Really Simple Cellular Automata Software

On the day that I was giving a lecture about cellular automata and excitable media, our department network went down. This left me in the situation of having to write some quick software for my notebook computer to display cellular automata and excitable media. Both programs are actually quite useful, though they obviously lack bells and whistles.

Feel free to modify the source code --- these programs are so simple that it's not hard to do if you are familiar with the C language.

Cellular automata

Get the C source code

This really simple program, called CA, implements a linear boolean cellular automata in which each element gets inputs from itself and its two neighbors. Periodic boundary conditions are used, meaning that the elements on the end of the array get their inputs from the element on the opposite end of the array. The program uses an ordinary terminal interface, and starts with random initial conditions. The syntax for running the program is
` CA ruleNumber NSteps Seed Width `

1. `ruleNumber` is a number that describes the boolean function of 3 inputs to be applied to the CA. This notation is explained in the textbook. It should be a number between 0 and 256. If you write this number in binary form, then the least significant bit gives the output from input 000, the next bit gives the output from input 001, and so on. To help the user, the bit pattern corresponding to the specified rule number is printed out on the first line of the output.
2. `NSteps` is the number of time steps to run the automata.
3. `Seed` sets the pseudorandom initial condition of the array. If you use the same seed in two runs, the initial conditions will be the same.
4. `Width` gives the number of elements in the CA. You will want to set this to be no larger than the character width of the terminal you are using, typically 80 characters. If you set it larger than the terminal width, the display will be quite ugly and hard to interpret.
An example:
` CA 90 20 343 40 ` gives
```
01011010
@  @@@@@@@@@@   @ @@ @@  @@@@     @@ @ @
@@@@        @@ @  @@ @@@@@  @@   @@@   @
@@      @@@  @@@@ @   @@@@@@ @@ @@ @@
@ @@@@    @@ @@@@  @  @ @@    @ @@ @@ @@
@ @  @@  @@@ @  @@@ @@  @@@  @  @@ @@ @
@@@@@@@ @  @@@ @ @@@@@ @@@ @@@@ @@
@@     @  @@@ @   @   @ @ @ @  @ @@@
@@@@   @ @@@ @  @ @ @ @       @@  @ @@
@@  @@ @  @ @  @@       @     @@@@@  @@@
@@@@@  @@   @@@@@     @ @   @@   @@@@
@@   @@@@@@ @@   @@   @   @ @@@@ @@  @@
@@@ @@    @ @@@ @@@@ @ @ @  @  @ @@@@@@
@ @ @@@  @  @ @ @  @      @@ @@  @    @
@ @@@ @@     @@ @    @@@ @@@@ @  @
@  @ @ @@@   @@@  @  @@ @ @  @  @@ @
@ @@    @ @@ @@ @@@ @@@@    @@ @@@@  @
@@  @@@  @  @@ @@ @ @ @  @@  @@@ @  @@@
@@@@@ @@@ @@@@ @@      @@@@@@@ @  @@@ @
@   @ @ @ @  @ @@@    @@     @  @@@ @
@ @       @@  @ @@  @@@@   @ @@@ @  @ @

```
while ``` CA 14 20 343 40 ``` give:
```
00001110
@  @@@@@@@@@@   @ @@ @@  @@@@     @@ @ @
@@           @@ @  @  @@       @@  @ @
@@           @@  @ @@ @@       @@  @@ @
@           @@  @@ @  @       @@  @@  @
@          @@  @@  @ @@      @@  @@  @@
@         @@  @@  @@ @      @@  @@  @@
@@        @@  @@  @@  @     @@  @@  @@
@        @@  @@  @@  @@    @@  @@  @@  @
@@  @@  @@  @@    @@  @@  @@  @@
@@  @@  @@  @@    @@  @@  @@  @@
@@  @@  @@  @@    @@  @@  @@  @@
@@  @@  @@  @@    @@  @@  @@  @@
@@  @@  @@  @@    @@  @@  @@  @@
@@  @@  @@  @@    @@  @@  @@  @@
@@  @@  @@  @@    @@  @@  @@  @@
@@  @@  @@  @@    @@  @@  @@  @@
@@  @@  @@  @@    @@  @@  @@  @@
@  @@  @@  @@    @@  @@  @@  @@        @
@@  @@  @@    @@  @@  @@  @@        @@
@@  @@  @@    @@  @@  @@  @@        @@
```

### Excitable Media

A second simple C program displays two types of Cellular Automata that are described in the book: the Game of Life, and a simple model of cardiac conduction.

Compiling this Program: The display of this program is oriented around the UNIX curses utilities. These utilities are also available on DOS and WINDOWS machines. When you compile this progam you will have to link to the curses library, using a command like:
` cc life.c -o life -lcurses -ltermcap `
Note: some Linux systems have a bug in their curses library that makes the display flash off. I have not had this problem on other systems or even on older Linux systems. The syntax is:
`life ruletype starttype seed sleep `
where

1. `ruletype` is either L or H, depending on whether you want to use Life, or the cardiac conduction model.

The rules of Life are these: Elements are either on or off. If an element is on, and 2 or 3 of its eight neighboring elements are on, then the element stays on. Otherwise it turns off. If the element is off, and 3 of its eight neighbors are on, the element turns on.

The cardiac conduction rules are described in the textbook. Here, the refractory time is 5 time steps.

2. `starttype` tells how to start the model. If this is 0, then a random initial condition is used. This is often quite interesting. If this is 1, then a highly ordered initial condition is used. For Life, this is just a cluster of 4 on elements. For the cardiac model, this is a line of excited elements on top of a line of refractory elements. This configuration produces a spiral wave. If the startcode is 2, then the cardiac conduction model will be started with a single point stimulus.

For the Life rule, you can specify a startype which is a pattern of the initial condition. For instance, using
` 11111-10001-10001-10001-11111 `
will put a 5 by 5 hollow square in the center of the field.

3. `Seed` sets the pseudorandom initial condition of the array. If you use the same seed in two runs, the initial conditions will be the same.

4. `sleep` tells how long to wait in seconds between iterations. This must be an integer. Set it to 0 to run the display quickly. Setting it to 1 or 2 usually gives enough time to figure out what is happening for simple configurations. Note that you can always use to stop the display so that you can look at it longer.

The height and width of the display are compiled into the code in the variables XSIZE and YSIZE. These can easily be changed. Keep in mind that they should be no bigger than the size of your display, otherwise the program will crash. (It wouldn't be hard to change the program so that XSIZE and YSIZE were set automatically to the size of the display, but then the program wouldn't be so simple.)

#### Examples:

``` life L 101-011-010 343 0 ```
produces a "glider". Try it out.
```
@ @
@@
@
```

` life H 1 343 0 `
produces a spiral wave in the cardiac conduction model. Note that `@` mean excited, while `+` and `.` mean refractory. A blank space means the element is quiescent and therefore excitable.
```                          @+@         ..+++@
@+++@        ..+++@
@+++++@       ..+++@
@+++.+++@      ..+++@
@+++...+++@     ..+++@
@+++.. ..+++@    ..+++@
@+++..   ..+++@   ..+++@
@+++..  @  ..+++@  ..+++@
@+++..  @+@  ..+++@ ..+++@
@+++..  @++  ..+++@  ..+++@
@+++..  @+++...+++@  ..+++@
@+++..  @+++.+++@  ..+++@
@+++..  @+++++@  ..+++@
@+++..  @+++@  ..+++@
@+++..  @+@  ..+++@
@+++..  @  ..+++@
@+++..   ..+++@
@+++.. ..+++@
@+++...+++@

```