Ornstein-Uhlenbeck brownian motion for TouchDesigner. A Script CHOP that generates smooth, mean-reverting procedural noise with rotation support and fractal detail — perfect for organic camera drift, floating objects, generative motion, and anything that needs to feel alive.
Unlike random noise, Ornstein-Uhlenbeck motion always pulls back toward center — so you get natural, bounded wandering instead of unbounded drift.
- Exact OU math — Gillespie 1996 analytical transition, zero discretization error
- Implicit spring — Klak-style filter, unconditionally stable at any timestep
- Rotation noise — independent OU process with its own speed and per-axis amplitude
- 1/f pink noise detail — Voss-McCartney algorithm adds organic micro-texture
- Per-axis range — different min/max bounds per axis
- Speed-independent smoothing — texture changes without affecting perceived speed
- Deterministic — set a seed for repeatable motion
- 26 automated tests — validated at extreme parameters
Requires TouchDesigner 2025+
- Download the .tox from Releases
- Drag into your TouchDesigner project
- Wire the CHOP output to whatever needs motion
Outputs six channels: tx, ty, tz, rx, ry, rz.
| Parameter | Default | Description |
|---|---|---|
| Speed | 1.0 |
Time-scale multiplier. 1 = real-time, 5 = 5x faster. 0 = frozen (instant stop). Transitions are smoothed. |
| Amplitude | 1.0 |
Output multiplier. 0 = silence, 1 = full range. |
| Center Pull | 2.0 |
How strongly motion pulls back toward anchor (theta). High = tight orbit. Low = lazy wander. 0 = pure Brownian, no pull. |
| Smoothing | 0.5 |
Spring filter. 1 = very smooth (~2s settling). 0 = minimal filtering. Controls texture, not speed. |
| Detail | 0.0 |
Voss-McCartney 1/f pink noise micro-texture. 0 = off. Respects Smoothing. |
| Detail Layers | 3 |
Fractal octaves for Detail (1-5). More = richer frequency content. |
| Parameter | Default | Description |
|---|---|---|
| Range Min / Max | [-1, 1] |
Output bounds. Normalized OU state maps to this range. Set to [0, 100] and channels wander between 0 and 100. |
| Per-Axis Range | Off |
Toggle per-axis min/max. On = each axis gets its own bounds. |
| Range Min/Max X, Y, Z | [-1, 1] |
Per-axis bounds (visible when Per-Axis Range on). |
| Parameter | Default | Description |
|---|---|---|
| Enable Rotation | Off |
Master toggle. When off, rx/ry/rz output zero. |
| Rotation Speed | 1.0 |
Independent speed for rotation. Separate from position Speed. |
| Pitch / Yaw / Roll | 5 / 5 / 0 |
Amplitude in degrees per axis. 0 disables that axis. Shares Center Pull and Smoothing with position. |
| Parameter | Default | Description |
|---|---|---|
| Affect X / Y / Z | All on |
Per-axis enable toggles. Disabled axes output zero. |
| Parameter | Default | Description |
|---|---|---|
| Anchor X / Y / Z | 0 |
Drift target in normalized [-1, 1] space. 0 = center of range. 0.5 = hang out in upper half. |
| Seed | 0 |
0 = unseeded (different every run). Any other value = deterministic, same motion after Reset. |
| Independent Axes | On |
ON = each axis gets its own noise (3D wandering). OFF = shared noise (lockstep diagonal). |
| Reset | Pulse |
Snap to anchor positions and re-seed. Fresh start. |
Three-stage pipeline, all running without substep loops:
1. Exact OU Transition (Gillespie 1996)
decay = exp(-theta * dt)
X = mu + (X - mu) * decay + sigma * sqrt((1 - exp(-2*theta*dt)) / (2*theta)) * Z
Where theta is Center Pull, mu is Anchor, and sigma = 0.55 * sqrt(2*theta) is tuned so the stationary distribution fills ~80% of the [-1,1] range regardless of theta. Zero discretization error at any timestep.
2. Voss-McCartney 1/f Detail (applied before spring)
Multiple independent OU processes updating at halved rates (layer 0 every frame, layer 1 every 2 frames, layer 2 every 4, etc.), summed with halving amplitude. Produces true 1/f pink noise — the spectral profile humans perceive as "natural." Added to the OU state before filtering so Smoothing controls detail too.
3. Implicit Spring Filter (Klak-style)
vel = (vel - (pos - target) * omega^2 * dt) / (1 + omega * dt)^2
pos += vel * dt
Unconditionally stable at any timestep. Omega scales with sqrt(speed) so smoothing character is preserved at all speeds. Runs on real frame time (decoupled from simulation speed).
MIT — use it however you want.