Treść książki
Przejdź do opcji czytnikaPrzejdź do nawigacjiPrzejdź do informacjiPrzejdź do stopki
Searchingthespaceofcellularautomatabasingontheanalysis...
9
CCW
NES
11
00
01
10
sum5=0sum5=1
000
sum5=3
001
010
100
sum5=2
sum5=4
011
101
110
sum5=5
111
Fig.2.Thetruthtableforaruleofthe2DcellularautomatawithvonNeumannneighbourhood.
Sixareas(markedwithdifferentpatternordifferentshade)withthesamenumberofonesin
configurationϑ(t)(sum5=i,i=0,1,2,3,4,5)aredifferentiated
Forthefirstgroupofconfigurationsonlytwofunctionsarepossible-newstate
is0ornewstateis1.Forthesecondgroup-thereare32differentrules.Theycan
beeasylistedonebyone.Butforthethirdgroupthereare1024rules.Itispossible
toputthemtothedifferentclassesthankstotheanalysisofspecialgraphsof
connections.
3.GRAPHSOFCONNECTIONS
Thenewstateofthecellularautomatoncellis“1”ifoneofchosen
configurationsoccurs.Letusputtheattentiontothethird(sum5=2)groupof
configuration.Inthiscasethereare10possibleconfigurations.Theyareshownin
theTable1.Cellsinthestate“1”areblackandtheseinoppositestate“0”are
white.
Table1.Configurationswithsum5=2
{{z
z{{
{
x1
{
z
z
x
{{{
z{z
y1
{
{
z
z
y
{{z
z{{
{
{
z
z1
z
z
{zz
zz{
{
{
{
{
τ1
τ3
{z{
{z{
τ2
z
τ4
{
{
z
Thegraphcreatedforthechosensetofm(m=0,..,10)configurationscontains
all“1”inthenodesandlinesconnecting“1”cellsintheconfigurationareits
branches.Graphscanbeeitheruniqueforgivensetofmconfigurationsorlook
likethesameforafewsetsofmconfigurations.Foreachgraphtheappropriateset
ofrulesdeterminesthesamebehaviourofacellularautomaton.Forinstancethe
