{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pynamical: quick overview\n",
    "\n",
    "**Citation info**: Boeing, G. 2016. \"[Visual Analysis of Nonlinear Dynamical Systems: Chaos, Fractals, Self-Similarity and the Limits of Prediction](http://geoffboeing.com/publications/nonlinear-chaos-fractals-prediction/).\" *Systems*, 4 (4), 37. doi:10.3390/systems4040037.\n",
    "\n",
    "Pynamical documentation: http://pynamical.readthedocs.org\n",
    "\n",
    "This notebook provides a quick overview of using pynamical."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pynamical import logistic_map, simulate, bifurcation_plot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simulate a model and visualize its bifurcation diagram:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pops = simulate(model=logistic_map, num_gens=100, rate_min=0, rate_max=4, num_rates=1000, num_discard=100)\n",
    "bifurcation_plot(pops)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zoom into a slice of this bifurcation diagram to see its [fractal structure](pynamical-demo-logistic-model.ipynb):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "pops = simulate(model=logistic_map, num_gens=100, rate_min=3.7, rate_max=3.9, num_rates=1000, num_discard=100)\n",
    "bifurcation_plot(pops, xmin=3.7, xmax=3.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot a two-dimensional [phase diagram](pynamical-demo-phase-diagrams.ipynb) of the logistic map:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pynamical import phase_diagram\n",
    "pops = simulate(model=logistic_map, num_gens=4000, rate_min=3.6, rate_max=4.0, num_rates=50, num_discard=100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "phase_diagram(pops, xmin=0.25, xmax=0.75, ymin=0.8, ymax=1.01, size=7, color='viridis')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or a three-dimensional phase diagram of the [cubic map](pynamical-demo-other-models.ipynb):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pynamical import cubic_map, phase_diagram_3d\n",
    "pops = simulate(model=cubic_map, num_gens=3000, rate_min=3.5, num_rates=30, num_discard=100)\n",
    "phase_diagram_3d(pops, xmin=-1, xmax=1, ymin=-1, ymax=1, zmin=-1, zmax=1, alpha=0.2, color='viridis', azim=330)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or animate them with [pynamical-demo-3d-animation.ipynb](pynamical-demo-3d-animation.ipynb):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import IPython.display as IPdisplay\n",
    "IPdisplay.Image(url='images/phase-animate/05-logistic-3d-phase-diagram-chaotic-regime.gif')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or create animated cobweb plots with [pynamical-demo-cobweb-plots.ipynb](pynamical-demo-cobweb-plots.ipynb):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "IPdisplay.Image(url='images/animated-logistic-cobweb.gif')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## For more info:\n",
    "  - [Read the journal article](http://geoffboeing.com/publications/nonlinear-chaos-fractals-prediction/)\n",
    "  - [Pynamical documentation](http://pynamical.readthedocs.org)\n",
    "  - [Chaos Theory and the Logistic Map](http://geoffboeing.com/2015/03/chaos-theory-logistic-map/)\n",
    "  - [Visualizing Chaos and Randomness with Phase Diagrams](http://geoffboeing.com/2015/04/visualizing-chaos-and-randomness/)\n",
    "  - [Animated 3D Plots in Python](http://geoffboeing.com/2015/04/animated-3d-plots-python/)"
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python (pynamical)",
   "language": "python",
   "name": "pynamical"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}