fractal.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "n = 1024\n",
    "x0 = -1.5; x1 = 0.5\n",
    "y0 = -1; y1 = 1\n",
    "iter_number = 100\n",
    "image_size = 5\n",
    "\n",
    "x = numpy.linspace(x0,x1, n)\n",
    "y = numpy.linspace(y0,y1, n)\n",
    "reC = numpy.ones((n,1)).dot(x.reshape(1,n))\n",
    "imC = y.reshape(n,1).dot(numpy.ones((1,n)))\n",
    "C = reC + 1j * imC\n",
    "\n",
    "Z = numpy.zeros((n,n)).astype(\"complex\")\n",
    "for i in xrange(iter_number):\n",
    "    Z = Z**2 + C\n",
    "\n",
    "# img = 1.0/(1.0+numpy.sqrt(numpy.real(Z * numpy.conj(Z))))\n",
    "img = numpy.sqrt(numpy.real(Z * numpy.conj(Z))) < 1.0\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(image_size, image_size))\n",
    "ticks = numpy.linspace(0,n-1,11).astype(int)\n",
    "ax.set_xticks(ticks)\n",
    "ax.set_yticks(ticks)\n",
    "ax.set_xticklabels(map(lambda q: \"%.2g\" % q,x[ticks]))\n",
    "ax.set_yticklabels(map(lambda q: \"%.2gi\" % q,y[ticks[::-1]]))\n",
    "plt.imshow(img, cmap=\"bone\", aspect=(y1-y0)/(x1-x0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.3rc2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}