LCAU.DOC

Harold V. McIntosh
Departamento de Aplicación de Microcomputadoras,
Instituto de Ciencias, Universidad Autónoma de Puebla,
Apartado postal 461, 72000 Puebla, Puebla, México.
E-mail:mcintosh@servidor.unam.mx

April 8, 1988
revised October 12, 1992

Abstract:

Previous collections of cellular automata programs have grown, both as the analysis of new aspects of their behavior has continually been included, and as the range of parameters of the automata has increased. During all this time, the programs have lacked an operation manual, which is the substance of the present document. Previously, it has been necessary to rely on the source code, which has always been made available along with programs, but whose commentary has never been expository. A set of lecture notes, Linear Cellular Automata accompanies the programs, and explains most of their features.

The first collection, LCA, covered a small range of radii and state numbers, with supplementary programs to calculate cycles and de Bruijn diagrams. Most of the rules were required to be totalistic.

The second collection, LCAU , contained three principal extensions:

1. General rules, not just totalistic rules, could be analyzed.

2. Cell densities and block probabilities were calculated according to mean field theory and local structure theory using options in a new submenu.

3. The option to produce de Bruijn diagrams was incorporated in a submenu.

Consequently a more detailed and convenient analysis of (k,1), k=2,3,4 and (2,2) automata could be made than previously.

The current revision, LCAU (second series), extends the range of the parameters k and l considerably, including half-integer values for r. An entirely new submenu, for the calculation of ancestors, has been introduced, based on de Bruijn diagrams. Configurations deduced from the de Bruijn diagrams can now be transferred back to the main menu, so that their full screen evolution can be observed.

The programming language REC has been included, whose principal application lies in organizing demonstrations, but it will eventually allow storing and retrieving demonstrations from disk.

Finally, extensive provision has been made for random and partially random connections of the cells. To study a related phenomenon, the Chaté-Manneville effect, higher dimensional homologues of many of the automata can be studied.

Some slight provision has been made for a mouse.