generates a list representing the evolution of the aggregation system with the specified rule from initial condition init for t steps.
Details and Options
This uses the generalized aggregation model from A New Kind of Science Chapter 7.
Neighborhood configurations are as specified by an outer totalistic cellular automaton rule.
While entering the rule number, one must make sure that "Dimension" is set to 2.
Possible forms for rule are:
{n,{2,1},{1,1}}
9-neighbor totalistic rule
{n,{2,{{0,1,0},{1,1,1},{0,1,0}}},{1,1}}
5-neigbbor totalistic rule
{n,{2,{{0,2,0},{2,1,2},{0,2,0}}},{1,1}}
5-neighbor outer totalistic rule
The following keys can be used to specify a rule given as an association:
"TotalisticCode"
n
totalistic code
"OuterTotalisticCode"
n
outer totalistic code
"Dimension"
d
overall dimension (always 2)
"Neighborhood"
type
neigborhood
"Range"
r
range of rule
"Colors"
k
number of colors
"GrowthCases"
{g1,g2,…}
make a cell 1 whengi of its neighbors are 1
"GrowthSurvivalCases"
{{g1,…},{s1,…}}
1 for gi neighbors; unchanged for si
"GrowthDecayCases"
{{g1,…},{d1,…}}
1 for gi neighbors; 0 for di
Possible settings for "Neighborhood" include:
5 or "VonNeumann"
9 or "Moore"
The number of possible aggregation system rules is as follows:
2D general rules
2512
2D 9-neighbor totalistic rules
210
2D 5-neighbor totalistic rules
26
2D 5-neighbor outer totalistic rules
210
2D outer totalistic rules
217+1
The initial condition specification should be of the form aspec, {aspec,bspec} or {{{aspec1,off1},{aspec2,off2},…,{aspecn,offn}},bspec} (for n>0). Each aspec must be a non-empty array of rank 2 whose elements at level 2 are integers i in the range 0≤i≤"Colors"-1 ("Colors"=2 by default).
tshould be a natural number. If tis specified as a list of a certain depth, then the first element of the flattened list will be taken as the input.