2025-05-30

segmentation

divides time into discrete regions via equal durations, proportional ratios, or custom breakpoints-these segments anchor change and transformation.

introduction

the segmentation domain belongs to the structure layer and is responsible for slicing the temporal continuum into static, precomputed regions. segments serve as anchors for applying transformations, layering behaviors, or signaling high-level events. unlike hierarchy (which nestes segments recursively) or ordering (which sequences them), segmentation defines where and how long each region lasts.

overview

each form deterministically partitions a fixed total duration into segments:

0. equal_division

  • behavior: splits total span into n equally long segments
  • analogy: slicing a pie into identical pieces

  • parameters:

    • a: number of segments (2 to 16)

    • b: global phase offset (0 → 1 maps to 0% → 100% shift of the entire grid)

1. ratio_partition

  • behavior: divides span into n* segments whose lengths form a geometric progression
  • analogy: arranging columns whose widths grow by a constant ratio

  • parameters:

    • a: number of segments (2 to 16)

    • b: ratio constant (maps 0 → 1 to r ∈ [1.1 → 3.0])

2. breakpoint_lookup

  • behavior: uses a user-supplied sorted list of fractional breakpoints to define segment boundaries
  • analogy: marking timestamps on a timeline by selecting points from a pre-computed list

  • parameters:

    • a: circular index offset into the breakpoint list (0 → list_length)

    • b: uniform jitter amplitude (0 → 1 maps to ±0% → ±10% of total duration)

parameter behavior summary

  • equal_division

    • a: integer segment count
    • b: fractional shift of the grid

  • ratio_partition

    • a: integer segment count
    • b: geometric growth ratio

  • breakpoint_lookup

    • a: rotation through user breakpoints

    • b: maximum relative jitter applied to all points

why these were chosen

  • complete yet minimal: covers uniform, proportional, and arbitrary (user-defined) slicing methods.
  • orthogonal behaviors: no form can mimic another without external data or additional parameters.
  • two-parameter clarity: each form's a selects topology (count or list index) while b shapes spacing (phase, ratio, jitter).
  • deterministic segmentation: ensures all boundaries are fully known prior to runtime, supporting repeatable downstream processing.

what is not included

  • event-driven or dynamic triggers: those belong to onset domains (grid, field, etc.).
  • nested segmentation or fractal recursion: handled by the hierarchy domain.
  • reordering of segments: managed by ordering.
  • content-based breakpoints (e.g., peaks in amplitude): outside static segmentation scope.

conclusion

the segmentation domain provides three compact, deterministic methods for slicing time-equal, ratio-based, and user-driven-anchoring the broader structure layer in a clear, parametric framework while leaving room for hierarchical or sequential elaboration in adjacent domains.