{
 "cells": [
  {
   "cell_type": "markdown",
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   "source": [
    "\\begin{equation}\n",
    "x_{n+1} = r(x_n)(1-x_n)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "# see https://youtu.be/ovJcsL7vyrk?t=322 for more context\n",
    "\n",
    "# The following program carries out the iterative calculation stated above,\n",
    "# sweeping across different values of r.\n",
    "# n == number of iterations (x-axis)\n",
    "from logistics_bifurcation import *\n",
    "for r in reversed_logspace(2.9,3.84,num=200):\n",
    "    fig, ax = plt.subplots()\n",
    "    scat = ax.scatter(np.arange(NUM_ITER), get_series(r), marker=\"+\")\n",
    "    ax.set_title(f\"{r=}\")\n",
    "    ax.set_xlabel(\"number of iterations\")\n",
    "    if np.isclose(r, 3.83, atol=1E-2):\n",
    "        ax.set_title(rf\"{r=},$\\approx$ period 3!\")\n",
    "    plt.show(block=False)\n",
    "    plt.close(fig)"
   ]
  }
 ],
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