Linear progression scalar to vector
Coupled interactions and vector-like dynamics within the Independent Asymmetrical Determinate Systems (IADS) subsets of this cellular automaton system: Symmetrical Determinate System (SDS): A one-dimensional array of points P = {p1, p2, ..., pn} Each point pi has a scalar value vi Uniform rules apply across the SDS Independent Asymmetrical Determinate Systems (IADS): Subsets Pk ⊂ P, each governed by a rate ri These subsets exhibit coupled interactions as ri increases Limits and Rates: Limit L: A constant parameter that restricts the maximum range of value transfer Rate ri: A variable parameter that determines the influence of neighboring points within an IADS subset Coupled Dynamics: For a point pi within an IADS governed by rate ri: When ri = 1: vi(t+1) = vi(t) + f(vi(t)) The value at pi depends only on its current value When ri > 1: vi(t+1) = vi(t) + Σ(j=-L to L) wij * f(vi+j(t)) wij represents the weight/influence of neighboring point pi+j on pi f(vi+j(t)) describes the cont...