.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "example_gallery/patterns/game_of_life.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_game_of_life.py>`
        to download the full example code.

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

.. _sphx_glr_example_gallery_patterns_game_of_life.py:


.. _example game of life:

Cellular automata: Conway's game of life
========================================

Cellular automata are a small set of rules relating to cells on a grid that can create complex patterns when applied repeatedly.
There is a near infinite veriety of rules, but far and away the most well known set of rules is that of the so called Conway's game of life.
The setup is as follows:
 - The board is a 2d rectangular grid
 - The 8 neighbouring cells are considered, so this includes the diagonal neighbours
 - A cell has two possbile states: alive or dead

The rules as taken from https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life:

 1. Any live cell with fewer than two live neighbours dies, as if by underpopulation.
 2. Any live cell with two or three live neighbours lives on to the next generation.
 3. Any live cell with more than three live neighbours dies, as if by overpopulation.
 4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

Initial conditions
------------------

All cellular automata simulations are highly dependent on the initial conditions. We have to start with some dead cells and some live cells.
After all, according to these rules, if all cells are live, the cells will die in the next generation and if all cells are dead, they stey dead
for they would need three live neighbours to become a live cell. Therefore we need to start with something that is at least halfway interesting.
Let's set up a starting scenario. Feel free to download this script as a notebook and start fiddeling yourself.
The particular starting scenario I chose will replicate itself in three generations, which makes it convenient for creating
a looping animation.

.. GENERATED FROM PYTHON SOURCE LINES 31-70

.. code-block:: Python



    import matplotlib.pyplot as plt
    import numpy

    from gridkit import BoundedRectGrid
    from gridkit.doc_utils import plot_polygons

    # Initialize
    shape = (17, 17)
    data = numpy.zeros(shape)
    data[2, 4:7] = 1
    data[2, 10:13] = 1
    data[7, 4:7] = 1
    data[7, 10:13] = 1
    data[9, 4:7] = 1
    data[9, 10:13] = 1
    data[14, 4:7] = 1
    data[14, 10:13] = 1
    data[4:7, 2] = 1
    data[10:13, 2] = 1
    data[4:7, 7] = 1
    data[10:13, 7] = 1
    data[4:7, 9] = 1
    data[10:13, 9] = 1
    data[4:7, 14] = 1
    data[10:13, 14] = 1

    grid = BoundedRectGrid(data=data)

    neighbours = grid.neighbours(grid.indices, connect_corners=True)
    neighbours = neighbours = numpy.stack(
        grid.grid_id_to_numpy_id(neighbours.ravel())
    ).T.reshape((*shape, 8, 2))

    plt.imshow(grid, extent=grid.mpl_extent, cmap="gray_r")
    plt.title("Starting configuration")
    plt.show()




.. image-sg:: /example_gallery/patterns/images/sphx_glr_game_of_life_001.png
   :alt: Starting configuration
   :srcset: /example_gallery/patterns/images/sphx_glr_game_of_life_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 72-77

The naive method
----------------

We can convert the rules into code. The naive but intuitive way would look something like:


.. GENERATED FROM PYTHON SOURCE LINES 78-99

.. code-block:: Python


    data_second_gen = data.copy()
    for i in range(1, shape[0] - 1):
        for j in range(1, shape[1] - 1):
            nb = neighbours[i, j]
            nr_nb_live = data[nb.T[0], nb.T[1]].sum()
            if data[i, j] == 1:  # live cell
                if nr_nb_live == 2 or nr_nb_live == 3:
                    data_second_gen[i, j] = 1
                else:
                    data_second_gen[i, j] = 0
            else:  # Dead cell
                if nr_nb_live == 3:
                    data_second_gen[i, j] = 1
                else:
                    data_second_gen[i, j] = 0

    plt.imshow(data_second_gen, extent=grid.mpl_extent, cmap="gray_r")
    plt.title("Second generation")
    plt.show()




.. image-sg:: /example_gallery/patterns/images/sphx_glr_game_of_life_002.png
   :alt: Second generation
   :srcset: /example_gallery/patterns/images/sphx_glr_game_of_life_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 100-106

The performant method
---------------------

The unfortunate thing about this method is that it loops over all cells in python, which is slow.
As a first optimization we can get rid of the conditionals by adding all the contributions.
This can looks something like:

.. GENERATED FROM PYTHON SOURCE LINES 107-122

.. code-block:: Python

    data_third_gen = data.copy()
    for i in range(1, shape[0] - 1):
        for j in range(1, shape[1] - 1):
            nb = neighbours[i, j]
            nr_nb_live = data_second_gen[nb.T[0], nb.T[1]].sum()
            data_third_gen[i, j] = (
                0
                + (data_second_gen[i, j] == 1) * (nr_nb_live == 2 or nr_nb_live == 3)
                + (data_second_gen[i, j] != 1) * (nr_nb_live == 3)
            )

    plt.imshow(data_third_gen, extent=grid.mpl_extent, cmap="gray_r")
    plt.title("Third generation")
    plt.show()




.. image-sg:: /example_gallery/patterns/images/sphx_glr_game_of_life_003.png
   :alt: Third generation
   :srcset: /example_gallery/patterns/images/sphx_glr_game_of_life_003.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 123-126

With the code written like this, it is clear that we can also remove the double python loop by utilizing numpy slices:



.. GENERATED FROM PYTHON SOURCE LINES 127-142

.. code-block:: Python


    nb = data_third_gen[
        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_fourth_gen = (
        0 + is_live * ((nr_nb_live == 2) | (nr_nb_live == 3)) + ~is_live * (nr_nb_live == 3)
    )

    plt.imshow(data_fourth_gen, extent=grid.mpl_extent, cmap="gray_r")
    plt.title("Fourth generation")
    plt.show()




.. image-sg:: /example_gallery/patterns/images/sphx_glr_game_of_life_004.png
   :alt: Fourth generation
   :srcset: /example_gallery/patterns/images/sphx_glr_game_of_life_004.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 143-149

Note how this fourth generation looks the same as the starting conditions. The pattern loops every three frames/generations.

Written this way, you could even run this logic on a GPU using PyTorch or wgpu,
but since most time is now spent plotting using matplotlib you might also want to consider
a different visualization method (for example py-gfx) if a speedup for larger grids is desired.


.. GENERATED FROM PYTHON SOURCE LINES 152-158

Animation
---------

Since we are iterating over time, cellular automata lend itself well for an animation.
Given the logic above, the animation code can look like so:


.. GENERATED FROM PYTHON SOURCE LINES 159-187

.. code-block:: Python



    def update_frame(frame):
        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) | (nr_nb_live == 3))
            + ~is_live * (nr_nb_live == 3)
        )
        ax.clear()
        ax.imshow(data, extent=grid.mpl_extent, cmap="gray_r")
        ax.set_title(frame)
        ax.set_axis_off()


    # Create animation
    from matplotlib.animation import FuncAnimation

    fig, ax = plt.subplots()
    ax.set_aspect("equal")
    ax.imshow(data, extent=grid.mpl_extent, cmap="gray_r")
    anim = FuncAnimation(fig, update_frame, frames=range(0, 6), repeat=True, interval=300)
    plt.show()



.. 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 =
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         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()
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       }

       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()
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             this.reverse_animation();
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             this.pause_animation();
             this.last_frame();
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       Animation.prototype.anim_step_reverse = function()
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       Animation.prototype.pause_animation = function()
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       Animation.prototype.play_animation = function()
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         this.direction = -1;
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         if (!this.timer) this.timer = setInterval(function() {
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         }, 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_imgbd28614fa5ff4178a9e39ada637b8fe1">
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         /* set a timeout to make sure all the above elements are created before
            the object is initialized. */
         setTimeout(function() {
             animbd28614fa5ff4178a9e39ada637b8fe1 = new Animation(frames, img_id, slider_id, 299.0,
                                      loop_select_id);
         }, 0);
       })()
     </script>







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

   **Total running time of the script:** (0 minutes 0.830 seconds)


.. _sphx_glr_download_example_gallery_patterns_game_of_life.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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