Creating Cellular Automatas with Mathematica

    I started my experimentation on Cellular Automatas in Mathematica, simply because I am very experienced with Mathematica and it is a very convenienty environment for me to work in.  In addition, I also found some good examples for Cellular Automatas written by Stephen Wolfram, so I was able to base much of my work around his code.
    The images of Cellular Automatas above were generated by my Mathematica code.  The interface to my code is rather simple.  You call a function display1DBW, with 3 parameters: first, the rule number; second, the width of the Cellular Automata; third, the amount of time you want the Cellular Automata to run for.  Here are some examples

    In addition, the function can take the option Last, which specifies how many of the last time frames you want visually rendered.  This can be very useful if you want to see the long term behavior of a Cellular Automata.  For example, suppose you wanted to see the 2000 time frame of rule 110.  That would give a large graphic and would also take a very long time to render.  But if you only render from time frame 1950 -> 2000, it becomes manageable.  For example:

    I also created a somewhat multi-dimensional version of Cellular Automatas.  Instead of treating each square as one point, I treated it as three -- one that holds the red value, one that holds the green value, and one that holds the blue value, for RGB.  The number of rules with this combination is prohibitively large, so I just chose a random rule (I was iinterested in this only for later experiments with sonification anyway.)  To see these Cellular Automata, call the function display1DRGB with 2 parameters.  The first paramter is the width, and the second is the amount of time the Cellular Automata should run for.  This function also accepts the Last option.

    For more details on my Mathematica code, please see my Mathematica code & examples.  (Note that if you are viewing this document as a Mathematica document, the above functions will not execture properly until you have run the code in my other Notebook.)