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Conference Papers Year : 2008

The spatial structure of odometers in certain cellular automata

Marcus Pivato
Reem Yassawi
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Abstract

Recent work has shown that many cellular automata (CA) have configurations whose orbit closures are isomorphic to odometers. We investigate the geometry of the spacetime diagrams of these `odometer configurations'. For boolean linear CA, we exactly determine the positions of the consecutive `gears' of the odometer mechanism in the configuration. Then we characterize and explain the self-similar structure visible in the spacetime diagrams of odometer configurations for two classes of nonlinear CA: ratchet CA and Coven CA.

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Other [cs.OH]
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Dates and versions

hal-00273988 , version 1 (16-04-2008)

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  • HAL Id : hal-00273988 , version 1

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Marcus Pivato, Reem Yassawi. The spatial structure of odometers in certain cellular automata. JAC 2008, Apr 2008, Uzès, France. pp.119-129. ⟨hal-00273988⟩

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