hierarchy

the hierarchy domain resides in the structure layer, building nested segment architectures by recursively subdividing or combining segments defined by segmentation.
it determines how segments are layered across multiple levels, producing trees, fractals, or mosaic-like tilings.
all hierarchies are static: once parameters a and b are set, the complete multi-level structure is precomputed with no runtime side-effects.

each form constructs a multi-level segmentation map over a fixed total duration:

• nested_equal

  • behavior: every segment is split into d equal parts at each level
  • analogy: russian nesting dolls of identical slices

  • parameters:

    • a: subdivisions per segment (2–8)
    • b: recursion depth (1–4 levels)

• recursive_ratio

  • behavior: applies a geometric partition (ratio r) recursively to each segment
  • analogy: fractal columns whose widths grow by a fixed factor

  • parameters:

    • a: growth ratio r (1.1–3.0)
    • b: recursion depth (1–4)

• fractal_tree

  • behavior: constructs a branching tree where each segment splits into k child segments at every node
  • analogy: a genealogical tree or plant branching pattern

  • parameters:

    • a: branch factor k (2–5)
    • b: tree depth (1–4)

• mosaic_pattern

  • behavior: uses a predefined ratio pattern to subdivide each segment, repeating that pattern recursively
  • analogy: recursive mosaic tiling with a fixed tile shape

  • parameters:

    • a: pattern selector (chooses one of five built-in ratio arrays)
    • b: recursion depth (1–4)

• nested_equal

  • a: how many equal parts each segment yields
  • b: how many levels of recursion

• recursive_ratio

  • a: constant ratio for geometric splits
  • b: recursion levels

• fractal_tree

  • a: number of child branches per segment
  • b: depth of branching

• mosaic_pattern

  • a: index selecting a fixed ratio pattern
  • b: recursion levels

• archetypal coverage: spans the principal recursive paradigms - uniform, proportional, branching, and patterned subdivision
• orthogonal logic: each form embodies a distinct nesting principle, irreducible to the others
• full pre-computation: given a, b, the entire hierarchy is determined offline, ensuring repeatability
• two-parameter purity: every form navigates its space with exactly two meaningful controls

• event-driven or onset-based recursion: belongs in the onset layer
• segment reordering or permutation: handled by the ordering domain
• context-sensitive or dynamic grammars: outside static hierarchy scope
• overlapping/non-nested windows (e.g. sliding): not part of hierarchical segmentation

the hierarchy domain's four forms deliver a compact, deterministic toolkit for multi-level temporal architectures - enabling deep, repeatable structures that integrate seamlessly with upstream segmentation and downstream ordering, without any runtime complexity.