{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def distance(A, B):\n",
    "    '''Taxicab distance between two tuples'''\n",
    "    return abs(A[0]-B[0])+abs(A[1]-B[1])\n",
    "distance((0,0),(3,5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# http://www.ipythonblocks.org/\n",
    "from ipythonblocks import BlockGrid\n",
    "import math"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "adaYellow=(245,225,52)\n",
    "adaPurple=(149,96,159)\n",
    "adaGreen=(161,200,84)\n",
    "adaCoral=(236,98,113)\n",
    "adaBlue=(108,184,231)\n",
    "adaOrange=(246,131,82)\n",
    "\n",
    "adaBlack=(9,20,8)\n",
    "adaGrey=(134,136,140)\n",
    "adaLightGrey=(211,212,211)\n",
    "adaWhite=(255,255,255)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from ipywidgets import interact"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An interactive. For playing with the 'eccentricity' $e$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid = BlockGrid(31,31,block_size=5,fill=(255,255,255))\n",
    "# Directrix is col=0\n",
    "d = 0\n",
    "# Focus is at row 0, col 1\n",
    "F = (5,16)\n",
    "def draw(e):\n",
    "    for block in grid:\n",
    "        distance_from_edge = block.col\n",
    "        distance_from_focus = distance((block.col, block.row), F)\n",
    "        if distance_from_edge == round(e*distance_from_focus):\n",
    "            block.set_colors(*adaBlack)\n",
    "        else:\n",
    "            block.set_colors(*adaWhite)\n",
    "        if block.col == d:\n",
    "            block.set_colors(*adaPurple)\n",
    "        if (block.col, block.row) == F:\n",
    "            block.set_colors(*adaBlue)\n",
    "    return grid\n",
    "interact(draw, e=(0,3,0.1));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To save a bunch of images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "grid = BlockGrid(31,31,block_size=5,fill=(255,255,255))\n",
    "# Directrix is col=0\n",
    "d = 0\n",
    "# Focus is at row 0, col 1\n",
    "F = (5,16)\n",
    "for i in range(0,21,1):\n",
    "    e = i/10\n",
    "    for block in grid:\n",
    "        distance_from_edge = block.col\n",
    "        distance_from_focus = distance((block.col, block.row), F)\n",
    "        if distance_from_focus == round(e*distance_from_edge):\n",
    "            block.set_colors(*adaBlack)\n",
    "        else:\n",
    "            block.set_colors(*adaWhite)\n",
    "        if block.col == d:\n",
    "            block.set_colors(*adaPurple)\n",
    "        if (block.col, block.row) == F:\n",
    "            block.set_colors(*adaBlue)\n",
    "    grid.save_image(\"eccentricity_{}.png\".format(e))"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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