Cellular Automata has 1 rating and 0 reviews. Cellular automata are a class of spatially and temporally discrete mathematical systems characterized by lo. Cellular automata (CAs) are discrete spatially extended dynamical systems, capable of a vast variety of behaviors. Some people study them for their own sake;. A cellular automaton is a discrete model studied in computer science, mathematics, physics, .. As Andrew Ilachinski points out in his Cellular Automata, many scholars have raised the question of whether the universe is a cellular automaton.
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Cellular automata CAs are discrete spatially extended dynamical systems, capable of a vast variety of behaviors.
Some people study them for their own sake; some use them to model real phenomena; and some speculate that they underlie fundamental physics. The present volume is the most comprehensive single-author book on CAs to date, and provides a useful unified reference to many ideas scattered through the literature.
While aimed at an audience of physicists, it should be useful and comprehensible to mathematicians and computer scientists. While no one book could exhaust such a wide subject, there are several places where this one falls short, and others where it is too generous to ideas that, while popular ten years ago in the complex systems community, have not borne fruit. After an introduction and a lengthy chapter on formalism mostly discrete mathematicsthe author begins with a phenomenological exploration of ilachjnski CA rules.
He discusses periodic domains and particles, temporal and spatial correlations, mean-field theory, and Wolfram’s grouping of CAs into four rather ill-defined classes.
Cellular automaton – Wikipedia
Unfortunately, he repeats early claims that CAs must evolve towards the edge of chaos in order to perform computational tasks, even though this was thoroughly demolished by MitchellHraber and Crutchfield in After a nice discussion of Conway’s game of life and a sketch of the proof that it can perform universal computation, in Chapter 4 the author gives an introduction to the theory of wutomata dynamical systems, and how notions like invariant measure carry over into CAs.
Chapter 5 mainly enumerates periodic orbits and bounds transient times. Chapter 6 gives an introduction to the theory of languages and automata, including non-regular languages. It focuses, however, on the dynamics of the regular languages generated by CAs. That CAs can give rise to context-free and context-sensitive languages is reduced to a brief mention of the work of Hurd.
Also, the author misses all of the recent work of Machta andrrw al.
Chapter 7 discusses probabilistic CAs and gives an introduction to scaling, phase transitions, and the Ising model of magnetism.
It also explains why naive CA simulations often produce unphysical results, and how Creutz and others have designed CA rules that avoid this. It does not explain why most computational physicists still prefer traditional Monte Carlo autlmata to CAs.
Chapter 8 has some excellent material on reversible CAs, and on work by MargolusTakesuePomeau, Goles and Automsta on building thermodynamics from microscopically reversible dynamics. After discussing coupled map lattices and spatio-temporal intermittency, the chapter concludes with a smorgasbord of ilachinskj complex systems, including Kauffman’s Boolean Nk networks, random maps, and sandpiles.
There is a brief section on reaction-diffusion systems, which is the only place in the book where CAs appear as models of pattern formation. The section on quantum CAs, unfortunately, ignores work by MeyerWatrous and others.
Chapter 9 gives a good introduction to lattice gasesdiscussing why CAs can, sometimes, efficiently simulate hydrodynamics and its generalizations.
In general, fluid motion in a lattice gas inherits the unphysical anisotropy of the lattice.
Cellular Automata: A Discrete Universe
If the lattice has the right symmetry properties, however, isotropy reappears on aautomata scales. It presents the author’s detailed model of land combat. This certainly has interesting dynamics, but we are left to wonder whether it is llachinski all realistic. In a sense, students of topological quantum field theories are pursuing this idea. CAs are possible candidates for such a physics, and FredkinToffoliMargolus and Wolfram have advocated this vigorously.
Many subtle issues are involved: Unfortunately, this chapter is simply a potpourri of speculative theories, without any exploration of whether these have led to any progress in physics.
The author is entitled andre philosophize, but not to indiscriminately mix field theory, mystical triads, quantum computation and Fritjof Capra. It would have been far better to work through a few models with detail and rigor, and let readers judge their worth. The book ends with two appendices, one describing currently available CA hardware and software, and the other listing web pages related to CAs.
The bibliography is extensive, anndrew far from complete. Overall, the author’s choice of topics is suboptimal: Nonetheless, there is much useful material here, and we are not aware of anything better with a comparable scope. CA enthusiasts will want copies on their shelves.