“Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit points, limit cycles and chaotic attractors. The fourth class is probably capable of universal computation, so that properties of its infinite time behaviour are undecidable.”

[10, 1–2, January 1984, 1–35, Physica D: Nonlinear Phenomena, Universality and complexity in cellular automata, 10.1016/0167-2789(84)90245-8]

Adopted from Wikiquote. Last update July 23, 2025. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Eviden…" by Stephen Wolfram?
Stephen Wolfram photo
Stephen Wolfram 16
British-American computer scientist, mathematician, physici… 1959

Related quotes

Stephen Wolfram photo

“Problem 9. What is the correspondence between cellular automata and continuous systems?”

Stephen Wolfram (1959) British-American computer scientist, mathematician, physicist, writer and businessman

(originally published in 1985 in Physica Scripta T9: 170–183)
Context: Problem 9. What is the correspondence between cellular automata and continuous systems?
Cellular automatat are discrete in several respects. First, they consist of a discrete spatial lattice of sites. Second, they evolve in discrete steps. And finally, each site has only a finite discrete set of possible values.
The first two forms of discreteness are addressed in the numerical analysis of approximate solutions to, say, differential equations....
The third form of discreteness in cellular automata is not so familiar from numerical analysis. It is an extreme form of round-off, in which each "number" can have only a few possible values (rather than the usual 216 or 232).

Edsger W. Dijkstra photo
Joseph Goebbels photo
Edward Fredkin photo

“Cellular automata are now being used to model varied physical phenomena normally modelled by wave equations, fluid dynamics, Ising models, etc. We hypothesize that there will be found a single cellular automaton rule that models all of microscopic physics; and models it exactly. We call this field DM, for digital mechanics.”

Edward Fredkin (1934) American physicist and computer scientist, a pioneer of digital physics

[An informational process based on reversible universal cellular automata, Physica D: Nonlinear Phenomena, 45, 1–3, September 1990, 254–270, https://www.sciencedirect.com/science/article/pii/016727899090186S, 10.1016/0167-2789(90)90186-S]

Oswald Spengler photo

“All young sects are at bottom hostile to State and property, class and rank, and are attracted to universal equality.”

Oswald Spengler (1880–1936) German historian and philosopher

The Hour of Decision (1933)

Richard Dedekind photo
Bertrand Russell photo
Karl Marx photo
C. N. R. Rao photo

Related topics