Symbolic dynamics of glider guns for some one-dimensional cellular automata

Jin, Weifeng; Chen, Fangyue

doi:10.1007/s11071-016-2935-6

Cited by 6 publications

(1 citation statement)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Signals allow to store and transmit information, to start a process, to synchronise, etc. The use of signals in the context of CA is widespread in the literature: collision computing (Adamatzky, 2002), gliders Jin and Chen (2016), solitons (Jakubowski et al, 1996, 2000, 2017Siwak, 2001), particles (Boccara et al, 1991;Mitchell, 1996;Hordijk et al, 1998), Turing-computation (Lindgren and Nordahl, 1990;Cook, 2004), synchronisation (Varshavsky et al, 1970;Yunès, 2007), geometrical constructions (Cook, 2004), signals (Mazoyer and Terrier, 1999;Delorme and Mazoyer, 2002), etc.…”

Section: Introductionmentioning

confidence: 99%

Abstract Geometrical Computation 10: An Intrinsically Universal Family of Signal Machines

Becker,

Besson,

Durand-Lose

et al. 2018

Preprint

View full text Add to dashboard Cite

Signal machines form an abstract and idealised model of collision computing. Based on dimensionless signals moving on the real line, they model particle/signal dynamics in Cellular Automata. Each particle, or signal, moves at constant speed in continuous time and space. When signals meet, they get replaced by other signals. A signal machine defines the types of available signals, their speeds and the rules for replacement in collision.A signal machine A simulates another one B if all the space-time diagrams of B can be generated from space-time diagrams of A by removing some signals and renaming other signals according to local information. Given any finite set of speeds S, we construct a signal machine that is able to simulate any signal machine whose speeds belong to S. Each signal is simulated by a macro-signal, a ray of parallel signals. Each macro-signal has a main signal located exactly where the simulated signal would be, as well as auxiliary signals which encode its id and the collision rules of the simulated machine.The simulation of a collision, a macro-collision, consists of two phases. In the first phase, macro-signals are shrunk, then the macro-signals involved in the collision are identified and it is ensured that no other macro-signal comes too close. If some do, the process is aborted and the macro-signals are shrunk, so that the correct macro-collision will eventually be restarted and successfully initiated. Otherwise, the second phase starts: the appropriate collision rule is found and new macro-signals are generated accordingly.Considering all finite set of speeds S and their corresponding simulators provides an intrinsically universal family of signal machines.

show abstract