Monte Carlo method

py.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 62,
   "source": [
    "from PIL import Image\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "def b(x, y):\n",
    "    return x**2+y**2 > 1 and y < x\n",
    "\n",
    "\n",
    "def g(x, y):\n",
    "    return x**2+y**2 < 1 and x**2+(y-0.5)**2 > 0.25 and x < y\n",
    "\n",
    "\n",
    "def r(x, y):\n",
    "    return (x-0.5)**2+y**2 < 0.25 and x < y\n",
    "\n",
    "\n",
    "im = Image.new('L', (300, 300))\n",
    "N = 10000000\n",
    "n = 0\n",
    "ratio = []\n",
    "for i in range(N):\n",
    "    x = np.random.rand()\n",
    "    y = np.random.rand()\n",
    "    f = b(x, y) or g(x, y) or r(x, y)\n",
    "    n += 1 if f else 0\n",
    "    im.putpixel((int(300*x), 299-int(300*y)), 255 if f else 128)\n",
    "    ratio.append(n/(i+1))\n",
    "im"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "image/png": "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",
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      "text/plain": [
       "<PIL.Image.Image image mode=L size=300x300>"
      ]
     },
     "metadata": {},
     "execution_count": 62
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "source": [
    "plt.ylim((0.245, 0.255))\n",
    "plt.axhline([.25])\n",
    "plt.grid()\n",
    "plt.plot(ratio)"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x297e23b20>]"
      ]
     },
     "metadata": {},
     "execution_count": 63
    },
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {}
    }
   ],
   "metadata": {}
  }
 ],
 "nbformat": 4,
 "nbformat_minor": 2,
 "metadata": {
  "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
  }
 }
}