Domov Technology Cellular automata

# Cellular automata

## Relatedcontent

Figure1Demonstrationprogramofcellularautomata(3photos)

Cellularautomatatheorymainlystudiesthetheoreticalmodelofsmallcomputersorcomponentsthatareconnectedinaneighborhoodconnectionmodeintolargercomputersorcomponentsthatworkinparallel.

Mostcellularautomataproduceboringmonotonouspatterns,butsomeofthemarebeyondpeople’sexpectations.

## Classification

(1)Thesimplestone-dimensionalcellularautomata

blackThesquareofisthecurrentcell,andthegraysquaresonbothsidesareitsneighbors.Sincethestatesethasonlytwostates{0,1},thatistosay,thesquarecanonlyhavetwocolorsofblackandwhite,thenanyonesquareplusitstwoneighbors,thestatecombinationofthesethreesquaresThereare8kindsintotal.

(2)Rulesandnumbers

si,t+1=f(si-1,t,si,t,si+1,t)

,Si,t∈{0,1},foranyiandt

Becauseinoursimplestcellularautomaton,allpossiblecombinationsofeachcellanditsneighborstatesarelistedaboveThereare8types,soitsinputisoneofthe8combinationslistedabove.Theoutputrepresentsthestateofeachcellatthenextmoment,andthestatecanonlybe0or1,sotheoutputoftheruleiseither0,or1.Inthisway,anyruleisoneorasetofconversions,

si,t+1=1,Ifsi-1,t+si,t+si+1,t=1

si,t+1=0,ifsi-1,t+si,t+si+1,t=2

si,t+1=1,ifsi-1,t+si,t+si+1,t=3

si,t+1=0,ifsi-1,t+si,t+si+1,t=0

wheresi,t∈{0,1},foranyiandt

Inthiscase,thereareonly4casesofinput,sothefollowingtablecanbeobtained:

Forthesamereason,wecanencodeitas:0101,whichis5indecimal.Obviously,thiscodingmethodisshorterthanthepreviousone,butthiscodingmethodcannotreflectallcellularautomata.

(3)Thedynamicbehaviorofthesimplestone-dimensionalcellularautomata

LookatCellularAutomataNo.208again,itisanumberofdiagonallines.Sinceourboundaryiscyclic,itcanbepredictedthatafterseveralperiodsofoperation,thecellularautomatawillreturntoitsoriginalstate,sosuchacellularautomataiscyclic.Thetimestepelapsedbetweentwoidenticalstatesisthecycleofthiscellularautomaton.LookingatthecellularautomataNo.150andNo.151,theyobviouslyhaveneitherafixedperiodnorapointthattheyareattractedto.Theyareinachaoticanddisorderedstate,whichwecallachaoticstate.Byrepeatedlyrunningthesimplestcellularautomataprogram,itisnotdifficulttofindthatall256typesofcellularautomatacanbeclassifiedintooneofthesethreecategories:fixedvalue,periodiccycle,andchaos.

Basedontheabovediscussion,weclassifycellularautomataintofourcategories,whichare:

I.Fixedvaluetype:cellularautomatastaysinAfixedstate;

II,Periodictype:Cellularautomatacyclicallycirculatesbetweenseveralstates;

III,Chaostype:CellularautomataisinacompletedisorderInarandomstate,thereishardlyanylaw;

IV,complextype:Thecellularautomatamayproducecomplexstructuresintheprocessofoperation.Thisstructureisneithercompletelyrandomnorfixed.Cycleandstatus.