# diffusion
defines the apparent size or spread of a source: from tight point sources to fully spatialized textures. may be mapped per-frequency or per-partial.

## introduction
The diffusion domain sits in the spatial layer, after `position` (static anchor) and `motion` (time-varying trajectories).
It controls how broadly energy is distributed around each source point-shaping apparent size or texture.
All diffusion is precomputed, additive, and deterministic: once `a` and `b` are set, every partial's or frequency band's spread is fixed.

## overview
Each form disperses energy according to a distinct spatial model:
### 0. `uniform_circle`
- Behavior: spreads each partial uniformly within a circular region around its anchor point
- Analogy: scattering pebbles evenly in a disk
- Parameters:
  - `a`: radius of the circle (0 = point → 1 = full stereo half-width)
  - `b`: edge concentration (0 = uniform fill → 1 = all points at the perimeter)
### 1. `gaussian_blur`
- Behavior: distributes energy by a Gaussian profile centered on the anchor
- Analogy: blurry spotlight with soft fall-off
- Parameters:
  - `a`: standard deviation σ relative to field size (0 → narrow → 1 → very wide)
  - `b`: amplitude skew (0 = symmetric → 1 = tail bias toward one side)
### 2. `spectral_spread`
- Behavior: varies spread radius by frequency band, mapping lows vs. highs to different widths
- Analogy: bass feels close and tight, treble feels wide and airy
- Parameters:
  - `a`: cutoff frequency (0 → 20 Hz … 1 → 20 kHz) separating “narrow” vs. “wide” bands
  - `b`: slope of spread change (−1 = wide lows & narrow highs → 0 = neutral → +1 = narrow lows & wide highs)
### 3. `random_texture`
- Behavior: assigns each partial a pseudorandom fixed offset within a specified range, creating a textured cloud
- Analogy: stars sprinkled randomly across the sky
- Parameters:
  - `a`: pseudorandom seed (0…1)
  - `b`: maximum radial deviation (0 = no spread → 1 = full stereo half-width)

## parameter behavior summary
- uniform\_circle
  - `a` controls overall radius;
  - `b` shifts density toward the edge.
- gaussian\_blur
  - `a` sets blur width (σ);
  - `b` skews the Gaussian tail.
- spectral\_spread
  - `a` selects the spectral breakpoint;
  - `b` adjusts how steeply spread changes with frequency.
- random\_texture
  - `a` picks the randomization pattern;
  - `b` scales maximum displacement.

## why these were chosen
- Coverage of diffusion archetypes: uniform, Gaussian, frequency-dependent, and pseudorandom textures capture the main perceptual modes of spatial spread.
- Orthogonal dimensions: each form's logic is distinct and cannot be replicated by parameter tweaking in another form.
- Two-parameter purity: `a` selects topology or pattern, `b` shapes intensity or bias-maintaining parametric simplicity.
- Deterministic and additive: all spreads are computed in advance, aligning with the engine's no-runtime-logic mandate.

## what is not included
- Time-varying or reactive diffusion: those are in the `motion` or structural layers.
- Reverberation or convolution-based spread: outside pure spatial mapping.
- 3D surround or elevation cues: limited to 2D pan-field here.
- Dynamic density changes: onset-driven or envelope-shaped diffusions belong elsewhere.

## conclusion
The diffusion domain delivers four compact, deterministic models for spreading sound sources in space-ranging from precise point-like emission to rich, static textures-complementing `position` and `motion` and fulfilling the project's goal of fully precomputed, structurally grounded spatial synthesis.