Cellular Automata

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1、ThePlan•AutomataCellularAutomata–VonNeumanntoWolfram•DemonstrationsThegameoflifeoranewkindof–GameofLifeprogramscience?–DevelopedbyJimFix–BehaviorsdevelopedbyhighschoolstudentsRichardLadner–SophisticatedbehaviorsimplementedbySamCoskey12WhatareCellularWhatareCellularAutomata?Au

2、tomata?“Cellularautomatahavebeeninventedmanytimesunder“WhenImademyfirstdiscoveriesaboutcellularautomatadifferentnames…Inpuremathematicstheycanberecognizedintheearly1980sIsuspectedthatIhadseenthebeginningasabranchoftopologicaldynamics,inelectricalengineeringofsomethingimportan

3、t.ButIhadnoideajusthowimportanttheyaresometimescallediterativearrays,andhighschoolitwouldallultimatelyturnouttobe.Andindeedoverthepastkidsmayknowthemasasortofhome-computergame.twentyyearsIhavemademorediscoveriesthanIeverthoughtTheyhavebeenusedandabusedbyinterdisciplinarypossi

4、ble.AndanewkindofsciencethatIhavespentsomuchscientistsaswellasinterdisciplinarybumblers.”effortbuildinghasseemedanevermorecentralandcriticaldirectionforfutureintellectualdevelopment.”ToffoliandMargousCellularAutomataMachinesStephenWolfram1987ANewKindofScience320024Automata?Au

5、tomatonExample•AutomataisthepluralofautomatonCokemachine•Simplecomputingdevice–Inputs:•Propertiescoins,bills,returnbutton,choicebuttons–Finitesetofstates–State:–Transitionsfromstatetostatemoneyenteredsofar,…•Sensetheenvironment.–Outputs:•Possiblychangetheenvironment.coke,spri

6、te,dr.pepper,•Gotoanewstate,returnedcoins,…561OtherExamplesCellularAutomata•Automataarearrangedgeometrically•Allautomataareidentical•Allautomatachangestatesimultaneouslycell4Neighbors8Neighbors78CommunicationOne-Dimensionalrule……•Eachcellhasaleftandrightneighbor•Allcellsident

7、ical•Inputsarestatesofneighborsandself•Cellcanbeinitializedtodifferentstates•Outputisthestate(indicatedbycolor)910TwoStateExampleRule90Rule254128643216842Rule90=64168211122Rule90Rule301314Two-DimensionalGameofLife•Eachcellis“live”or“dead”•Transitionrules–N=numberofliveneighbo

8、rsamongthe8–N
1death(loneliness)–N=2nochange–N=3birth–N4death(o