- [
] 1984, with J. Doyne Farmer, Tommaso Toffoli*Cellular Automata*. *Mathematica: the Student Book*. 1990, with George Beck1994*Cellular Automata and Complexity*.*The Mathematica Book: 4th edn*. 1999*A New Kind of Science*. 2002

- Cellular Automata. 1983. (In
)*Cellular Automata and Complexity* - Statistical mechanics of Cellular Automata. 1983. (In
)*Cellular Automata and Complexity* - Algebraic properties of Cellular Automata. 1984. (In
)*Cellular Automata and Complexity* - Cellular automata as models of complexity. 1984. (In
*Nonlinear Physics for Beginners*) - Computation theory of Cellular Automata. 1984. (In
)*Cellular Automata and Complexity* - Computers in science and mathematics. 1984. (In
)*Cellular Automata and Complexity* - Geometry of binomial coefficients. 1984. (In
)*Cellular Automata and Complexity* - Universality and complexity in Cellular Automata. 1984
- Origins of randomness in physical systems. 1985. (In
)*Cellular Automata and Complexity* - Thermodynamics and hydrodynamics of Cellular Automata. 1985. (In
)*Cellular Automata and Complexity* - Twenty problems in the theory of Cellular Automata. 1985. (In
)*Cellular Automata and Complexity* - Two dimensional Cellular Automata. 1985. (In
)*Cellular Automata and Complexity* - Undecidability and intractability in theoretical physics. 1985
- Approaches to complexity engineering. 1986. (In
)*Cellular Automata and Complexity* - Cellular Automaton fluids: basic theory. 1986. (In
)*Cellular Automata and Complexity* - Cryptography with Cellular Automata. 1986. (In
)*Cellular Automata and Complexity* - Minimal Cellular Automaton approximations to continuum systems. 1986. (In
)*Cellular Automata and Complexity* - Random sequence generation by Cellular Automata. 1986. (In
)*Cellular Automata and Complexity* - Tables of Cellular Automaton properties. 1986. (In
)*Cellular Automata and Complexity* - Cellular Automaton supercomputing. 1988. (In
)*Cellular Automata and Complexity* - Complex systems theory. 1988
- What Alan Turing might have discovered. 2016. (In
*The Once and Future Turing*)

- • Norman H. Margolus.
**Physics-like models of computation**.*Physica*10D. 1984 - • Stephen Wolfram.
**Universality and complexity in Cellular Automata**. 1984 - • Douglas A. Lind.
**Applications of ergodic theory and sofic systems to Cellular Automata**. 1984 - • Michael S. Waterman.
**Some applications of information theory to Cellular Automata**. 1984 - • Peter Grassberger.
**Chaos and diffusion in deterministic Cellular Automata**. 1984 - Encode the 1D CA state
…
*s*_{-2}*s*_{-1}*s*_{0}*s*_{1}*s*_{2}… as the 2D point (0.*s*_{0}*s*_{1}*s*_{2}…, 0.*s*_{-1}*s*_{-2}…) • "similar" states are "close" in space (with a bias to similarity near cell*c*_{0}, consistent with the Cantor set topology explained in [Toffoli 1984a] below) • time evolution is a trajectory in this space • some CA rules have dynamics that exhibit an "attractor"-like structure (although not completely identical) in this space - • T. E. Ingerson, R. L. Buvel.
**Structure in asynchronous Cellular Automata**. 1984 - asynchronous 1D CA investigations • random, and own clock • these models are more "natural" • some self-organisin behaviour of synchronous 1D CAs comes from the synchronisation • some further interesting behaviour appears with asynchronous models
- • Stephen J. Willson.
**Growth rates and fractional dimensions in Cellular Automata**. 1984 - • R. Wm. Gosper.
**Exploiting regularities in large cellular spaces**. 1984 - Optimisation algorithm for 2D CAs, using quadrant decomposition of cellular space, cacheing of results, and hashing to find previously used quadrants
- • Gerard Y. Vichniac.
**Simulating physics with Cellular Automata**. 1984 - CAs exactly computable models, and non-numerical simulations • a naive CA implementation of a spin glass gives poor results
- • Tommaso Toffoli.
**Cellular Automata as an alternative to (rather than an approximation of) differential equations in modeling physics**. 1984 - why CAs are appropraite for direct modelling of physical systems • Cantor set topology of infinite CAs
- • Stephen M. Omohundro.
**Modelling Cellular Automata with partial differential equations**. 1984 - • Christopher G. Langton.
**Self-reproduction in Cellular Automata**. 1984 - requirement that self-replicator be a
*universal*constructor is too strong: natural self-replicators (organisms!) aren't universal constructors • relax therequirement simply to: the "self-replicating" configuration must treat its stored information both as*interpreted*instructions and*uninterpreted*data • adaptation of Codd's 1968 universal constructor, with a different transition rule • states comprise instructions for constructing a new loop • instructions travel around the loop, memory -*uninterpreted*• instructions construct new loop -*interpreted* - • Stuart A. Kauffman.
**Emergent properties in random complex automata**. 1984 *N*cells with boolean state, each getting input from*K*other randomly chosen cells, combined by a randomly chosen boolean function •*K*= 2 dynamics properties : number of states = 2, yet cycle length, number of distinct cycles (basins of attraction) ~^{N}*N*^{1/2}; cycles relatively stable to small perturbations •*canalising rules*, and*forcing structures*- subgraphs that "crystallise" at their canalised values - and so partition the remaining graph into isolated subclusters • as simple models of geneetic regulatory networks- • Christian Burks, J. Doyne Farmer.
**Towards modeling DNA sequences as automata**. 1984 - • Steven A. Smith, Richard C. Watt, Stuart R. Hameroff.
**Cellular Automata in cytoskeletal lattices**. 1984 - • Forrest L. Carter.
**The molecular device computer: point of departure for large scale Cellular Automata**. 1984 - • Tommaso Toffoli.
**CAM: a high-performance Cellular-Automaton Machine**. 1984 - support for "watching 2D CA evolution • sequential processing, special-purpose hardware • 256x256 array of cells, periodic (toroidal) boundary conditions • each cell with up to 256 states • 60 timesteps per second display
- • Kendall Preston Jr.
**Four-dimensional logical transforms: data processing by Cellular Automata**. 1984 - • W. Daniel Hillis.
**The Connection Machine: a computer architecture based on Cellular Automata**. 1984 - • James P. Crutchfield.
**Space-time dynamics in video feedback**. 1984

- •
**Universality and complexity in Cellular Automata**. 1984 - •
**Statistical mechanics of Cellular Automata**.*Rev.Mod.Phys***55**:601-644. 1983 - • Stephen Wolfram, Olivier Martin, Andrew M. Odlyzko.
**Algebraic properties of Cellular Automata**.*Comm.Math.Phys***93**:219-258. 1984 - •
**Computation theory of Cellular Automata**.*Comm.Math.Phys***96**:15-57. 1984 - •
**Undecidability and intractability in theoretical physics**.*Phys.Rev.Lett***54**:735-738. 1985 - • Norman H. Packard, Stephen Wolfram.
**Two dimensional Cellular Automata**.*J.Stat.Phys***38**:901-946. 1985 - •
**Origins of randomness in physical systems**.*Phys.Rev.Lett***55**:449-452. 1985 - • Stephen Wolfram, James B. Salem.
**Thermodynamics and hydrodynamics of Cellular Automata**. 1985 - •
**Random sequence generation by Cellular Automata**.*Adv.Appl.Math***7**:123-169. 1986 - •
**Approaches to complexity engineering**.*Physica D***22**:385-399. 1986 - •
**Minimal Cellular Automaton approximations to continuum systems**. 1986 - •
**Cellular Automaton fluids: basic theory**.*J.Stat.Phys***45**:471-526. 1986 - •
**Cellular Automata**.*Los Alamos Science***9**:2-21. 1983 - •
**Computers in science and mathematics**.*Scientific American***251**:188-203. 1984 - •
**Geometry of binomial coefficients**.*American Mathematical Monthly***91**:566-571. 1984 - •
**Twenty problems in the theory of Cellular Automata**.*Physica Scripta***T9**:170-183. 1985 - •
**Cryptography with Cellular Automata**.*Crypto'85*, LNCS 218:429-432. Springer. 1986 - •
**Complex systems theory**. 1988 - •
**Cellular Automaton supercomputing**. 1988 - •
**Tables of Cellular Automaton properties**. 1986

Other reviews:

- Scott Aaronson. Book Review.
*QIC***2**(5):410-423. 2002 - Ray Kurzweil. Reflections on Stephen Wolfram's "A New Kind of Science". 2002
- Rudy Rucker. Review.
In
*Amer. Math. Monthly*, pp.851-861, November 2003 - Cosma Shalizi. A Rare Blend of Monster Raving Egomania and Utter Batshit Insanity, Bactra review #132, 2005
- Steven Weinberg.
Is the Universe a Computer?.
*New York Review of Books*, October 2002