Novel Synthesis Method III · 2026

Strange Attractor
Trajectory Synthesis

A particle traces an orbit through 3D chaotic phase space. Its trajectory — never repeating, never settling — becomes the audio waveform. Morph between Lorenz, Rössler and Thomas attractors in real time.

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X position
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Y position
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Z position
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Velocity |dr/dt|
Lorenz
Active Attractor
LORENZ
THOMAS
Phase Portrait (click + drag to rotate)
ODE Parameters
Lorenz σ · ρ · β
Rössler a · b · c
Thomas b
Audio Output
Out
Sound Shaping
LFO → Attractor Parameter Modulation
Reverb
Delay
RK4 Integration · Interpolated Attractor System
Lorenz: dx/dt = σ(y−x) · dy/dt = x(ρ−z)−y · dz/dt = xy−βz
Rössler: dx/dt = −y−z · dy/dt = x+ay · dz/dt = b+z(x−c)
Thomas: dx/dt = sin(y)−bx · dy/dt = sin(z)−by · dz/dt = sin(x)−bz

State vector [x,y,z] evolves via RK4. Morph parameter α∈[0,2] interpolates derivatives between all three systems. Audio output is any projection of the trajectory. Parameter bifurcations create sudden timbral jumps — ρ≈24.74 is the onset of chaos in Lorenz. b≈0.329 is Thomas bifurcation point.