# variation
defines systematic, stateless departures from a base behavior using transformation rules, pseudo-random perturbations, and probabilistic filters. adds local or global diversity without memory, accumulation, or temporal evolution.
### introduction
the variation domain introduces controlled, deterministic stateless modifications to motifs, sequences, or parameter sets. as part of the interplay layer, it applies single-pass transformations that alter content without retaining history - including rule-based changes, fixed-seed randomness, and probabilistic thinning. all behaviors are fully resolved before synthesis and require no internal accumulation or reset logic.
### overview
each form maps parameters `a` and `b` ∈ \[0,1] to perceptually meaningful controls. forms are irreducible, non-overlapping, and temporally flat:
* rule-based
  * behavior: applies a fixed transformation rule to all elements (e.g. rotation, inversion, transposition).
  * analogy: genetic mutation with a predetermined formula
  * a: selects transformation type
  * b: controls transformation intensity
* jitter
  * behavior: applies deterministic pseudo-random offsets to timing, dynamics, or other per-event values.
  * analogy: humanized variation with fixed personality
  * a: maximum perturbation magnitude
  * b: density of affected events
* filter
  * behavior: probabilistically retains or removes events using fixed-threshold logic and biasing.
  * analogy: sieve with adjustable holes
  * a: inclusion probability
  * b: clustering bias (uniform to grouped)
### parameter behavior summary
* rule-based
  * `a`: selects rule (e.g. rotation, inversion)
  * `b`: controls rule intensity or depth
* jitter
  * `a`: max deviation size
  * `b`: fraction of events affected
* filter
  * `a`: base probability of retention
  * `b`: degree of temporal grouping
### why these were chosen
* purity of operation: each form performs a complete, stateless transformation in one pass.
* orthogonality: no overlap between methods-transformative, pseudo-random, and reductive variation are each uniquely represented.
* reproducibility: even stochastic-seeming results are fully deterministic via fixed seeding.
* perceptual clarity: parameters control directly relevant musical attributes.
### what is not included
* accumulating or evolving changes over time: see the `mutation` domain for stateful transformations.
* reactive or conditional variations: dynamic, event-driven changes are handled in the `interaction` domain.
* generative algorithms (e.g. markov, unfolding grammars): these are addressed in `generative pitch` or `pattern`.
* timbre, envelope, or spatial changes: managed separately under their respective layers.
* true randomness: all pseudo-random elements are statically seeded and repeatable.
### conclusion
the `variation` domain offers a compact, deterministic toolkit for stateless transformation. its three forms-rule-based, jitter, and filter-deliver musical diversity with complete reproducibility and no internal memory. for all cases where material must change without evolving or accumulating, this domain defines the essential palette.