Last update: August 8, 2002

BACK

Publications on Cellular Automata :

• A. Adamatzky et al.:
  • Identification of cellular automata, 1994.
• J. Case et al.:
  • Lattice computers for approximating Euclidean space, 2001.
  • Spherical Wave Front Generation in Lattice Computers, 1994.
• D. Griffeath et al.:
  • Cellular Automaton Growth on Z²: Theorems, Examples, and Problems, 1998.
• S. K. Numrich et al.:
  • A Cellular Automaton Methodology for Solving the Wave Equation, 1993.
• K. Preston et al.:
  • Modern cellular automata: Theory & applications, 1984.

BibTeX references.

Links of interest:

• Cosma Shalizi's notes

In the context of mesh-like, parallel processing computers for (i) approximating continuous space and (ii) analog simulation of the motion of objects and waves in continuous space, the present paper is concerned with which mesh-like interconnection of processors might be particularly suitable for the task and why. Processor interconnection schemes based on nearest neighbor connections in geometric lattices are presented along with motivation. Then two major threads are exploded regarding which lattices would be good: the regular lattices, for their symmetry and other properties in common with continuous space, and the well-known root lattices, for being, in a sense, the lattices required for physically natural basic algorithms for motion. The main theorem of the present paper implies that thewell-known lattice An is the regular lattice having the maximum number of nearest neighbors among the n-dimensional regular lattices. It is noted that the only n-dimensional lattices that are both regular and root are An and Zn (Zn is the lattice of n-cubes. The remainder of the paper specifies other desirable properties of An including other ways it is superior to Zn for our purposes.

Web link: http://psoup.math.wisc.edu/extras/r1shapes/r1shapes.html

We survey the phenomenology of crystal growth and asymptotic shape for two-dimensional, two-state cellular automata. In the most tractable case of Threshold Growth, a detailed rigorous theory is available. Other less orderly examples with recursively computable updates illustrate the broad range of behavior obtained from even the simplest initial seeds and update rules. Still more exotic cases seem largely beyond the scope of exact analysis, but pose fascinating problems for experimentalists. The paper concludes with a discussion of connections between deterministic shape theory and important corresponding questions for systems with random dynamics.

SIGARCH : ACM Special Interest Group on Computer Architecture

We describe a parallel finite difference algorithm based on a grid form of Huygens' principle in the form of a cellular automaton for simulating wave propagation in the time domain. Since the algorithm solves the full form of the wave equation, without employing the far field approximation this approach is particularly effective for near- and intermediate field problems. As the iteration proceeds, real time animated displays depict the field evolution. The algorithm is perfectly matched to the architecture of "single instruction multiple data" (SIMD) parallel processors. On the CM-200, for example, it typically takes several minutes to compute wave fields and display them on a 512X512 grid. A good personal computer, however, is sufficient to develop many interesting classroom demonstrations of wave propagation phenomena.

Web link : http://www.ait.nrl.navy.mil/people/numrich/ACM/Title.html

BACK

Page created & maintained by Frederic Leymarie, 1999-2002.
Comments, suggestions, etc., mail to: leymarie@lems.brown.edu