.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "example_gallery/patterns/hexagonal_automata.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_example_gallery_patterns_hexagonal_automata.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_example_gallery_patterns_hexagonal_automata.py:


.. _example hexagonal automata:

Cellular automata: Hexagonal automata
=====================================


This script is based on the example shown in :ref:`game_of_life.py <example game of life>`, but here a Hexagonal grid is used with slightly differnt rules.
Here the 6 neighbours around a cell are used. The rules are:

    1. If a cell is alive, it stays alive if two and only two of it's neighbours are alive.
    2. If a cell is dead, it becomes alive if one and only one of it's neighbours is alive.

This makes remarkably beautiful patterns on larger scales.
A cell in a line has two neighbours, so it remains alive.
In this configuration, straight lines are stable and corners are not.
Because of this, the pattern can only grow form corners and not from a line. This results in remarkable patterns when played out over longer sessions.

Also pretty cool, notice that on frame 1 we have a ring that forms a hexagon and again on frames 3, 7 and 15.
Do you see the pattern?

I encourage you to play with this, though matplotlib as a backend is not very performant when animating many shapes.

.. GENERATED FROM PYTHON SOURCE LINES 25-75



.. container:: sphx-glr-animation

    .. raw:: html

        
     <link rel="stylesheet"
     href="https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css">
     <script language="javascript">
       function isInternetExplorer() {
         ua = navigator.userAgent;
         /* MSIE used to detect old browsers and Trident used to newer ones*/
         return ua.indexOf("MSIE ") > -1 || ua.indexOf("Trident/") > -1;
       }

       /* Define the Animation class */
       function Animation(frames, img_id, slider_id, interval, loop_select_id){
         this.img_id = img_id;
         this.slider_id = slider_id;
         this.loop_select_id = loop_select_id;
         this.interval = interval;
         this.current_frame = 0;
         this.direction = 0;
         this.timer = null;
         this.frames = new Array(frames.length);

         for (var i=0; i<frames.length; i++)
         {
          this.frames[i] = new Image();
          this.frames[i].src = frames[i];
         }
         var slider = document.getElementById(this.slider_id);
         slider.max = this.frames.length - 1;
         if (isInternetExplorer()) {
             // switch from oninput to onchange because IE <= 11 does not conform
             // with W3C specification. It ignores oninput and onchange behaves
             // like oninput. In contrast, Microsoft Edge behaves correctly.
             slider.setAttribute('onchange', slider.getAttribute('oninput'));
             slider.setAttribute('oninput', null);
         }
         this.set_frame(this.current_frame);
       }

       Animation.prototype.get_loop_state = function(){
         var button_group = document[this.loop_select_id].state;
         for (var i = 0; i < button_group.length; i++) {
             var button = button_group[i];
             if (button.checked) {
                 return button.value;
             }
         }
         return undefined;
       }

       Animation.prototype.set_frame = function(frame){
         this.current_frame = frame;
         document.getElementById(this.img_id).src =
                 this.frames[this.current_frame].src;
         document.getElementById(this.slider_id).value = this.current_frame;
       }

       Animation.prototype.next_frame = function()
       {
         this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));
       }

       Animation.prototype.previous_frame = function()
       {
         this.set_frame(Math.max(0, this.current_frame - 1));
       }

       Animation.prototype.first_frame = function()
       {
         this.set_frame(0);
       }

       Animation.prototype.last_frame = function()
       {
         this.set_frame(this.frames.length - 1);
       }

       Animation.prototype.slower = function()
       {
         this.interval /= 0.7;
         if(this.direction > 0){this.play_animation();}
         else if(this.direction < 0){this.reverse_animation();}
       }

       Animation.prototype.faster = function()
       {
         this.interval *= 0.7;
         if(this.direction > 0){this.play_animation();}
         else if(this.direction < 0){this.reverse_animation();}
       }

       Animation.prototype.anim_step_forward = function()
       {
         this.current_frame += 1;
         if(this.current_frame < this.frames.length){
           this.set_frame(this.current_frame);
         }else{
           var loop_state = this.get_loop_state();
           if(loop_state == "loop"){
             this.first_frame();
           }else if(loop_state == "reflect"){
             this.last_frame();
             this.reverse_animation();
           }else{
             this.pause_animation();
             this.last_frame();
           }
         }
       }

       Animation.prototype.anim_step_reverse = function()
       {
         this.current_frame -= 1;
         if(this.current_frame >= 0){
           this.set_frame(this.current_frame);
         }else{
           var loop_state = this.get_loop_state();
           if(loop_state == "loop"){
             this.last_frame();
           }else if(loop_state == "reflect"){
             this.first_frame();
             this.play_animation();
           }else{
             this.pause_animation();
             this.first_frame();
           }
         }
       }

       Animation.prototype.pause_animation = function()
       {
         this.direction = 0;
         if (this.timer){
           clearInterval(this.timer);
           this.timer = null;
         }
       }

       Animation.prototype.play_animation = function()
       {
         this.pause_animation();
         this.direction = 1;
         var t = this;
         if (!this.timer) this.timer = setInterval(function() {
             t.anim_step_forward();
         }, this.interval);
       }

       Animation.prototype.reverse_animation = function()
       {
         this.pause_animation();
         this.direction = -1;
         var t = this;
         if (!this.timer) this.timer = setInterval(function() {
             t.anim_step_reverse();
         }, this.interval);
       }
     </script>

     <style>
     .animation {
         display: inline-block;
         text-align: center;
     }
     input[type=range].anim-slider {
         width: 374px;
         margin-left: auto;
         margin-right: auto;
     }
     .anim-buttons {
         margin: 8px 0px;
     }
     .anim-buttons button {
         padding: 0;
         width: 36px;
     }
     .anim-state label {
         margin-right: 8px;
     }
     .anim-state input {
         margin: 0;
         vertical-align: middle;
     }
     </style>

     <div class="animation">
       <img id="_anim_imgbde64e801ef14465b1462b688222fdb5">
       <div class="anim-controls">
         <input id="_anim_sliderbde64e801ef14465b1462b688222fdb5" type="range" class="anim-slider"
                name="points" min="0" max="1" step="1" value="0"
                oninput="animbde64e801ef14465b1462b688222fdb5.set_frame(parseInt(this.value));">
         <div class="anim-buttons">
           <button title="Decrease speed" aria-label="Decrease speed" onclick="animbde64e801ef14465b1462b688222fdb5.slower()">
               <i class="fa fa-minus"></i></button>
           <button title="First frame" aria-label="First frame" onclick="animbde64e801ef14465b1462b688222fdb5.first_frame()">
             <i class="fa fa-fast-backward"></i></button>
           <button title="Previous frame" aria-label="Previous frame" onclick="animbde64e801ef14465b1462b688222fdb5.previous_frame()">
               <i class="fa fa-step-backward"></i></button>
           <button title="Play backwards" aria-label="Play backwards" onclick="animbde64e801ef14465b1462b688222fdb5.reverse_animation()">
               <i class="fa fa-play fa-flip-horizontal"></i></button>
           <button title="Pause" aria-label="Pause" onclick="animbde64e801ef14465b1462b688222fdb5.pause_animation()">
               <i class="fa fa-pause"></i></button>
           <button title="Play" aria-label="Play" onclick="animbde64e801ef14465b1462b688222fdb5.play_animation()">
               <i class="fa fa-play"></i></button>
           <button title="Next frame" aria-label="Next frame" onclick="animbde64e801ef14465b1462b688222fdb5.next_frame()">
               <i class="fa fa-step-forward"></i></button>
           <button title="Last frame" aria-label="Last frame" onclick="animbde64e801ef14465b1462b688222fdb5.last_frame()">
               <i class="fa fa-fast-forward"></i></button>
           <button title="Increase speed" aria-label="Increase speed" onclick="animbde64e801ef14465b1462b688222fdb5.faster()">
               <i class="fa fa-plus"></i></button>
         </div>
         <form title="Repetition mode" aria-label="Repetition mode" action="#n" name="_anim_loop_selectbde64e801ef14465b1462b688222fdb5"
               class="anim-state">
           <input type="radio" name="state" value="once" id="_anim_radio1_bde64e801ef14465b1462b688222fdb5"
                  >
           <label for="_anim_radio1_bde64e801ef14465b1462b688222fdb5">Once</label>
           <input type="radio" name="state" value="loop" id="_anim_radio2_bde64e801ef14465b1462b688222fdb5"
                  checked>
           <label for="_anim_radio2_bde64e801ef14465b1462b688222fdb5">Loop</label>
           <input type="radio" name="state" value="reflect" id="_anim_radio3_bde64e801ef14465b1462b688222fdb5"
                  >
           <label for="_anim_radio3_bde64e801ef14465b1462b688222fdb5">Reflect</label>
         </form>
       </div>
     </div>


     <script language="javascript">
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       /* The IDs given should match those used in the template above. */
       (function() {
         var img_id = "_anim_imgbde64e801ef14465b1462b688222fdb5";
         var slider_id = "_anim_sliderbde64e801ef14465b1462b688222fdb5";
         var loop_select_id = "_anim_loop_selectbde64e801ef14465b1462b688222fdb5";
         var frames = new Array(16);
    
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         /* set a timeout to make sure all the above elements are created before
            the object is initialized. */
         setTimeout(function() {
             animbde64e801ef14465b1462b688222fdb5 = new Animation(frames, img_id, slider_id, 299.0,
                                      loop_select_id);
         }, 0);
       })()
     </script>






.. code-block:: Python



    import matplotlib.pyplot as plt
    import numpy
    from matplotlib.animation import FuncAnimation

    from gridkit import BoundedHexGrid
    from gridkit.doc_utils import plot_polygons

    # Initialize
    shape = (33, 33)
    data = numpy.zeros(shape)
    grid = BoundedHexGrid(data=data)
    geoms = grid.to_shapely()  # Used for plotting

    neighbours = grid.neighbours(grid.indices)
    neighbours = numpy.stack(grid.grid_id_to_numpy_id(neighbours.ravel())).T.reshape(
        (*shape, 6, 2)
    )

    # Animate
    fig, ax = plt.subplots()
    ax.set_aspect("equal")


    def init():
        data.ravel()[:] = 0
        data[16, 16] = 1


    def update_frame(frame):
        ax.clear()
        plot_polygons(geoms, colors=data.ravel(), cmap="gray_r", fill=True, ax=ax)
        ax.set_title(frame)
        ax.set_axis_off()
        nb = data[
            neighbours[1 : shape[0] - 1, 1 : shape[1] - 1, :, 0],
            neighbours[1 : shape[0] - 1, 1 : shape[1] - 1, :, 1],
        ]
        nr_nb_live = nb.sum(axis=-1)
        is_live = data[1 : shape[0] - 1, 1 : shape[1] - 1] == 1
        data[1 : shape[0] - 1, 1 : shape[1] - 1] = (
            0 + is_live * (nr_nb_live == 2) + ~is_live * (nr_nb_live == 1)
        )


    anim = FuncAnimation(
        fig, update_frame, init_func=init, frames=range(0, 16), repeat=True, interval=300
    )
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 5.350 seconds)


.. _sphx_glr_download_example_gallery_patterns_hexagonal_automata.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: hexagonal_automata.ipynb <hexagonal_automata.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: hexagonal_automata.py <hexagonal_automata.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: hexagonal_automata.zip <hexagonal_automata.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_