Cellular automata and complexity download

A concave relationship was uncovered in the density-complexity domain after initial transient activity. This indicates a likely optimal rule i. Moreover, since Life is used as the key ingredient to construct complex and Life-like patterns of a wide range of density and complexity values, Life appears to serve as an elementary constituent responsible for complex Life-like behavior to emerge in both lower and higher density configurations.

Future research directions include measuring spatio-temporal information transfers in Life-like patterns to investigate long-time and long-distance correlations Lizier et al. The work presented here further sheds light on why John Horton Conway's Game of Life is considered the canonical Life-like rule and continues to be studied by students and academics even today—certainly making it a life worth mentioning. We would like to recognize and honor the work and life of the late mathematician John Horton Conway—the creator of the Game of Life among many other major contributions in the field of mathematics and beyond.

Hiroki Sayama supervised the work, provided critical feedback, and helped shape the research and manuscript. The data sets generated and analyzed for this study are available from the corresponding author on reasonable request.

The code used to compile and analyze data was written in Python 3. The code to replicate analysis along with simulations of the rules mentioned in this article are available from the corresponding author on reasonable request.

Sign In or Create an Account. Advanced Search. User Tools. Sign In. Skip Nav Destination Article Navigation. Close mobile search navigation Article navigation. Volume 27, Issue 2. Previous Article Next Article. Author Contributions. Competing Interests. Data Availability. Code Availability. Article Navigation. November 02 This Site. Google Scholar. Hiroki Sayama Hiroki Sayama. Author and Article Information. Hiroki Sayama.

Online Issn: Artificial Life 27 2 : — Cite Icon Cite. Cellular automata , Game of Life , Life-like rules , complexity , conditional entropy , information. Conditional entropy has been used to characterize spatial correlations and aesthetic structure in 2D CA Andrienko et al. This measure was originally termed information gain complexity , but we use the term conditional entropy to avoid misleading nomenclature.

Figure 1. View large Download slide. Figure 2. Figure 3. The authors declare no competing interests. Physical review. E, Statistical, nonlinear, and soft matter physics. Fibroblasts, morphogenesis and cellular automata. Computation theory of cellular automata. Self-organizing behaviour in cellular automata is discussed as a computational process. Formal language theory is used to extend dynamical systems theory descriptions of cellular automata.

The sets … Expand. Twenty Problems in the Theory of Cellular Automata. Cellular automata are simple mathematical systems that exhibit very complicated behaviour. They can be considered as discrete dynamical systems or as computational systems.

Progress has recently been … Expand. View 1 excerpt, cites background. This project offers an overview of the use of Cellular Automata CA as a statistical technique to study complex systems. First, elementary CA, such as the ones studied by Wolfram, will be presented … Expand.

View 1 excerpt. Universality and complexity in cellular automata. Computer Science, Mathematics. Algebraic properties of cellular automata. Cellular automata are discrete dynamical systems, of simple construction but complex and varied behaviour. Algebraic techniques are used to give an extensive analysis of the global properties of a … Expand. Applications of ergodic theory and sofic systems to cellular automata. Abstract We indicate a mathematical framework for analysing the evolution of cellular automata.

Those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian … Expand. Veliger 24 , — Young, D. Guckenheimer, J.

Book Google Scholar. Hopcroft, J. Martin, O, Odlyzko, A. Grassberger, P. Physica 10 D , 52—58 Lind, D. Physica 10 D , 36—44 Margolus, N. Physica 10 D , 81—95 Smith, A.

Journal of the Association for Computing Machinery 18 , — Berlekamp, E. Winning Ways for your Mathematical Plays Vol. Gardner, M. Download references. You can also search for this author in PubMed Google Scholar. Reprints and Permissions. Cellular automata as models of complexity. Nature , — Download citation. Issue Date : 04 October Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article.