Skip to main content

Structurally Dynamic Cellular Automata

  • Reference work entry
  • First Online:
Cellular Automata

Part of the book series: Encyclopedia of Complexity and Systems Science Series ((ECSSS))

  • Originally published in
  • R. A. Meyers (ed.), Encyclopedia of Complexity and Systems Science, © Springer-Verlag 2009

Glossary

Adjacency matrix:

The adjacency matrix of a graph with N sites is an N Ã— N matrix [aij] with entries aij = 1 if i and j are linked, and aij = 0 otherwise. The adjacency matrix is symmetric (aij = aji) if the links in the graph are undirected.

Coupler link rules:

Coupler rules are local rules that act on pairs of next-nearest sites of a graph at time t to decide whether they should be linked at t + 1. The decision rules fall into one of three basic classes – totalistic (T), outer-totalistic (OT) or restricted-totalistic (RT) – but can be as varied as those for conventional cellular automata.

Decoupler link rules:

Decoupler rules are local rules that act on pairs of linked sites of a graph at time t to decide whether they should be unlinked at t + 1. As for coupler rules, the decision rules fall into one of three basic classes – totalistic (T), outer-totalistic (OT) or restricted-totalistic (RT) – but can be as varied as those for conventional cellular automata.

...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 549.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 799.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Bibliography

Primary Literature

  • Adamatzky A (1995) Identification of cellular automata. Taylor & Francis, London

    MATH  Google Scholar 

  • Albert J, Culik IIK (1987) A simple universal cellular automaton and its one-way and totalistic version. Complex Syst 1:1–16

    MathSciNet  MATH  Google Scholar 

  • Ali SM, Zimmer RM (1995) Games of proto-life in masked cellular automata. Complex Int 2. http://www.complexity.org.au

  • Ali SM, Zimmer RM (2000) A formal framework for emergent panpsychism. In: Tucson 2000: consciousness research abstracts. http://www.consciousness.arizona.edu/tucson2000/. Accessed 14 Oct 2008

  • Alonso-Sanz R (2006) The beehive cellular automaton with memory. J Cell Autom 1(3):195–211

    MathSciNet  MATH  Google Scholar 

  • Alonso-Sanz R (2007) A structurally dynamic cellular automaton with memory. Chaos, Solitons Fractals 32(4):1285–1304

    Article  MathSciNet  MATH  Google Scholar 

  • Alonso-Sanz R, Martin M (2006) A structurally dynamic cellular automaton with memory in the hexagonal tessellation. In: El Yacoubi S, Chopard B, Bandini S (eds) Lecture notes in computer science, vol 4173. Springer, New York, pp 30–40

    MATH  Google Scholar 

  • Applied Graph & Network Analysis software. http://benta.addr.com/agna/. Accessed 14 Oct 2008

  • Barabasi AL, Albert R (2002) Statistical mechanics of complex networks. Rev Mod Phys 74:47–97

    Article  MathSciNet  MATH  Google Scholar 

  • Bollobas B (2002) Modern graph theory. Springer, New York

    MATH  Google Scholar 

  • Borgatti SP (2002) NetDraw 1.0: network visualization software. Analytic Technologies, Harvard

    Google Scholar 

  • Chen C (2004) Graph drawing algorithms. In: Information visualization. Springer, New York

    Google Scholar 

  • Dadic I, Pisk K (1979) Dynamics of discrete-space structure. Int J Theor Phys 18:345–358

    Article  Google Scholar 

  • Doi H (1984) Graph theoretical analysis of cleavage pattern: graph developmental system and its application to cleavage pattern in ascidian egg. Develop Growth Differ 26(1):49–60

    Article  Google Scholar 

  • Durrett R (2006) Random graph dynamics. Cambridge University Press, New York

    Google Scholar 

  • Erdos P, Renyi A (1960) On the evolution of random graphs. Publ Math Inst Hung Acad Sci 5:11–61

    MathSciNet  MATH  Google Scholar 

  • Ferber J (1999) Multi-agent systems: an introduction to distributed artificial intelligence. Addison-Wesley, New York

    Google Scholar 

  • Ferreira A (2002) On models and algorithms for dynamic communication networks: the case for evolving graphs. In: 4th Recontres Francophones sur les Aspects Algorithmiques des Télécommunications (ALGOTEL 2002), Meze

    Google Scholar 

  • Gerstner W, Kistler WM (2002) Spiking neuron models. Single neurons, populations, plasticity. Cambridge University Press, New York

    Book  MATH  Google Scholar 

  • Grzegorz R (1997) Handbook of graph grammars and computing by graph transformation. World Scientific, Singapore

    MATH  Google Scholar 

  • Halpern P (1989) Sticks and stones: a guide to structurally dynamic cellular automata. Am J Phys 57(5):405–408

    Article  Google Scholar 

  • Halpern P (1996) Genetic algorithms on structurally dynamic lattices. In: Toffo T, Biafore M, Leao J (eds) PhysComp96. New England Complex Systems Institute, Cambridge, pp 135–136

    Google Scholar 

  • Halpern P (2003) Evolutionary algorithms on a self-organized, dynamic lattice. In: Bar-Yam Y, Minai A (eds) Unifying themes in complex systems, vol 2. Proceedings of the second international conference on complex systems. Westview Press Cambridge

    Google Scholar 

  • Halpern P, Caltagirone G (1990) Behavior of topological cellular automata. Complex Syst 4:623–651

    MathSciNet  MATH  Google Scholar 

  • Harary F, Gupta G (1997) Dynamic graph models. Math Comp Model 25(7):79–87

    Article  MathSciNet  MATH  Google Scholar 

  • Hasslacher B, Meyer D (1998) Modeling dynamical geometry with lattice gas automata. Int J Mod Phys C 9:1597

    Article  Google Scholar 

  • Hillman D (1995) Combinatorial spacetimes. PhD dissertation, University of Pittsburgh

    Google Scholar 

  • Ilachinski A (1986) Topological life-games I. Preprint. State University of New York at Stony Brook

    Google Scholar 

  • Ilachinski A (1988) Computer explorations of self organization in discrete complex systems. Diss Abstr Int B 49(12):5349

    MathSciNet  Google Scholar 

  • Ilachinski A (2001) Cellular automata: a discrete universe. World Scientific, Singapore

    Book  MATH  Google Scholar 

  • Ilachinski A, Halpern P (1987a) Structurally dynamic cellular automata. Preprint. State University of New York at Stony Brook

    Google Scholar 

  • Ilachinski A, Halpern P (1987b) Structurally dynamic cellular automata. Complex Syst 1(3):503–527

    MathSciNet  MATH  Google Scholar 

  • Jourjine AN (1985) Dimensional phase transitions: coupling of matter to the cell complex. Phys Rev D 31:1443

    Article  MathSciNet  Google Scholar 

  • Kaplunovsky V, Weinstein M (1985) Space-time: arena or illusion? Phys Rev D 31:1879–1898

    Article  MathSciNet  Google Scholar 

  • Kniemeyer O, Buck-Sorlin GH, Kurth W (2004) A graph grammar approach to artificial life. Artif Life 10(4):413–431

    Article  Google Scholar 

  • Krivovichev SV (2004) Crystal structures and cellular automata. Acta Crystallogr A 60(3):257–262

    Article  MathSciNet  MATH  Google Scholar 

  • Lehmann KA, Kaufmann M (2005) Evolutionary algorithms for the self-organized evolution of networks. In: Proceedings of the 2005 conference on genetic and evolutionary computation. ACM Press, Washington, DC/New York

    Google Scholar 

  • Love P, Bruce M, Meyer D (2004) Lattice gas simulations of dynamical geometry in one dimension. Phil Trans Royal Soc A: Math Phys Eng Sci 362(1821):1667–1675

    Article  MathSciNet  MATH  Google Scholar 

  • Majercik S (1994) Structurally dynamic cellular automata. Master’s thesis, Department of Computer Science, University of Southern Maine

    Google Scholar 

  • Makowiec D (2004) Cellular automata with majority rule on evolving network. In: Lecture notes in computer science, vol 3305. Springer, Berlin, pp 141–150

    Google Scholar 

  • Mendes RV (2004) Tools for network dynamics. Int J Bifurc Chaos 15(4):1185–1213

    Article  MathSciNet  MATH  Google Scholar 

  • Meschini D, Lehto M, Piilonen J (2005) Geometry, pregeometry and beyond. Stud Hist Philos Mod Phys 36:435–464

    Article  MathSciNet  MATH  Google Scholar 

  • Miramontes O, Solé R, Goodwin B (1993) Collective behavior of random-activated mobile cellular automata. Physica D 63:145–160

    Article  MATH  Google Scholar 

  • Misner CW, Thorne KS, Wheeler JA (1973) Gravitation. W.H. Freeman, New York

    Google Scholar 

  • Mitchell M (1998) An introduction to genetic algorithms. MIT Press, Boston

    MATH  Google Scholar 

  • Moore EF (1962) Sequential machines: selected papers. Addison-Wesley, New York

    MATH  Google Scholar 

  • Muhlenbein H (1991) Parallel genetic algorithm, population dynamics and combinatorial optimization. In: Schaffer H (ed) Third international conference on genetic algorithms. Morgan Kauffman, San Francisco

    Google Scholar 

  • Murata S, Tomita K, Kurokawa H (2002) System generation by graph automata. In: Ueda K (ed) Proceedings of the 4th international workshop on emergent synthesis (IWES ‘02), Kobe University, pp 47–52

    Google Scholar 

  • Mustafa S (1999) The concept of poiesis and its application in a Heideggerian critique of computationally emergent artificiality. PhD thesis, Brunel University, London

    Google Scholar 

  • Newman M, Barabasi A, Watts DJ (2006) The structure and dynamics of networks. Princeton University Press, New Jersey

    MATH  Google Scholar 

  • Nochella J (2006) Cellular automata on networks. Talk given at the wolfram science conference (NKS2006), Washington, DC, 16–18 June

    Google Scholar 

  • Nooy W, Mrvar A, Batagelj V (2005) Exploratory social network analysis with Pajek. Cambridge University Press, New York

    Book  Google Scholar 

  • Nowotny T, Requardt M (1998) Dimension theory of graphs and networks. J Phys A 31:2447–2463

    Article  MathSciNet  MATH  Google Scholar 

  • Nowotny T, Requardt M (1999) Pregeometric concepts on graphs and cellular networks as possible models of space-time at the Planck-scale. Chaos, Solitons Fractals 10:469–486

    Article  MathSciNet  MATH  Google Scholar 

  • Nowotny T, Requardt M (2006) Emergent properties in structurally dynamic disordered cellular networks. arXiv:cond-mat/0611427. Accessed 14 Oct 2008

  • O’Sullivan D (2001) Graph-cellular automata: a generalized discrete urban and regional model. Environ Plan B: Plan Des 28(5):687–705

    Article  Google Scholar 

  • Prusinkiewicz P, Lindenmayer A (1990) The algorithmic beauty of plants. Springer, New York

    Book  MATH  Google Scholar 

  • Requardt M (1998) Cellular networks as models for Planck-scale physics. J Phys A 31:7997–8021

    Article  MATH  Google Scholar 

  • Requardt M (2003a) A geometric renormalisation group in discrete quantum space-time. J Math Phys 44:5588–5615

    Article  MathSciNet  MATH  Google Scholar 

  • Requardt M (2003b) Scale free small world networks and the structure of quantum space-time. arXiv.org:gr-qc/0308089

  • Rose H (1993) Topologische Zellulaere Automaten. Master’s thesis, Humboldt University of Berlin

    Google Scholar 

  • Rose H, Hempel H, Schimansky-Geier L (1994) Stochastic dynamics of catalytic CO oxidation on Pt(100). Physica A 206:421–440

    Article  Google Scholar 

  • Saidani S (2003) Topodynamique de Graphe. Les Journées Graphes, Réseaux et Modélisation. ESPCI, Paris

    Google Scholar 

  • Saidani S (2004) Self-reconfigurable robots topodynamic. In: IEEE international conference on robotics and automation, vol 3. IEEE Press, New York, pp 2883–2887

    Google Scholar 

  • Saidani S, Piel M (2004) DynaGraph: a Smalltalk environment for self-reconfigurable robots simulation. European Smalltalk User Group conference. http://www.esug.org/

  • Schliecker G (1998) Binary random cellular structures. Phys Rev E 57:R1219–R1222

    Article  Google Scholar 

  • Tomita K, Kurokawa H, Murata S (2002) Graph automata: natural expression of self-reproduction. Physica D 171(4):197–210

    Article  MathSciNet  MATH  Google Scholar 

  • Tomita K, Kurokawa H, Murata S (2005) Self-description for construction and execution in graph rewriting automata. In: Lecture notes in computer science, vol 3630. Springer, Berlin, pp 705–715

    Google Scholar 

  • Tomita K, Kurokawa H, Murata S (2006a) Two-state graph-rewriting automata. NKS 2006 conference, Washington, DC

    Google Scholar 

  • Tomita K, Kurokawa H, Murata S (2006b) Automatic generation of self-replicating patterns in graph automata. Int J Bifurc Chaos 16(4):1011–1018

    Article  MathSciNet  MATH  Google Scholar 

  • Tomita K, Kurokawa H, Murata S (2006c) Self-description for construction and computation on graph-rewriting automata. Artif Life 13(4):383–396

    Article  Google Scholar 

  • Weinert K, Mehnen J, Rudolph G (2002) Dynamic neighborhood structures in parallel evolution strategies. Complex Syst 13(3):227–244

    MathSciNet  MATH  Google Scholar 

  • Wheeler JA (1982) The computer and the universe. Int J Theor Phys 21:557

    Article  MathSciNet  Google Scholar 

  • Wolfram S (1984) Universality and complexity in cellular automata. Physica D 10:1–35

    Article  MathSciNet  MATH  Google Scholar 

  • Wolfram S (2002) A new kind of science. Wolfram Media, Champaign, pp 508–545

    MATH  Google Scholar 

  • Zuse K (1982) The computing universe. Int J Theor Phys 21:589–600

    Article  Google Scholar 

Books and Reviews

  • Battista G, Eades P, Tamassia R, Tollis IG (1999) Graph drawing: algorithms for the visualization of graphs. Prentice Hall, New Jersey

    MATH  Google Scholar 

  • Bornholdt S, Schuster HG (eds) (2003) Handbook of graphs and networks. Wiley-VCH, Cambridge

    MATH  Google Scholar 

  • Breiger R, Carley K, Pattison P (2003) Dynamical social network modeling and analysis. The National Academy Press, Washington, DC

    Google Scholar 

  • Dogogovtsev SN, Mendes JF (2003) Evolution of networks. Oxford University Press, New York

    Book  Google Scholar 

  • Durrett R (2006) Random graph dynamics. Cambridge University Press, New York

    Book  MATH  Google Scholar 

  • Gross JL, Yellen J (eds) (2004) Handbook of graph theory. CRC Press, Boca Raton

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Andrew Ilachinski .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag

About this entry

Check for updates. Verify currency and authenticity via CrossMark

Cite this entry

Ilachinski, A. (2009). Structurally Dynamic Cellular Automata. In: Adamatzky, A. (eds) Cellular Automata. Encyclopedia of Complexity and Systems Science Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-8700-9_528

Download citation

Publish with us

Policies and ethics