Mandelbrot Set with TensorFlow.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Calculate Mandelbrot Fractal using Tensorflow\n",
    "=======================\n",
    "\n",
    "Taken from [here](https://www.tensorflow.org/tutorials/mandelbrot)\n",
    "\n",
    "(Need TensorFlow, numpy and PIL (Python Imaging Library) to be installed in environment)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "ename": "ImportError",
     "evalue": "Traceback (most recent call last):\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow_internal.py\", line 18, in swig_import_helper\n    return importlib.import_module(mname)\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\__init__.py\", line 126, in import_module\n    return _bootstrap._gcd_import(name[level:], package, level)\n  File \"<frozen importlib._bootstrap>\", line 986, in _gcd_import\n  File \"<frozen importlib._bootstrap>\", line 969, in _find_and_load\n  File \"<frozen importlib._bootstrap>\", line 958, in _find_and_load_unlocked\n  File \"<frozen importlib._bootstrap>\", line 666, in _load_unlocked\n  File \"<frozen importlib._bootstrap>\", line 577, in module_from_spec\n  File \"<frozen importlib._bootstrap_external>\", line 919, in create_module\n  File \"<frozen importlib._bootstrap>\", line 222, in _call_with_frames_removed\nImportError: DLL load failed: No se puede encontrar el módulo especificado.\n\nDuring handling of the above exception, another exception occurred:\n\nTraceback (most recent call last):\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow.py\", line 41, in <module>\n    from tensorflow.python.pywrap_tensorflow_internal import *\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow_internal.py\", line 21, in <module>\n    _pywrap_tensorflow_internal = swig_import_helper()\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow_internal.py\", line 20, in swig_import_helper\n    return importlib.import_module('_pywrap_tensorflow_internal')\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\__init__.py\", line 126, in import_module\n    return _bootstrap._gcd_import(name[level:], package, level)\nImportError: No module named '_pywrap_tensorflow_internal'\n\n\nFailed to load the native TensorFlow runtime.\n\nSee https://www.tensorflow.org/install/install_sources#common_installation_problems\n\nfor some common reasons and solutions.  Include the entire stack trace\nabove this error message when asking for help.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow_internal.py\u001b[0m in \u001b[0;36mswig_import_helper\u001b[1;34m()\u001b[0m\n\u001b[0;32m     17\u001b[0m         \u001b[1;32mtry\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 18\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mimportlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mimport_module\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmname\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     19\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\__init__.py\u001b[0m in \u001b[0;36mimport_module\u001b[1;34m(name, package)\u001b[0m\n\u001b[0;32m    125\u001b[0m             \u001b[0mlevel\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 126\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0m_bootstrap\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_gcd_import\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mlevel\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpackage\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlevel\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    127\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\_bootstrap.py\u001b[0m in \u001b[0;36m_gcd_import\u001b[1;34m(name, package, level)\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\_bootstrap.py\u001b[0m in \u001b[0;36m_find_and_load\u001b[1;34m(name, import_)\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\_bootstrap.py\u001b[0m in \u001b[0;36m_find_and_load_unlocked\u001b[1;34m(name, import_)\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\_bootstrap.py\u001b[0m in \u001b[0;36m_load_unlocked\u001b[1;34m(spec)\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\_bootstrap.py\u001b[0m in \u001b[0;36mmodule_from_spec\u001b[1;34m(spec)\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\_bootstrap_external.py\u001b[0m in \u001b[0;36mcreate_module\u001b[1;34m(self, spec)\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\_bootstrap.py\u001b[0m in \u001b[0;36m_call_with_frames_removed\u001b[1;34m(f, *args, **kwds)\u001b[0m\n",
      "\u001b[1;31mImportError\u001b[0m: DLL load failed: No se puede encontrar el módulo especificado.",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     40\u001b[0m     \u001b[0msys\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msetdlopenflags\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_default_dlopen_flags\u001b[0m \u001b[1;33m|\u001b[0m \u001b[0mctypes\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mRTLD_GLOBAL\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 41\u001b[1;33m   \u001b[1;32mfrom\u001b[0m \u001b[0mtensorflow\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpython\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpywrap_tensorflow_internal\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     42\u001b[0m   \u001b[1;32mfrom\u001b[0m \u001b[0mtensorflow\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpython\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpywrap_tensorflow_internal\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0m__version__\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow_internal.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     20\u001b[0m             \u001b[1;32mreturn\u001b[0m \u001b[0mimportlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mimport_module\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'_pywrap_tensorflow_internal'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 21\u001b[1;33m     \u001b[0m_pywrap_tensorflow_internal\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mswig_import_helper\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     22\u001b[0m     \u001b[1;32mdel\u001b[0m \u001b[0mswig_import_helper\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow_internal.py\u001b[0m in \u001b[0;36mswig_import_helper\u001b[1;34m()\u001b[0m\n\u001b[0;32m     19\u001b[0m         \u001b[1;32mexcept\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 20\u001b[1;33m             \u001b[1;32mreturn\u001b[0m \u001b[0mimportlib\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mimport_module\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m'_pywrap_tensorflow_internal'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     21\u001b[0m     \u001b[0m_pywrap_tensorflow_internal\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mswig_import_helper\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\__init__.py\u001b[0m in \u001b[0;36mimport_module\u001b[1;34m(name, package)\u001b[0m\n\u001b[0;32m    125\u001b[0m             \u001b[0mlevel\u001b[0m \u001b[1;33m+=\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 126\u001b[1;33m     \u001b[1;32mreturn\u001b[0m \u001b[0m_bootstrap\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_gcd_import\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mname\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mlevel\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpackage\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlevel\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    127\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mImportError\u001b[0m: No module named '_pywrap_tensorflow_internal'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[1;31mImportError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-2-783ff6529107>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# Import libraries for simulation\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[1;32mimport\u001b[0m \u001b[0mtensorflow\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mtf\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m \u001b[1;31m# Imports for visualization\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\__init__.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     22\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     23\u001b[0m \u001b[1;31m# pylint: disable=wildcard-import\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 24\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[0mtensorflow\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpython\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[1;33m*\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     25\u001b[0m \u001b[1;31m# pylint: enable=wildcard-import\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     26\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\__init__.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     49\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     50\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 51\u001b[1;33m \u001b[1;32mfrom\u001b[0m \u001b[0mtensorflow\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpython\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mpywrap_tensorflow\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     52\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     53\u001b[0m \u001b[1;31m# Protocol buffers\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m     50\u001b[0m \u001b[1;32mfor\u001b[0m \u001b[0msome\u001b[0m \u001b[0mcommon\u001b[0m \u001b[0mreasons\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0msolutions\u001b[0m\u001b[1;33m.\u001b[0m  \u001b[0mInclude\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mentire\u001b[0m \u001b[0mstack\u001b[0m \u001b[0mtrace\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     51\u001b[0m above this error message when asking for help.\"\"\" % traceback.format_exc()\n\u001b[1;32m---> 52\u001b[1;33m   \u001b[1;32mraise\u001b[0m \u001b[0mImportError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     53\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     54\u001b[0m \u001b[1;31m# pylint: enable=wildcard-import,g-import-not-at-top,unused-import,line-too-long\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mImportError\u001b[0m: Traceback (most recent call last):\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow_internal.py\", line 18, in swig_import_helper\n    return importlib.import_module(mname)\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\__init__.py\", line 126, in import_module\n    return _bootstrap._gcd_import(name[level:], package, level)\n  File \"<frozen importlib._bootstrap>\", line 986, in _gcd_import\n  File \"<frozen importlib._bootstrap>\", line 969, in _find_and_load\n  File \"<frozen importlib._bootstrap>\", line 958, in _find_and_load_unlocked\n  File \"<frozen importlib._bootstrap>\", line 666, in _load_unlocked\n  File \"<frozen importlib._bootstrap>\", line 577, in module_from_spec\n  File \"<frozen importlib._bootstrap_external>\", line 919, in create_module\n  File \"<frozen importlib._bootstrap>\", line 222, in _call_with_frames_removed\nImportError: DLL load failed: No se puede encontrar el módulo especificado.\n\nDuring handling of the above exception, another exception occurred:\n\nTraceback (most recent call last):\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow.py\", line 41, in <module>\n    from tensorflow.python.pywrap_tensorflow_internal import *\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow_internal.py\", line 21, in <module>\n    _pywrap_tensorflow_internal = swig_import_helper()\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\site-packages\\tensorflow\\python\\pywrap_tensorflow_internal.py\", line 20, in swig_import_helper\n    return importlib.import_module('_pywrap_tensorflow_internal')\n  File \"C:\\Software\\Anaconda\\envs\\tensorflow_gpu\\lib\\importlib\\__init__.py\", line 126, in import_module\n    return _bootstrap._gcd_import(name[level:], package, level)\nImportError: No module named '_pywrap_tensorflow_internal'\n\n\nFailed to load the native TensorFlow runtime.\n\nSee https://www.tensorflow.org/install/install_sources#common_installation_problems\n\nfor some common reasons and solutions.  Include the entire stack trace\nabove this error message when asking for help."
     ]
    }
   ],
   "source": [
    "# Import libraries for simulation\n",
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "\n",
    "# Imports for visualization\n",
    "import PIL.Image\n",
    "from io import BytesIO\n",
    "from IPython.display import Image, display"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define a function to actually display the image once we have iteration counts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def DisplayFractal(a, fmt='jpeg'):\n",
    "  \"\"\"Display an array of iteration counts as a\n",
    "     colorful picture of a fractal.\"\"\"\n",
    "  a_cyclic = (6.28*a/20.0).reshape(list(a.shape)+[1])\n",
    "  img = np.concatenate([10+20*np.cos(a_cyclic),\n",
    "                        30+50*np.sin(a_cyclic),\n",
    "                        155-80*np.cos(a_cyclic)], 2)\n",
    "  img[a==a.max()] = 0\n",
    "  a = img\n",
    "  a = np.uint8(np.clip(a, 0, 255))\n",
    "  f = BytesIO()\n",
    "  PIL.Image.fromarray(a).save(f, fmt)\n",
    "  display(Image(data=f.getvalue()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Session and variable initialization..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sess = tf.InteractiveSession()\n",
    "\n",
    "# Use NumPy to create a 2D array of complex numbers\n",
    "Y, X = np.mgrid[-1.4:1.4:0.005, -2.5:1:0.005]\n",
    "Z = X+1j*Y\n",
    "\n",
    "# These are our variables for the Tensorflow calculation\n",
    "xs = tf.constant(Z.astype(np.complex64))\n",
    "zs = tf.Variable(xs)\n",
    "ns = tf.Variable(tf.zeros_like(xs, tf.float32))\n",
    "\n",
    "tf.global_variables_initializer().run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mandelbrot recurrence formula: \n",
    "$$ z^2 + x \\to z $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Compute the new values of z: z^2 + x\n",
    "zs_ = zs*zs + xs\n",
    "\n",
    "# Have we diverged with this new value?\n",
    "not_diverged = tf.abs(zs_) < 4\n",
    "\n",
    "# Operation to update the zs and the iteration count.\n",
    "#\n",
    "# Note: We keep computing zs after they diverge! This\n",
    "#       is very wasteful! There are better, if a little\n",
    "#       less simple, ways to do this.\n",
    "#\n",
    "step = tf.group(zs.assign(zs_), ns.assign_add(tf.cast(not_diverged, tf.float32)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(200): step.run()\n",
    "\n",
    "DisplayFractal(ns.eval())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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