2025-05-30

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.