Usage
The core of the Bifurcator is the iterative logistic map function: xn+1 = rxn(1 - xn) When iterated across 2 ≤ r ≤ 4, this produces the characteristic bifurcation diagram. In Bifurcator:- Current output (and initial “load value”) ranges from 0 to 65535, mapping to x in range 0.0 to 1.0
- Parameter ranges from 0 to 65535, mapping to r in range 2.0 to approximately 4.0
Load Value
The first value of x is set with the load value. It must be set to a non-zero value, otherwise the next iteration would also be zero… and the next one too… and so on, generating silence. Default is 1. Different load values will cause different “attack” sounds before the iterations stabilize (if they do).Parameter
By varying the parameter, the values of x may change drastically, producing a variety of sounds. The higher the parameter, the more “chaos” is present, effectively yielding noise.- Below 32768: Output converges to a single value (effectively no sound)
- 32768 to 47496: Output bifurcates to oscillate between 2 values, generating a square wave
- 47497 to 51433: Bifurcates again to a period of 4 values
- Beyond that: System rapidly becomes chaotic (noise)
- Around 59914: An “island of stability” where output oscillates between 3 values, then bifurcates from there
Effects
10xx: Set low byte of load state11xx: Set high byte of load state12xx: Set low byte of parameter13xx: Set high byte of parameter