Temporal Turing Morph — User Guide

Applies a 1D reaction-diffusion (Turing) process to a sequence of audio segments, using the emergent stripe pattern to creatively reorder them in time. Unlike granular synthesis (ms-scale grains), this operates at the EVENT scale (5ms–2000ms).

Author: Shai Cohen Version: 1.0 (2025) Technique: 1D Turing Reaction-Diffusion Category: Temporal / Experimental / Composition Citation: Cohen, S. (2025). Praat AudioTools

Contents:

What this does Quick start Turing Reaction-Diffusion Theory Preset Strategies Parameters & Controls Visualization & Analysis Applications

What this does

This script implements a Temporal Turing Morph — a creative reordering engine that applies a 1D reaction-diffusion (Turing) process to a sequence of audio segments. The emergent stripe pattern from the Turing instability becomes the reordering logic, creating novel temporal structures based on mathematical pattern formation.

🧪 What is a Turing Reaction-Diffusion Process?

Alan Turing's 1952 paper on morphogenesis proposed that interacting chemicals could form stable patterns (stripes, spots) through reaction-diffusion dynamics. The 1D Gierer-Meinhardt model used here:

dA/dt = D_a·∇²A + r·A·(1 - A/K) - s·A·I dI/dt = D_i·∇²I + r·A - s·I where: A = activator (self-enhancing) I = inhibitor (suppresses activator) D_i >> D_a = Turing instability condition

When D_i >> D_a, the system spontaneously forms periodic stripe patterns. In this tool, the 1D "space" is the sequence of audio segments, and the emergent stripes determine how segments are reordered.

Key Features:

6 Preset Strategies — Temporal Stutter to Tectonic Rupture, plus Custom
Event-Scale Operation — Segments from 5ms to 2000ms (grains to phrases)
Gierer-Meinhardt 1D R-D — Fully implemented with explicit Euler integration
3 Reorder Modes — Sort (Turing rank), Displace (Turing shift), StripeRev (palindrome within stripes)
Arc Modes — Expand-Collapse, Collapse-Regrow, Pulse — shape reaction rate over iterations
Drift & Rupture — Moving hotspot and stochastic burst injection for complex dynamics
Morph Blend — Interpolate between original and Turing order (0-1)
Energy Seeding — RMS envelope seeds the activator so pattern "grows out of" the audio
Comprehensive Visualization — 6-panel display with activator stripe, permutation map, waveforms, energy evolution

Technical Implementation: (1) Segmentation: Divide source into N fixed-length segments. (2) R-D Initialization: Flat+noise or energy-seeded. (3) Iteration: Explicit Euler with reflective boundaries, arc-shaped reaction rate, drift bias, rupture events. (4) Permutation: Compute from final activator pattern (sort, displace, or striperev). (5) Morph Blend: Interpolate with identity, resolve duplicates. (6) Assembly: Apply cosine crossfade, concatenate in final order.

Quick start

In Praat, select exactly one Sound object (minimum 50 ms, any content).
Run script… → select Temporal_Turing_Morph.praat.
Choose Preset (2-7 for specific strategies, 1 for custom).
Set chunk duration (ms) — determines segment size and count.
Configure R-D parameters (diffusion, reaction, inhibition, iterations).
Select reorder mode and adjust max displacement if using Displace mode.
Set morph amount (0 = original order, 1 = full Turing order).
Enable Draw_visualization for analysis display.
Click OK — engine segments, runs R-D, computes permutation, reassembles.

Quick tip: Start with Phrase Scrambler preset on a 10-20 second recording with clear phrasing. Enable visualization — you'll see the Turing activator stripe (blue-orange gradient), the permutation map (deviation from diagonal), and the energy evolution. Listen to how segments are reordered based on the mathematical pattern. The output appears as "source_TemporalTuring" in the Objects window.

Important: CHUNK DURATION determines segment count — must be small enough to give at least 2 segments. TURING INSTABILITY requires D_i >> D_a (the script sets D_i = 4.0 × diffusion_rate, D_a = 0.08 × diffusion_rate). STABILITY of explicit Euler is ensured by dtSafe = 0.85/(4.0×D_i). RUPTURE EVENTS inject bursts of activator energy, creating sudden changes in pattern — use with caution. MORPH BLEND interpolates between identity and Turing order; duplicate resolution ensures valid permutation.

Turing Reaction-Diffusion Theory

The Gierer-Meinhardt Model

📈 1D Reaction-Diffusion Equations

Activator: ∂A/∂t = D_a·∇²A + r·A·(1 - A/K) - s·A·I Inhibitor: ∂I/∂t = D_i·∇²I + r·A - s·I Where: ∇²A = discrete 1D Laplacian over segment index axis: ∇²A[i] = A[i-1] - 2·A[i] + A[i+1] (reflective boundaries) Parameters: D_a, D_i = diffusion rates (D_i >> D_a for Turing instability) r = reaction rate (activator self-enhancement) s = inhibition strength K = saturation ceiling (fixed at 5.0 in script)

Turing instability condition: D_i / D_a must be sufficiently large (typically > 10) for periodic stripe patterns to emerge spontaneously from noise.

Discrete Implementation

For N segments, vectors A[1..N], I[1..N] evolve via explicit Euler: For each iteration: 1. Pad arrays with reflective boundaries: A[0]=A[2], A[N+1]=A[N-1] 2. Compute Laplacian: L[i] = A[i-1] - 2·A[i] + A[i+1] 3. Update: dA[i] = D_a·L_act[i] + r·A[i]·(1 - A[i]/K) - s·A[i]·I[i] dI[i] = D_i·L_inh[i] + r·A[i] - s·I[i] 4. A[i] += dt·dA[i] + noise I[i] += dt·dI[i] 5. Clamp to [0, K] and enforce non-negativity

Arc Modes — Shaping Reaction Rate

📊 Temporal Dramaturgy

The reaction rate r varies over iterations according to arc_mode:

Mode	Description	r(t) profile
Off	Constant r throughout	r(t) = r_base
Expand-Collapse	Rises to peak at 65%, sharp drop after	r(t) = r_base × (1 - arc_strength + arc_strength × f(t)) where f(t) increases to 1 at 65%, then drops rapidly
Collapse-Regrow	U-shaped, minimum at midpoint	r(t) = r_base × (1 - arc_strength + arc_strength × (1 - 4·t·(1-t)))
Pulse	Two sinusoidal cycles of tension/release	r(t) = r_base × (0.5 + 0.5·cos(4π·t))

Arc_strength controls the depth of modulation (0 = constant, 1 = full modulation).

Drift & Rupture

Drift: A Gaussian hotspot moves across segment positions: bias[i] = 1 + drift_strength × exp(-(i - center)² / σ²) where center moves linearly from segment 1 to N over iterations. Rupture: Stochastic bursts of activator energy: With probability rupture_prob per iteration: pick random center, inject burst = rupture_strength × exp(-dist²/2) into activator at nearby positions (distance ≤ 4)

Reorder Modes

Mode	Description	Musical Effect
Sort (Turing rank)	Output segments sorted by ascending Turing activator value	Clusters of similar "energy" — rhythmic crystallization, repeating blocks
Displace (Turing shift)	Each segment shifts forward/back by amount proportional to (A[i] - mean)	Local smearing, memory erosion — Turing high spots pull segments forward, low spots push them back
StripeRev	Within each contiguous Turing stripe (high or low band), internal segment order is reversed	Palindromic micro-structures, retrograde pockets inside forward motion

Morph Blend & Duplicate Resolution

blended[j] = round((1-morph) × j + morph × turingOrder[j]) Duplicate resolution (first-come-first-served): 1. Place unique indices first 2. Fill remaining slots with unused indices in order This ensures final permutation is valid (bijection 1..N → 1..N).

Preset Strategies

Preset 2: Temporal Stutter

⏱️ Frozen Stripe Pattern

Chunk: 20 ms | Diffusion: 2.5 | Reaction: 0.35 | Inhibition: 0.30

Iterations: 50 | Reorder: Sort | Seed: Flat+noise

Character: Short chunks, high diffusion → frozen stripe pattern, stutter-like repetition

Use on: Percussion, glitch textures, rhythmic material

Preset 3: Phrase Scrambler

🔄 Mid-Level Reordering

Chunk: 250 ms | Diffusion: 1.5 | Reaction: 0.60 | Inhibition: 0.30

Iterations: 7 | Reorder: Sort | Seed: Energy-seeded

Character: Medium chunks, volatile reaction — scrambles phrases based on energy

Use on: Speech, instrumental phrases, melodic material

Preset 4: Memory Erosion

🌊 Gradual Displacement

Chunk: 400 ms | Diffusion: 1.2 | Reaction: 0.25 | Inhibition: 0.40

Iterations: 20 | Reorder: Displace | Seed: Energy-seeded

Morph: 0.75 | Max displace: 8

Character: Long chunks, displacement mode — segments shift gradually, eroding original order

Use on: Ambient, drone, long-form textures

Preset 5: Rhythmic Crystal

💎 Tight Stripe Clusters

Chunk: 50 ms | Diffusion: 0.05 | Reaction: 0.15 | Inhibition: 0.85

Iterations: 80 | Reorder: Sort | Seed: Flat+noise

Character: High inhibition → very tight stripes, sorted into crystalline clusters

Use on: Rhythmic patterns, crystallized textures

Preset 6: Narrative Arc

📈 Expand then Collapse

Chunk: 120 ms | Diffusion: 1.2 | Reaction: 0.30 | Inhibition: 0.25

Iterations: 40 | Reorder: Sort | Seed: Energy-seeded

Arc: Expand-Collapse (strength=0.9)

Character: Reaction rate expands then collapses, creating narrative tension arc

Use on: Narrative structures, dramatic builds

Preset 7: Tectonic Rupture

🌋 Drift + Burst Events

Chunk: 80 ms | Diffusion: 1.5 | Reaction: 0.25 | Inhibition: 0.30

Iterations: 35 | Reorder: Displace | Seed: Energy-seeded

Drift: 1.2 | Rupture prob: 0.12

Character: Drifting hotspot plus stochastic bursts — creates sudden ruptures in pattern

Use on: Experimental, chaotic textures, tectonic shifts

Parameters & Controls

Segment Parameters

Parameter	Default	Description
Chunk_duration_ms	80.0	Length of each segment (5-2000 ms)

Reaction-Diffusion Parameters

Parameter	Default	Description
Diffusion_rate	1.0	Scales both D_a (0.08×) and D_i (4.0×) — larger = faster diffusion
Reaction_rate	0.20	Base reaction rate r (activator self-enhancement)
Inhibition_strength	0.30	Inhibition strength s (how strongly inhibitor suppresses activator)
Iterations	25	Number of R-D time steps (1-200)
Pattern_density	0.05	Initial noise amplitude for Flat+noise seed mode

Reorder Parameters

Parameter	Default	Description
Reorder_mode	Sort	Sort (Turing rank), Displace (Turing shift), or StripeRev
Max_displacement_segments	10	Maximum shift in Displace mode (segments)
Morph_amount	1.0	0 = original order, 1 = full Turing order

Seed Mode

Parameter	Default	Description
Seed_mode	Flat+noise	Flat+noise (pure mathematical) or Energy-seeded (RMS envelope)

Arc & Dramaturgy Parameters

Parameter	Default	Description
Arc_mode	Off	Off, Expand-Collapse, Collapse-Regrow, Pulse
Arc_strength	0.8	Depth of arc modulation (0-1)
Drift_strength	0.0	Intensity of moving hotspot (0-3)
Rupture_prob	0.0	Probability of burst event per iteration (0-0.5)

Output Parameters

Parameter	Default	Description
Crossfade_ms	5.0	Cosine fade duration between segments
Normalize_output	1	Scale output to peak 0.99
Draw_visualization	1	Generate 6-panel analysis display
Play_result	1	Audition after processing

Visualization & Analysis

6-Panel Display

Temporal Turing Morph Visualization: Panel 1: TITLE • Script name, source name, segment count, chunk size, iterations, reorder mode, morph amount Panel 2: TURING ACTIVATOR STRIPE • X-axis: Segment index (1 to N) • Y-axis: Activator value A(i) • Vertical bars colored blue→orange gradient (low→high) • Dotted line = mean activator value • Title: "1D Turing activator (stripe structure → reordering)" Panel 3: PERMUTATION MAP • X-axis: Original segment index • Y-axis: Output position • Dotted diagonal = identity • Colored ticks (same gradient) show mapping from original segment to output position • Title: "Permutation map (diagonal = identity, deviation = Turing reorder)" Panel 4: INPUT WAVEFORM • Original waveform with amplitude scale • Title: "Original: filename" Panel 5: OUTPUT WAVEFORM • Reordered waveform in green • Title: "output_filename" • X-axis: Time (s) Panel 6: ACTIVATOR ENERGY EVOLUTION • X-axis: Iteration (1 to iterations) • Y-axis: Mean activator value • Color gradient from blue (early) to orange (late) • Gold dotted line = initial energy • Faint gold line = arc profile (if arc_mode active) • Title: "Activator energy (gold = arc profile, color = iteration progress)" Panel 7: R-D PARAMETER SUMMARY • Diffusion rates, reaction/inhibition, dt, iterations, segment count • Chunk size, morph amount, arc mode & strength, drift, rupture probability • Reorder mode

Reading the Activator Stripe

What the stripes tell you:

Vertical bars: Height = activator value A[i] — higher values indicate "hotter" segments in Turing space
Color gradient: Blue = low, orange = high — visualizes the pattern
Mean line: Segments above/below mean form "stripes" — contiguous runs on same side
Stripe structure: The pattern of highs and lows determines reordering (e.g., in StripeRev mode, each contiguous run is reversed internally)

Reading the Permutation Map

What the ticks mean:

Each tick represents one segment in the output
Horizontal position: Original segment index
Vertical position: Output position (row)
Deviation from diagonal: How much reordering occurred — large deviations = radical restructuring
Clusters: Groups of ticks near same vertical region indicate segments that stayed together in output
Color: Same as activator stripe — helps trace which segments moved where

Applications

Electroacoustic Composition

Use case: Creating novel temporal structures from existing material

Technique: Narrative Arc or Memory Erosion presets on varied sources

Workflow:

Select a 20-60 second recording with clear segmentation potential
Adjust chunk duration to get 20-50 segments
Apply Narrative Arc preset for dramatic shape
Listen to how the Turing pattern creates tension arc
Export and use as movement in larger work

Rhythmic & Glitch Effects

Use case: Creating stutter, glitch, or crystallized rhythms

Technique: Temporal Stutter or Rhythmic Crystal presets on percussive material

Settings:

Stutter: Temporal Stutter (20ms chunks, Sort mode) — creates repeating micro-patterns
Glitch: Tectonic Rupture with drift + rupture — creates chaotic burst textures
Crystallized rhythms: Rhythmic Crystal (50ms, high inhibition) — tight stripe clusters

Sound Design for Media

Use case: Creating evolving textures, transitions, ruptures

Technique: Tectonic Rupture or Memory Erosion on appropriate sources

Applications:

Horror/thriller: Tectonic Rupture with rupture_prob=0.2 — sudden bursts of energy
Sci-fi: Memory Erosion with Displace mode — gradual temporal drift
Transitions: Narrative Arc — builds to peak then collapses

Research & Education

Use case: Demonstrating Turing patterns, reaction-diffusion, morphogenesis

Technique: Enable visualization, compare presets on simple test signals

Learning outcomes:

See how Turing instability creates periodic stripe patterns
Understand relationship between diffusion ratio and pattern formation
Observe how arc modes shape evolution over time
Hear how mathematical patterns translate to temporal structures

Practical Workflow Examples

🎬 Film Scene: Tension Buildup

Goal: Create 45-second tension cue from 30-second drone

Settings:

Source: 30-second low drone
Preset: Narrative Arc
Custom: chunk=150 ms, iterations=60, arc_strength=1.0
Reorder: Sort (Turing rank)

Result: Turing pattern expands then collapses, creating tension arc

🎚️ Electronic Music: Glitch Breakdown

Goal: Create glitchy breakdown from 8-bar drum loop

Settings:

Source: 8-bar drum loop
Preset: Tectonic Rupture
Custom: chunk=30 ms, rupture_prob=0.25, drift_strength=2.0

Result: Chaotic glitch texture with sudden burst events

🎙️ Voice Processing: Temporal Displacement

Goal: Create "memory erosion" effect on spoken phrase

Settings:

Source: 10-second spoken phrase
Preset: Memory Erosion
Custom: morph_amount=0.6 (partial reordering)

Result: Segments gradually shift, creating sense of temporal distortion

Troubleshooting Common Issues

Problem: No pattern formation (activator remains flat)
Cause: Diffusion ratio too low (D_i/D_a < 10), or iterations too few
Solution: Increase diffusion_rate, increase iterations, check inhibition_strength

Problem: Pattern too chaotic/random
Cause: reaction_rate too high, inhibition_strength too low
Solution: Reduce reaction_rate, increase inhibition_strength

Problem: Output has clicks at segment boundaries
Cause: Crossfade too short or not applied
Solution: Increase crossfade_ms (10-20 ms), ensure crossfade applied

Problem: Fewer segments than expected
Cause: chunk_duration_ms too large for source duration
Solution: Reduce chunk_duration_ms, ensure at least 2 segments

Problem: Duplicate resolution creating unexpected order
Cause: morph_amount causing many conflicts
Solution: Reduce morph_amount, or accept that duplicates are resolved deterministically

Advanced Techniques

Custom reaction-diffusion parameters:

Modify the Gierer-Meinhardt equations in the script to use different kinetics (e.g., FitzHugh-Nagumo, Brusselator) for different pattern types.

Multi-channel processing:

For stereo sources, the script converts to mono. To preserve stereo, modify to process each channel separately with same R-D pattern (or different seeds).

Time-varying chunk size:

The script uses fixed chunk duration. For variable segmentation, pre-segment using TextGrid and modify extraction accordingly.

Externally seeded patterns:

Use Energy-seeded mode to have the RMS envelope influence initial pattern. For even more control, modify script to accept external activation vector.