CHAOS AS MUSIC

Hear the Bifurcation Diagram

Developed by Gauransh Bansal

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CHAOS AS MUSIC

Logistic Map: x_n+1 = r x_n (1 - x_n)

Developed by Gauransh Bansal - LinkedIn

r (parameter) 3.679

2.5 (Stable) 4.0 (Chaos)

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What You Hear

As r increases, the system evolves from order to chaos. The musical structure directly reflects this mathematical truth.

Stable (r < 3.0)

Continuous single note.

Period-2 (3.0 < r < 3.45)

Two-note alternating rhythm.

Period-4 (3.45 < r < 3.54)

Four-note repeating pattern.

Chaos (r > 3.57)

Aperiodic, complex texture.

Mapping

Value (x_n) -> Pitch
Velocity (|x_n-x_n-1|) -> Filter
Lyapunov (lambda) -> Dissonance

Lyapunov

lambda 0.0000

Bifurcation Diagram x vs r

Audio Output