{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Basic Fractals Stuff" ] }, { "cell_type": "raw", "metadata": {}, "source": [ "Main reference:\n", "The Fractal Nature of Bezier Curves, Ron Goldman, Year?\n", "\n", "Also, wikipedia." ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Definitions" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fractals are *attractors* Fixed points of *iterated function systems*. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "An iterated function system: $W = \\left\\{w_1, ... w_n\\right\\}$ (collection of *maps* w_i)" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Stierpinski Triangle Generation" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import random" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 192 }, { "cell_type": "code", "collapsed": false, "input": [ "def stierpinski(n, x0 = (0,0)):\n", " \"\"\" Generates the Stierpinski Triangles using Iterated Function System \"\"\"\n", " # Define the maps in the iterated function system W\n", " W = [lambda p : (0.5*p[0], 0.5*p[1])] # scale\n", " W += [lambda p : (0.5*p[0]+0.25, 0.5*p[1] + 0.25*sqrt(3))] # scale & shift up&right\n", " W += [lambda p : (0.5*p[0]+0.5, 0.5*p[1])] # scale & shift right\n", " x = [x0]\n", " # Repeatedly randomly select one of the maps in W\n", " # As the number of iterations approaches infinity this becomes equivelant to the definition\n", " # (I think. I mean, it seems to work)\n", " for i in xrange(n):\n", " x.append(random.choice(W)(x[i]))\n", " return x\n", " " ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 193 }, { "cell_type": "code", "collapsed": false, "input": [ "points = stierpinski(10000, (0.5, 0.5))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 194 }, { "cell_type": "code", "collapsed": false, "input": [ "# Silly matplotlib needs x and y as seperate lists\n", "x = [p[0] for p in points]\n", "y = [p[1] for p in points]" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 195 }, { "cell_type": "code", "collapsed": false, "input": [ "scatter(x, y, marker=',', s = 1e-3)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 196, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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LFi2itLQUgJSUFDo7O1EoFGRlZbFjxw7S0tIAyMvLY926dQQHB7N06VKsra05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"text": [ "" ] } ], "prompt_number": 196 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Koch Snowflake Generation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I worked this one out myself. You might say I'm a special *snowflake*." ] }, { "cell_type": "code", "collapsed": false, "input": [ "def koch1(n, x0 = (0,0), x1 = (1,0)):\n", " \"\"\" Recursively generates a Koch Curve between two points \"\"\"\n", " s = asarray([x1[0] - x0[0], x1[1] - x0[1]]) # Get displacement from x0 to x1\n", " # Calculate normal vector\n", " normal = asarray([-s[1], s[0]])\n", " normal = normal / sum(normal*normal)**0.5\n", " # Calculate the three points \n", " # (I *think* that in the definition these are the maps that form the iterated function system)\n", " a = asarray(x0) + s/3. # 1/3 from x0 to x1\n", " b = asarray(x0) + 2.*s/3. # 2/3 from x0 to x1\n", " c = asarray(x0) + 0.5*s + ((sum(s*s)**0.5)/3.)*normal # Form an equilateral triangle with a & b\n", " \n", " # Make first generation of points\n", " p = [x0, tuple(a), tuple(c), tuple(b), x1]\n", " \n", " if (n <= 1):\n", " return p\n", " \n", " result = []\n", " for i in xrange(len(p)-1):\n", " result += koch1(n-1, p[i], p[i+1])[:-1]\n", " \n", " return result + [p[-1]]\n", "\n", "def koch(n, p):\n", " \"\"\" Generate Koch Curves between every two points in p, including between the last and first \"\"\"\n", " result = []\n", " for i in xrange(len(p)-1):\n", " result += koch1(n, p[i], p[i+1])[:-1]\n", " return result + koch1(n, p[-1], p[0])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 351 }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot some iterations of it.\n", "for n in xrange(5):\n", " points = koch(n, [(0,0),(0.5, 0.75), (1,0)])\n", " x = [p[0] for p in points]\n", " y = [p[1] for p in points]\n", " plot(x, y, ',-')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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B5ERwLbV29UQfduVo93zyIssZ8UMkaS+XEdYrkMoiB8xP5jSsLhXRdI7ygvxa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\n+yzZf6dAF29McccDJHoo2CcIhAI6cygt1WPSRhcZl+pH3tyVmkxmRjE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"text": [ "" ] } ], "prompt_number": 373 }, { "cell_type": "code", "collapsed": false, "input": [ "# Plot performance\n", "# Python doesn't have an actual (good) profiler because apparently we don't care about efficiency :P\n", "# (It has profilers but they all just print to stdout and don't actually return values)\n", "from time import time\n", "\n", "nAverages = 5\n", "nMax = 10\n", "\n", "costs = []\n", "stddevs = []\n", "for n in xrange(nMax):\n", " cost = []\n", " for i in xrange(nAverages):\n", " t0 = time()\n", " koch(n, [(0,0),(0.5, 0.75), (1,0)])\n", " cost += [time() - t0]\n", " costs += [mean(cost)]\n", " stddevs += [var(cost)**0.5]\n", " \n", "figure()\n", "errorbar(range(nMax), costs, xerr=0, yerr=stddevs)\n", "title(\"Avg Time (s) vs n\")\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 432, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 432 }, { "cell_type": "markdown", "metadata": {}, "source": [ "So I worked it out, but I didn't work it out very efficiently.\n", "It appears to be $O(n^4)$ :S" ] }, { "cell_type": "code", "collapsed": false, "input": [ "plot(range(nMax), costs)\n", "for deg in xrange(4,5):\n", " fit = numpy.polynomial.polynomial.polyfit(range(nMax), costs, deg)\n", " plot(linspace(0, nMax), map(lambda x : sum([fit[i]*x**i for i in xrange(len(fit))]), linspace(0, nMax)))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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