Topic
Wolfram code
About: Wolfram code is a research topic. Over the lifetime, 16 publications have been published within this topic receiving 171 citations.
Papers
26 Jun 2004
TL;DR: This papers provides elements of answer, as it describes how another universal cellular automaton than the Game of Life (Life) was sought and found using evolutionary algorithms.
Abstract: In Twenty Problems in the Theory of Cellular Automata, Stephen Wolfram asks “how common computational universality and undecidability [are] in cellular automata.” This papers provides elements of answer, as it describes how another universal cellular automaton than the Game of Life (Life) was sought and found using evolutionary algorithms. This paper includes a demonstration that consists in showing that the presented R automaton can both implement any logic circuit (logic universality) and a simulation of Life (universality in the Turing sense).
26 citations
TL;DR: Using symbolic dynamics and formal languages, it is proved that the limit language of the elementary CA of rule 122 is neither regular nor context-free.
Abstract: S. Wolfram initiated the use of formal languages and automata theory in study of cellular automata (CAs). By means of extensive experiments with computer, he classified all CAs into four classes and conjectured that the limit languages of the third class of CAs, which produce chaotic aperiodic behavior, are not regular. Using symbolic dynamics and formal languages, we prove that the limit language of the elementary CA of rule 122 is neither regular nor context-free.
25 citations
TL;DR: A group which allows the formal study of interactions between particles in one-dimensional cellular automata and using the new algebraic classification of Rapaport proves that rule 54 is not simple.
Abstract: One-dimensional cellular automata are known to be able to present complex behaviors. In some cases, their evolution may be understood as movings, collisions, or creations of particles. In the case of the special Wolfram's rule 54, Boccara has previously pointed out basic particles. In this paper, we introduce a group which allows the formal study of interactions between these particles. Coming back to the complexity of rule 54 and using the new algebraic classification of Rapaport, we prove that rule 54 is not simple.
24 citations
Journal Article•
TL;DR: Using symbolic dynamical theory, the temporal evolution orbits of cellular automata are coarse-grain and it is proved that its width 1-evolution language is regular, but for every n " 2 its width n-evolved language is not context free but context sensitive.
Abstract: Cellular automata are classes of mathematical systems characterized by discreteness (in space, time, and state values), determinism, and local interaction. Using symbolic dynamical theory, we coarse-grain the temporal evolution orbits of cellular automata. By means of formal languages and automata theory, we study the evolution complexity of the elementary cellular automaton with local rule number 18 and prove that its width 1-evolution language is regular, but for every n " 2 its width n-evolution language is not context free but context sensitive.
14 citations
Journal Article•
TL;DR: It is shown that the dynamical system defined by rule 40 is Devaney chaos on a class of configurations of some particular type and has every periodic point except prime period one, four, or six.
Abstract: This paper examines the chaotic properties of the elementary cellular automaton rule 40. Rule 40 has been classified into Wolfram’s class I and also into class 1 by G. Braga et al. These classifications mean that the time-space patterns generated by this cellular automaton die out in a finite time and so are not interesting. As such, we may hardly realize that rule 40 has chaotic properties. In this paper we show that the dynamical system defined by rule 40 is Devaney chaos on a class of configurations of some particular type and has every periodic point except prime period one, four, or six. In the process of the proof, it is noticed that the dynamical properties of rule 40 can be related to some interval dynamical systems. These propositions are shown in Theorems 2 and 4.
11 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2016 | 1 |
| 2015 | 1 |
| 2012 | 1 |
| 2010 | 1 |
| 2008 | 2 |
| 2007 | 1 |