OCA:Paterson's worms
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Paterson's worms are a family of cellular automata devised in 1971 by Mike Paterson and John Horton Conway. The worms were described by Michael Beeler in June 1973, and presented in November of that year in Martin Gardner's "Mathematical Games" column in Scientific American.
Rules
The worm starts at some point of an infinite triangular grid. It starts moving along one of the six gridlines that meet at each point and, once it has travelled one unit of distance, it arrives at a new point.
The worm then decides, based on the distribution of traversed and untraversed gridlines, what direction it will take. The directions are relative to the worm's point of view. If the worm has not encountered this exact distribution before it may leave along any untraversed gridline. From then on, if it encounters that distribution again, it must move in the same way.
If there are no untraversed gridlines available, the worm dies and the simulation ends.
The six directions are numbered as follows:
Direction 0 indicates the worm continues to travel straight ahead, direction 1 indicates the worm will make a right turn of 60° and similarly for the other directions. The worm cannot travel in direction 3 because that is the gridline it has just traversed. Thus a worm with rule {1,0,5,1} decides to travel in direction 1 the first time it has to make a choice, in direction 0 the next time it has to make a choice and so on. If there is only one available gridline, the worm has no choice but to take it and this is usually not explicitly listed.
See also
External links
- Paterson's worms at Wikipedia