Function Repository Resource:

AggregationSystem

Evolve a 2D array of cells by randomly adding new cells at positions with certain neighborhood configurations

Contributed by: Kabir Khanna and Jonathan Gorard

ResourceFunction["AggregationSystem"][rule,init,t]

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"

totalistic code

"OuterTotalisticCode"

outer totalistic code

"Dimension"

overall dimension (always 2)

"Neighborhood"

type

neigborhood

"Range"

range of rule

"Colors"

number of colors

"GrowthCases"

{g₁,g₂,…}

make a cell 1 when g_i of its neighbors are 1

"GrowthSurvivalCases"

{{g₁,…},{s₁,…}}

1 for g_i neighbors; unchanged for s_i

"GrowthDecayCases"

{{g₁,…},{d₁,…}}

1 for g_i neighbors; 0 for d_i

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},…,{aspec_n,off_n}},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).

t should be a natural number. If t is specified as a list of a certain depth, then the first element of the flattened list will be taken as the input.