LEADER 04677nam 2200697 a 450 001 9910464522503321 005 20200520144314.0 010 $a1-283-23502-1 010 $a9786613235022 010 $a981-4343-64-1 035 $a(CKB)3400000000016486 035 $a(EBL)840565 035 $a(OCoLC)748215484 035 $a(SSID)ssj0000535909 035 $a(PQKBManifestationID)12215972 035 $a(PQKBTitleCode)TC0000535909 035 $a(PQKBWorkID)10545987 035 $a(PQKB)10540299 035 $a(MiAaPQ)EBC840565 035 $a(WSP)00008119 035 $a(Au-PeEL)EBL840565 035 $a(CaPaEBR)ebr10493544 035 $a(CaONFJC)MIL323502 035 $a(EXLCZ)993400000000016486 100 $a20110623d2011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDiscrete systems with memory$b[electronic resource] /$fRamon Alonso-Sanz 210 $aSingapore ;$aHackensack, N.J. $cWorld Scientific$dc2011 215 $a1 online resource (478 p.) 225 1 $aWorld Scientific series on nonlinear science. Series A, Monographs and treatises ;$vv. 75 300 $aDescription based upon print version of record. 311 $a981-4343-63-3 320 $aIncludes bibliographic references and index. 327 $aPreface; Contents; Chapter 1 Cellular Automata and memory; 1.1 Cellular Automata; 1.2 Memory; Disclaimer; Chapter 2 Average type memory; 2.1 Average memory; 2.2 Two-dimensional lattices; 2.2.1 Totalistic rules; 2.2.2 LIFE; 2.3 One-dimensional layers; 2.3.1 Elementary rules; 2.3.2 Nearest and next-nearest neighbors; Chapter 3 Other memories; 3.1 Average-like memory; 3.2 Limited trailing memory; 3.3 Majority of the last three state memory; 3.4 Elementary rules as memory; 3.5 Minimal memory; Chapter 4 Asynchrony and probabilistic rules; 4.1 Asynchrony; 4.2 Probabilistic rules 327 $aChapter 5 Cycles and random sequences5.1 Cycles; 5.2 Random number generation by CA; Chapter 6 Three state automata; 6.1 Totalistic rules; 6.2 Excitable systems; Chapter 7 Reversible dynamics; 7.1 Characterization; 7.2 Reversible rules with memory; Chapter 8 Block cellular automata; 8.1 Characterization; 8.2 Density classification task; Chapter 9 Structurally dynamic systems; 9.1 Introduction; 9.1.1 Reversible SDCA; 9.2 SDCA with memory; 9.2.1 Two state SDCA with memory; 9.2.2 Three state SDCA; Chapter 10 Boolean networks; 10.1 Automata on networks; 10.2 Boolean networks 327 $a10.3 Automata on proximity graphsChapter 11 Coupled layers; 11.1 Coupled cellular automata; 11.2 Coupled Boolean networks; Chapter 12 Continuous state variable; 12.1 Continuous-valued automata; 12.2 Finite difference equations; 12.2.1 One-dimensional maps; 12.2.2 Two-dimensional maps; 12.3 Plane curves; 12.4 Stochastic processes; Chapter 13 Spatial games; 13.1 The prisoner's dilemma; 13.2 Degrees of cooperation and strategies; 13.3 The structurally dynamic PD (SDPD); 13.4 Pavlov versus anti-Pavlov (PAP) in the PD; 13.5 Other spatial games; Appendix A Average memory starting at random 327 $aAppendix B Dynamic with short-term memoryAppendix C Heterogeneous and coupled networks; Appendix D Continuous state variable; Appendix E Spatial games; Bibliography; List of Figures; List of Tables; Index 330 $aMemory is a universal function of organized matter. What is the mathematics of memory? How does memory affect the space-time behaviour of spatially extended systems? Does memory increase complexity? This book provides answers to these questions. It focuses on the study of spatially extended systems, i.e., cellular automata and other related discrete complex systems. Thus, arrays of locally connected finite state machines, or cells, update their states simultaneously, in discrete time, by the same transition rule. The classical dynamics in these systems is Markovian: only the actual configurati 410 0$aWorld Scientific series on nonlinear science.$nSeries A,$pMonographs and treatises ;$vv. 75. 606 $aCellular automata$xMathematical models 606 $aDiscrete-time systems$xMathematical models 606 $aDynamics 608 $aElectronic books. 615 0$aCellular automata$xMathematical models. 615 0$aDiscrete-time systems$xMathematical models. 615 0$aDynamics. 676 $a511.3/5 676 $a511.35 676 $a530.15 700 $aAlonso-Sanz$b Ramon$0959522 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910464522503321 996 $aDiscrete systems with memory$92174334 997 $aUNINA