Cantor Function Approximation

Cantor.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "17941713",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "f57d5874",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_cantor(a=0, b=1, depth=1, h=0.5, base=3, max_depth=6, color='C0'):\n",
    "    \"\"\"\n",
    "    Parameters\n",
    "    ----------\n",
    "    (a, b): (int, int)\n",
    "        Interval that's being chunked out\n",
    "    depth: int \n",
    "        Depth of recursion (how many bits in we are)\n",
    "    h: float\n",
    "        Height at which we're drawing the interval\n",
    "    base: int\n",
    "        Base of domain, should be >= 3\n",
    "    max_depth: int\n",
    "        Maximum level of recursion\n",
    "    color: string\n",
    "        Color with which to draw point\n",
    "    \"\"\"\n",
    "    assert(int(base) == base and base >= 3)\n",
    "    c = a + (b-a)/base\n",
    "    d = b - (b-a)/base\n",
    "    dh = 2**(-depth-1)\n",
    "    plt.plot([c, d], [h, h], c=color, linewidth=1)\n",
    "    if depth < max_depth:\n",
    "        plot_cantor(a, c, depth+1, h-dh, base, max_depth, color)\n",
    "        plot_cantor(d, b, depth+1, h+dh, base, max_depth, color)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4275a9dd",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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67PmLwO1V9eKgeZt7XfZ8BfBu4IPAa4EfJHm4qp4cd3Fj0mXPHwZ+CHwA+APg35J8v6r+d8y1TUvv+TXLgb6IH07daT9J3gncAxysql9OqLZx6bLnFeD4RpjvBG5Icq6qvjmRCvvX9e/2c1X1PPB8kgeBa4B5DfQue74FuLMGA+a1JD8F3gH812RKnLje82uWRy6L+OHUW+45yTJwH/CJOe7Whm2556raW1V7qmoP8M/AX89xmEO3v9vfAv40yRVJfhu4DvjJhOvsU5c9P8XgfyQkeQvwduD0RKucrN7za2Y79FrAD6fuuOfPAm8CvrLRsZ6rOb5TXcc9N6XLnqvqJ0m+CzwCvATcU1UjL3+bBx1/z58H7k3yYwbjiNuram5vq5vk68D1wM4k68DngNfA+PLLt/5LUiNmeeQiSboEBrokNcJAl6RGGOiS1AgDXZIaYaBLUiMMdElqxP8BGdKr3GcYNnMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cantor(max_depth=10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "356637b8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZA74EvAEml1/e+i9JjdjJUy6SpMtgoEtSIwx0SWqEgS5JjTDQJakRBrokNcJAl6RG/D+LmtjJTI6o7AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_cantor(base=5, max_depth=10, color='C1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "97088b67",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}