Walsh Hadamard Agreement & Disagreement for the iterated system HD
This interactive sketch explores how a binary diagonal matrix D interacts with the Walsh–Hadamard mixing matrix H. Each entry of D can be flipped between +1 and -1, dividing the nodes into two groups. The code visualizes two derived operators: ● X = HD + DH ● Y = HD - DH These have a surprisingly clean interpretation: ● X keeps interactions between nodes with the same sign (“agreement”). ● Y keeps interactions between nodes with opposite signs (“disagreement”). Because the Walsh–Hadamard matrix contains only ±1 entries, the resulting matrix values become simple: ● reinforcement: +2 ● cancellation: 0 ● opposite reinforcement: -2 The graph views make this intuitive: ● The graph of X splits into same-sign clusters. ● The graph of Y becomes a bipartite interaction graph between opposite-sign groups. As entries of D are flipped, the system transitions between: ● uniform structure (all signs e...