Recursive Patterns & Decomposition

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Abstractions about nested symbolic patterns, recursive number sequences, perceptual matching, and divide-and-conquer decomposition.

5 abstractions in this family — domain-specific abstractions that sit near one another in structural-signature space (k-means over structural-signature embeddings). Each is shown with its short description.

• ABACABA pattern — A recursively generated word obtained by placing a new central symbol between two copies of the preceding word, producing lengths one less than powers of two.
• Divide-and-conquer algorithm — Solve a problem by splitting each non-base instance into smaller related subproblems, solving those recursively, and combining their results into the original answer.
• Gestalt pattern matching — A recursive string-similarity algorithm that anchors on a longest common substring and repeats on the unmatched left and right regions.
• Nested word — A finite or infinite linear word augmented with a properly nested matching relation between call and return positions, representing sequential order and hierarchical structure in one object.
• Ulam number — Generate a seed-dependent increasing integer sequence by repeatedly choosing the least larger integer having exactly one representation as a sum of two distinct earlier terms.