AutomaLab         
 
                                 by            
 
                            Michael Creutz      
                          Physics Department
                    Brookhaven National Laboratory
                           Upton, NY 11973

                        creutz@wind.phy.bnl.gov         

9 September 1991
This program and source is freely distributable. 

Play God over your own universe.  With AutomaLab you control the 
microphysics of a discrete world of cellular automata.  This
two-dimensional land is an array of 192 by 180 cells displayed as pixels on
the Amiga screen.  Each cell can be alive or empty, with evolution
occurring in discrete time steps.  Empty cells are black, newborn ones are
yellow, older living ones are red, and cells that have just died are
magenta.  

In one time step, the fate of each cell depends on the number of living
neighbors.  Using Boolean gadgets, you control when a new live cell will be
born on an empty site and when a living one will survive.  Another gadget
determines whether the cells count only their four nearest neighbors or
also include the nearest cells in the diagonal direction, for a total of
eight neighbors.  With menu selections you determine whether the boundary
of your universe is dead, alive, or periodic.  There is also a menu
controlling the size of the cells.  The speed, pause, and clear gadgets
should be self explanatory.  You can also sketch and kill cells by pressing
the left mouse button over your world.

There are 2^18=262,144 possible rules with the eight neighborhood, and
2^10=1,024 more with the four cell neighborhood.  Indeed, it is unlikely
that you will be able to try them all.

In addition, the number of possible universes is further doubled using the
"Xpast" gadget, which probably needs some explanation.  When this is
activated, the new state is finally XOR'ed with the history one time step
back.  Thus if a cell was alive in the past, the new state is the opposite
of what the birth and survivor gadgets want.  The reason for doing this is
to produce reversable rules.  If the history and current states are
interchanged, the system will go backwards through the sequence of
configurations from which it came.  An analogy is reversing all the momenta
of a bunch of atoms.  This interchange is accomplished by the "Rev."
gadget, which interchanges young and moribund cells.  Without the Xpast
gadget set, the Rev. gadget is boring, it only delays things one time step.

If this seems confusing, try this: With the Xpast gadget set, clear the
screen, draw some small picture, select a random rule from the birth and
survivor gadgets, and let the system evolve until the screen becomes a
mess.  Then hit the Rev. button and watch the initial picture reappear.

The program starts out with Conway's classic cellular automaton model
"life."  Here a new cell is born for exactly three neighbors, while a
living cell dies with less than 2 (lonely) or more than 4 (overcrowding)
neighbors. 

Another well-known rule is Fredkin's modulo two model which uses the 4 cell
neighborhood.  Here a state flips if it has an odd number of active
neighbors and is unchanged otherwise.  Start with some small picture and
observe how the initial state is replicated.

The program is written in C and compiles with PDC.  It uses direct access
to the blitter for speed, but should multitask with no problem.  An earlier
version was published in the May 1991 issue of Jumpdisk.  Following their
liberal policy on program ownership, I now make it freely distributable. 
The main additions to that version are a custom pointer, variable block
size, and the ability to  XOR with the past.