Implementation notebook dx2028 v0.1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Magnet Set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def magnetSet(nx=1024, ny=728, N=100, z_max=30, d_min=0.01):\n",
    "\n",
    "    x = np.linspace(0.5, 1.25, nx)\n",
    "    y = np.linspace(-0.2, 0.2, ny)\n",
    "    X, Y = np.meshgrid(x, y)\n",
    "    C = X + 1j * Y\n",
    "\n",
    "    nrows, ncols = C.shape\n",
    "    results = np.zeros_like(X)\n",
    "    \n",
    "    for idx in range(nrows):\n",
    "        for jdx in range(ncols):\n",
    "            z = 0 + 0j\n",
    "            for n in range(N):\n",
    "                z_old = z\n",
    "                z = np.sqrt((z ** 2 + C[idx, jdx] - 1) / (2 * z + C[idx, jdx] - 2) )\n",
    "                if abs(z) > z_max or abs(z-z_old) < d_min:\n",
    "                    results[idx, jdx] = n\n",
    "                    break\n",
    "\n",
    "    return X, Y, results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y, fractalSet = magnetSet(N=20, d_min=0.000001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x1d985b2e6a0>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16, 8))\n",
    "ax = fig.gca()\n",
    "ax.set_aspect('equal')\n",
    "ax.pcolor(X, Y, fractalSet, shading='auto')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-6-d690960f0c8e>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mget_ipython\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrun_line_magic\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'timeit'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'X, Y, fractalSet = magnetSet(N=20, d_min=0.000001)'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\IPython\\core\\interactiveshell.py\u001b[0m in \u001b[0;36mrun_line_magic\u001b[1;34m(self, magic_name, line, _stack_depth)\u001b[0m\n\u001b[0;32m   2342\u001b[0m                 \u001b[0mkwargs\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'local_ns'\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mget_local_scope\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mstack_depth\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2343\u001b[0m             \u001b[1;32mwith\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mbuiltin_trap\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 2344\u001b[1;33m                 \u001b[0mresult\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfn\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   2345\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mresult\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   2346\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\decorator.py\u001b[0m in \u001b[0;36mfun\u001b[1;34m(*args, **kw)\u001b[0m\n\u001b[0;32m    229\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mkwsyntax\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    230\u001b[0m                 \u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkw\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfix\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkw\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0msig\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 231\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mcaller\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mfunc\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mextras\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkw\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    232\u001b[0m     \u001b[0mfun\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    233\u001b[0m     \u001b[0mfun\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__doc__\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfunc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__doc__\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\IPython\\core\\magic.py\u001b[0m in \u001b[0;36m<lambda>\u001b[1;34m(f, *a, **k)\u001b[0m\n\u001b[0;32m    185\u001b[0m     \u001b[1;31m# but it's overkill for just that one bit of state.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    186\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0mmagic_deco\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 187\u001b[1;33m         \u001b[0mcall\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;32mlambda\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m*\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mk\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    188\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    189\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mcallable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0marg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\IPython\\core\\magics\\execution.py\u001b[0m in \u001b[0;36mtimeit\u001b[1;34m(self, line, cell, local_ns)\u001b[0m\n\u001b[0;32m   1171\u001b[0m                     \u001b[1;32mbreak\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1172\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1173\u001b[1;33m         \u001b[0mall_runs\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtimer\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrepeat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrepeat\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mnumber\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1174\u001b[0m         \u001b[0mbest\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mall_runs\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m/\u001b[0m \u001b[0mnumber\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1175\u001b[0m         \u001b[0mworst\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mall_runs\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m/\u001b[0m \u001b[0mnumber\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\timeit.py\u001b[0m in \u001b[0;36mrepeat\u001b[1;34m(self, repeat, number)\u001b[0m\n\u001b[0;32m    203\u001b[0m         \u001b[0mr\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    204\u001b[0m         \u001b[1;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[1;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mrepeat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 205\u001b[1;33m             \u001b[0mt\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtimeit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnumber\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    206\u001b[0m             \u001b[0mr\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mt\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    207\u001b[0m         \u001b[1;32mreturn\u001b[0m \u001b[0mr\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m~\\anaconda3\\lib\\site-packages\\IPython\\core\\magics\\execution.py\u001b[0m in \u001b[0;36mtimeit\u001b[1;34m(self, number)\u001b[0m\n\u001b[0;32m    167\u001b[0m         \u001b[0mgc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdisable\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    168\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 169\u001b[1;33m             \u001b[0mtiming\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0minner\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mit\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtimer\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    170\u001b[0m         \u001b[1;32mfinally\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    171\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mgcold\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<magic-timeit>\u001b[0m in \u001b[0;36minner\u001b[1;34m(_it, _timer)\u001b[0m\n",
      "\u001b[1;32m<ipython-input-5-30f2d9f8c802>\u001b[0m in \u001b[0;36mmagnetSet\u001b[1;34m(nx, ny, N, z_max, d_min)\u001b[0m\n\u001b[0;32m     15\u001b[0m                 \u001b[0mz_old\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mz\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     16\u001b[0m                 \u001b[0mz\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mz\u001b[0m \u001b[1;33m**\u001b[0m \u001b[1;36m2\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mC\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0midx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mjdx\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m/\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m2\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mz\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mC\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0midx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mjdx\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m-\u001b[0m \u001b[1;36m2\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 17\u001b[1;33m                 \u001b[1;32mif\u001b[0m \u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mz\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m>\u001b[0m \u001b[0mz_max\u001b[0m \u001b[1;32mor\u001b[0m \u001b[0mabs\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mz\u001b[0m\u001b[1;33m-\u001b[0m\u001b[0mz_old\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m<\u001b[0m \u001b[0md_min\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     18\u001b[0m                     \u001b[0mresults\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0midx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mjdx\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mn\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     19\u001b[0m                     \u001b[1;32mbreak\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "%timeit X, Y, fractalSet = magnetSet(N=20, d_min=0.000001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Fast magnet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def magnetSetFast(nx=1024, ny=728, N=100, z_max=30, d_min=0.01):\n",
    "\n",
    "    x = np.linspace(0.5, 1.25, nx)\n",
    "    y = np.linspace(-0.2, 0.2, ny)\n",
    "    X, Y = np.meshgrid(x, y)\n",
    "    C = X + 1j * Y\n",
    "\n",
    "    nrows, ncols = C.shape\n",
    "    results = np.zeros_like(X)\n",
    "    z0 = np.zeros_like(X)\n",
    "    z = z0 + 0j\n",
    "    keep = np.full(X.shape, True)\n",
    "    for n in range(N):\n",
    "        z_old = z\n",
    "        z = np.sqrt((z ** 2 + C - 1) / (2 * z + C - 2) )\n",
    "        mask = (abs(z) > z_max) | (abs(z-z_old) < d_min) & keep\n",
    "        results[mask] = n\n",
    "        keep[mask] = False\n",
    "\n",
    "    return X, Y, results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.54 s ± 80.9 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)\n"
     ]
    }
   ],
   "source": [
    "%timeit X, Y, fractalSet = magnetSetFast(N=20, d_min=0.000001)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nova set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def magnetSet(nx=1024, ny=728, N=100, z_max=30, d_min=0.01):\n",
    "\n",
    "    x = np.linspace(0.5, 1.25, nx)\n",
    "    y = np.linspace(-0.2, 0.2, ny)\n",
    "    X, Y = np.meshgrid(x, y)\n",
    "    C = X + 1j * Y\n",
    "\n",
    "    nrows, ncols = C.shape\n",
    "    results = np.zeros_like(X)\n",
    "    \n",
    "    for idx in range(nrows):\n",
    "        for jdx in range(ncols):\n",
    "            z = 1\n",
    "            for n in range(N):\n",
    "                z_old = z\n",
    "                z = z - (z**3 - 1) / (3*z**2) + C[idx, jdx]\n",
    "                if abs(z) > z_max or abs(z-z_old) < d_min:\n",
    "                    results[idx, jdx] = n\n",
    "                    break\n",
    "\n",
    "    return X, Y, results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y, fractalSet = magnetSet(N=20, d_min=0.000001)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PolyCollection at 0x1d98c239070>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(16, 8))\n",
    "ax = fig.gca()\n",
    "ax.set_aspect('equal')\n",
    "ax.pcolor(X, Y, fractalSet, shading='auto')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}