Untitled.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(n):\n",
    "    if n >= 1000:\n",
    "        return n-3\n",
    "    else:\n",
    "        return f(f(n+5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "997"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f(84)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "N=1000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=np.linspace(0,N,N+1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y=np.array([f(x) for x in X])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x25c0c96a278>]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,Y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([997., 998., 997., ..., 997., 998., 997.])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
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}