# repetition
defines how motifs or sequences repeat: as copies, decaying echoes, nested variants, or time-shifted mirrors.

### introduction
the repetition domain governs how a core motif or sequence is reproduced over time without altering its intrinsic content. as part of the interplay layer, it enables structural cohesion and recognizability by mapping a motif onto itself through temporal copies, echoes, inversions, and hierarchical nests. all behaviors are pre-resolved and purely additive-no runtime modifications or reactive feedback.

### overview
each form uses parameters `a` and `b` in `[0,1]`, remapped to perceptually relevant variables. forms are irreducible and non-overlapping:
- copy
  - behavior: repeats the motif identically at regular intervals.
  - analogy: photocopy
  - a: number of repeats (1–8)
  - b: interval between repeats (as a proportion of motif length)
- echo
  - behavior: generates successive echoes with diminishing amplitude.
  - analogy: sound bouncing in a canyon
  - a: feedback amount (controls decay rate, 0–0.9)
  - b: delay between echoes (as a proportion of motif length)
- mirror
  - behavior: interleaves the original motif with a time-reversed version.
  - analogy: reflected image
  - a: mix of original vs mirrored (0 = only original, 1 = only mirrored)
  - b: offset before mirrored motif begins
- nested
  - behavior: recursively repeats the motif within scaled time layers.
  - analogy: russian nesting dolls
  - a: number of nesting levels (1–4)
  - b: duration scaling per level (0.5–1.0)

### parameter behavior summary
- copy
  - `a`: maps to repeat count (via `1 + floor(7·a)`)
  - `b`: controls spacing ratio between each repetition
- echo
  - `a`: feedback gain (0 = full decay, 0.9 = near-infinite)
  - `b`: delay time relative to motif length
- mirror
  - `a`: balance between original and mirrored version
  - `b`: time offset of mirrored entry
- nested
  - `a`: number of levels of recursion
  - `b`: duration shrinkage per nesting level

### why these were chosen
- completeness: captures the core types of repetition - literal, decaying, reversed, and nested.
- irreducibility: each form represents a unique behavioral subspace not derivable from combinations of others.
- perceptual clarity: parameters directly reflect musically interpretable quantities.
- structural purity: all repetitions are additive and statically resolved; no feedback or conditional behavior.

### what is not included
- transformational repetitions (e.g. transposition, rhythmic stretching): handled in the `variation` domain.
- stochastic or reactive repeats: non-deterministic variants belong to `field` or `variation`.
- dynamic or timbral evolution across repeats: addressed in `dynamics`, `decorators`, or `envelopes`.

### conclusion
the `repetition` domain defines how motifs reappear without transformation. its four forms-copy, echo, mirror, and nested-provide a compact, orthogonal set of strategies for creating recognizable structure through recurrence. fully deterministic and irreducibly distinct, they anchor the interplay layer with time-based cohesion.