+ENDVZZ/IYhi0fOELwM9+Jre9Sok9ZtRxI6ydyjAUK5cciwFNTRRh8957JIB1\nKC6FdHVRFu3ChdRS9JpraL+62jwC9rMZw6Bnqa6Okh9lmDsXOHhQz3H5CQv+EOA0jT5wgMrIirS3\nQmIxysb8yU/KO/qAcY+qOaWYqVD0Aslv8qO7wc/AAGXP+l0Z1ulauenvC1D2fG8vvZzC/Oyx4C8x\nIm1fB/n2VaY68GKPLxT+fhQKLKShAfjsZ4H77w9WUOoyYdkxNAQ8/rh/2/cCC/4S43crRICSwg4f\nDq/2wejFi7CORIBrryVttb9fv1IyMgJcfz3Q0wPs2wdccUXwAt8iiJcaQOe2e3e4lC8W/CXGy83X\n3w/s3En21aNHndcP4w3I6EXXDLK9PddlTZX8EuCpFN2rYbn3dGj7hkHPnkzXr7ApX9x6sYQkEmrf\ni8dpSv6f/wmcOgWsWyf3vRMnKOSNS85WLq+/XvzvTU1kepiaImHlxJEj7oV+czPdm7Nn59ogWhHv\n774bHqEPqJV5aGykF1hNDfnPjh2j85Lhk0/IUdzcXL5VP1nj14CTZpZIAFdeSZEMV19ND9TLLwPP\nPnvuA+TWXBSNAp/7XHW2nKtknO4Dw6AWig88oL6PeDz3QjAM2mcyKR8zHxacZtq9vcB//zdFLcVi\nwLZtxc9PdYZVrMJokLCppwTYTTOj0VwImeyD5GVq395O32XhXxn4abOuqaH70k4AlhOiSJ729mCe\nvUiEXiqlgk09JcDOtjgzQ9rU4sVy03HAmz33yBF6mJPJ8p1+MoRsDwcnLC2+r4+EYFsb0NFB99mh\nQ+Uv9AFx+OaRI/KhsE49AESYJs2e0unyMb2y4PeAzAO6dSsJY6cSsDKa+sCA8zonTnDzlnLGTSer\nQlpbScCvWkXJR/v2Udz6tm3kjDx6tHIEPiD3zHR3k6lVVGK6q8verHbeefSzv59eonZMT+ee9aVL\nw/8CYMHvATdawtCQuLepSDPp6yNH3rFjcvt66y2afsbj8jXVmXDg5p6aM4eEUVsbJQYeO0YC/umn\nKeO0UgS8HbLa/OnT9AKwE8aia37oENnwL7tM3pwzOQn89m/LrVsq2MbvAVU7bGENHr8Tv1Tb6THB\nU19v3yv/gevCAAAdSklEQVS3tpY0zz17ShszHwZUnplYjMwxhYEQfvlTLGe53zV/2MZfJnR2UgiZ\npYF4sS/KMDREAiPs00/GXui3tZHA37KFtNDHH69eoa9qDpuepsJyN9xw9rb8YmYm11s4bH431vg9\noENTOP98+aJROnAq4sWUhkwGePRRcWXJlSuBhx/msXOqVCpDNApccAHNvoPCr/FjjT8gMhl7od/Q\nQDa+4WG5bXkV+qkUOfTq6+XWn5gAFi1i7T9s7N3rXE7Ych46OSsrmUzGXugPDNDsdu1a8m+JmJnx\nJvQjESpZUVtLz7sMW7fSsxo27b/UBNm0xhNOnXy6u03zoov0dB1qbDy7A1E6bZrr1ql1Qipc8lvj\nMaVj/XrTTCTcj185twtUpaPD/npEItSdy02LSpllyRLTbGujNpOJhGkODp79/Knsb3JS3zWBQgeu\nMKHvSvhIJKL3prJbNm40zeFhupGHh51bwqnuZ2CgPNvNVRIiYRakAAk7qi0V3S6trXRdZZ679evF\nfYdFS3OzcxtJGcCC3190axL5i13TaBl0vIxGRvy5ZowYHfdUX191vLxVBaxoicfpxSsr6Aupq/N+\nDE1N3l4AYMHvL140M8A0zzsv96ZPp6lxdEeH97e+0377+4O5ARn3OI1JLGaaCxbIjV8lz950KV3p\nNClYNTVyjdu9HlO+qVa0WGYqFcCC3z9UbrxFi0iTmDvXNIeG/HkonY5rfNy9prR6deUKkLDhJKSm\nptyNXSJRmS9vt0pXLEb3/cgICflCu7wORNq+NXam6e64VV7eYMHvHzI3Xl2dvQOoVMfV16emGc2e\nzcLfb2Rs1pOTauNXSbZ/kXKTb+ZsaSEhH9S5O41BTw/Not2OnWG4e3lDQfBzHL8kduGbySSVfa2v\n97+nqJvj0gXH/fuD360CAWD16soo120Xt28YwNgYcPvtwJ13Bnueqr2QZXHT6J3LMvuE00Naqnrc\niYS3rkqAXAPqeBx49dXKr/0SJLGYu8bfXvZT7n2a43HKurWjFCVJdI1ffT3w4Yfi/bzwwtm9kwvh\nBC6fcOrws2JF8N14WlrUhX5TE5XntQp7OXH6NKWdl1PZ2TCTyXgTGjU18utOT9PYlWvJjq4usdAH\nKGmrtzfY81MZv0iExm50lDT688+nhE8R09NUYG758vIcPxn8McR5xG3scFtbMM41t46uVKp4BJFK\nbDQnfnnDMNxd77o6sl0XS95zO3blFvrp5tzi8WACE2QDPVIpkgdtbcWfvZUr9Tx7ULDx6+BaAHsA\nvArgJpt1bs/+fxLAMpt1/B0tBbyEkPn5gDU3OzuHLIHv5Ohy2pbdwqGf6jgpDuPjFAk2OGiaa9fa\n30eqCU3pdLDnq4rqs9fW5t+zt369fd5MLEZROXPnyj0bs2apnV/hyw0lEPwGgNcAdAKIA9gNYHHB\nOkMARrOf+wBss9mWPyPlAa9x+4D+CAORoF61yl0Siugmllm8xB5XK6Lxc5PJ6TWuPRYjjTOs2r+O\n8/Pj3rSbrakoQioRP/mLpf2jBIL/agBP5v3+l9klnx8A+Ere73sAzCmyLf2j5BGvQt9aWlr03YQy\n+5OJBdaVEBOPh1d4hBGZayqjLMgoJTIvdb8EpFd0ZMQClBGv6/yc8mGamuSfBafZWm+vac6bJzd+\nUBD8Xp278wDk15d8K/s3p3Xme9yv79iFhn3mM7nPVls2J06cIAfbM894OybZXqwTE8DChWJn0N13\nF/97bS397OsjJ7ATp09TSGsk4txestqRHT8ZZ56okmdLCzk8TQlxYDl/w1bx8+OP7f9ndaSTYWqK\nzk+Hc9QpmOK99+hZcHrOW1rs+wnU1FC1z/fflwvndHJ82xFT+9qnyL5pCkONin7v1ltv/fRzOp1G\nOp1WOigd2MXo7t9PQm73bookcMOKFed233KDm4Ytx4/nmq/v2nX2PjMZe6FgPXDf+Q4drxuGhrhm\nvAg3zUMmJoDZs4uHYjq9QE6cyL3AZbHaE3q5P3URjYpfWv/1X1RL3w0TE/QsqIZ+yr60gdxzYxjA\nzp3nhmKK4v9PnQL+4A+c7pWx7FI6+nG2qedmnOvg/QGA6/J+D72pR9XhKbNEImqRB15NM/nTXbdR\nJW6XcnEeBomXAmP55Zf9LBRoLTpNk24J4vw2bnR/XLqePX8qjAZv448B2Ady7ibg7NztRxk4d/2+\n8Yo90E7oENaW7Tio8+Owzxy6rqeOgIMwj19QZc+7u/XZ40v17MViVGgOKE045xoAr4Cie27O/u33\ns4vF97L/nwRwhc12/LubXKBjkFtb5WvkyMT9i7Qgcu7Qz5oa5/3perBkzy8aray6MSrYjd+sWXSv\nxOO5cQzbEuTY6Zppt7WZZn293LpOypeTPGhsVGuio7oUa8YEcJE2T7idZt5xBwnbaJR+T6VyQtzt\nC8Qw7B8yUYSDFZLnd5OKdPrspjBuHtJotHojf0Tj0tSUM/v5OX7LltEYDAzkBIbbbQTR7Uv1/Pr6\nSNhbBdrcPsc9Pfb3p+h79fX+dPwCcqW4k0kqmCgq3w6w4PeE0zTaMEhDk6mhrzLYicS52wmq61D+\nOQIk2EWlpFW3X23tAmVmWHPm6Bm7ZJLuob4+06yttVckVAWVn3Z/mWPq6qKfAwPiznQqZtFk0jTX\nrPHeUtHr0trqvoQ7wILfE3aDEYu5GwyvN0y+cPTb5tnf775eudcpebVo/0G8tJcuFWf3FsPL/vxq\n9mK3v/PPp9mKrMLg9dlbuza3Lb/9KfX1JFdk26vaXzsW/MqIoi4iEXeDouOGscot6LrJ5s+nc4xE\nKGpDtfOXLi3IjXOtXNEpJOJxcrbOn6/eotM09dnRdb4AnF6QHR3y+5J59i64QO7e1Gm7b20l5Wpw\nkI5RZ2MmgAW/ErLCTCbNXfRgWdO4L3xBr1AotrS0UPehaPTsbkBecZqBGIYVaSC3VHLNH11jqTO6\nRmQG2bCB7hc3Ak/Hsbl5GYk0f9FzvHBhbmZ7/fX+P3+GkXtR+31/Ayz4lXBrE2xvV7N9W+nxutLR\nrWXJEtIiBgbEtl0dOB2LqrOr0oS/GxOdFY3V1ORfi07TdNasx8eDHzuV/dnF4Tt9r6XFNK+7Tr/5\ndNEiGre1a72bbVQAC37VC6e2FGofQTqDLM0syHA7L0lIKtezXBHdBzfemPu8fLl7+7wfx6RjUS2H\nrGoWLZZkFtSzZxikZOk22agCcOtF13jtYpXfmtCuRZwX6uqoWUMkAlx6KZVtePbZ0qTV+93mEaiM\nkg+i7kxLlwJbtgR/fuedJ67vo4P2dio1IHtuOtoXWvdLe7v3bnQiUimSFdu2lb6kRSEqHbjCROBv\nSp1akFeHrqVN19eTNuE20sZvvGr71vRaZpqdH1lRbshE8kQiwSe1WbkmQSyiuPh8nLbT0hLcMVtL\nfj+EMGjzMgBs6nGFna29qelse3kQD0opbIOyeH1B9vbmzu+ii+S+Yxjhrhdvhxv7cVDn52X86utJ\nqZmcpPGT/Z7IDyZzTJbZz69wZstU2tcXPiXLLWDB7/aCiZe1a/256az0/KDaNHrFjTM6mRTHJrt9\nkGOxYNrp6UBVwPr9AnAzfhs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