Paul Rendell's Holstein Cellular Automata Page

Checker Board Patterns A set of asymmetrical checkerboard patterns where a pair of edges perform a drunkards walk until it collapse into stripes

Diagonal Band Patterns A set of asymmetrical diagonal bands patterns where the edges of the bands perform a drunkards walk unitl they meet and band collapes to nothing.

Holstein Rules Cellular Automata

This is one of a class of Cellular Automata. A Cellular Automata consists of a field of cells. A cell must be in one of fixed number of states. For these rules there are just 2 states called live and dead. The state of a cell in the next generation is dependant only on its current state and the current state of its 8 neighbour. There are an astonishing number of patterns that change in interesting ways. Conway's Game Life is the most widely know set of rules in this class.

The Holstein rules are:
  A cell is born in an empty square if there are: 3, 5, 6, 7 or 8 neighbouring live cells.  
  A cell survives if there are: 4, 6, 7, or 8 live cells. 

These rules are symmetrical. They can be rewritten:
  A live cell is dies if there are: 3, 5, 6, 7 or 8 neighbouring dead cells.  
  A cell is not born if there are: 4, 6, 7, or 8 dead cells. 

The patterns formed by these rules are very limited. Their are a handful of period 2 oscillators and stable patterns and not much else. However 3 Gliders have been found - see D. Eppstein - Gliders in Life-Like Cellular Automata

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Non Holstein: Game of Life

State Symmetrical Cellular Automata

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Last Update 05/November/23

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