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Paterson's Worms

Inspired by computer simulations of fossilized worms trails published by Raup and Seilacher (1969), computer scientist Mike Paterson at the University of Warwick and mathematician J. H. Conway created in early 1971 a simple set to rules to study idealized worms traveling along regular grids. Mike Beeler of the MIT Artificial Intelligence Laboratory subsequently published a study Paterson's worms in which he considered paths on a triangular grid (Beeler 1973).

The following table summarizes the number of steps required for a number of long-running worms to terminate (Rokicki).

patternsteps to terminate
1042015>1.3×10^(18)
104202057493855205939
104202257493855205905
1252121>1.1×10^(17)
1420221infinite
142022416811365528
1450221infinite
145022416811365528
1525115>1.4×10^(17)
20141423563608205
214514287996218
24541423563608205

Paterson's worms are featured in the 2003 Stephen Low IMAX film Volcanoes of the Deep Sea.

See also

Langton's Ant, Spirolateral, Turing Machine, Turmite

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References

Beeler, M. "Paterson's Worms." Cambridge, MA: MIT Artificial Intelligence Memo, No. 29. June 1973.Chaffin, B. "Paterson's Worms." http://wso.williams.edu/~bchaffin/patersons_worms/.Gardner, M. "Worm Paths." Ch. 17 in Knotted Doughnuts and Other Mathematical Entertainments. New York: W. H. Freeman, pp. 205-221, 1986.Hayes, B. "In Search of the Optimal Scumsucking Bottomfeeder." Amer. Sci. 91, 392, 2003. http://www.americanscientist.org/template/AssetDetail/assetid/25692/page/3.Kahrkling, S. "Worm Paths: Fantastic Patterns Traced by Programmed 'Worms.' " http://www.accessv.com/~sven/worms/.Pegg, E. Jr. "Math Games: Paterson's Worm Revisited." Oct. 27, 2003. http://www.maa.org/editorial/mathgames/mathgames_10_24_03.html. Pegg, E. Jr. "Paterson's Worms Revisited." http://library.wolfram.com/infocenter/MathSource/5050/.Rasmussen, B.; Bengtson, S.; Fletcher, I. R.; and McNaughton, N. J. "Discoidal Impressions and Trace-Like Fossils More Than 1200 Million Years Old." Science 296, 1112-1115, 2002.Raup, D. and Seilacher, A. "Fossil Foraging Behavior: Computer Simulation." Science 166, 994-995, 1969.Rokicki, T. "My Results on Paterson's Worms." http://tomas.rokicki.com/worms.html.Seilacher, A. Sci. Amer. 217, No. 2, 72, 1967.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 930, 2002.

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Paterson's Worms

Cite this as:

Weisstein, Eric W. "Paterson's Worms." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PatersonsWorms.html

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