sc3.synth.ugens.chaos module¶

Non-linear Dynamic Sound Generators¶

Lance Putnam 2004 | lance@uwalumni.com

This is a set of iterative functions and differential equations that are known to exhibit chaotic behavior. Internal calculations are done with 64-bit words to ensure greater accuracy.

The name of the function is followed by one of N (none), L (linear), or C (cubic). These represent the interpolation method used between function iterations.

class ChaosGen(*args, **kwargs)¶

Bases: sc3.synth.ugen.UGen

Base class for chaos generators.

class QuadN(*args, **kwargs)¶

Bases: sc3.synth.ugens.chaos.ChaosGen

x1 = a * x0 ** 2 + b * x0 + c

classmethod ar(freq=None, a=1, b=- 1, c=- 0.75, xi=0)¶

class QuadL(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.QuadN

class QuadC(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.QuadN

class CuspN(*args, **kwargs)¶

Bases: sc3.synth.ugens.chaos.ChaosGen

x1 = a - b * sqrt(abs(x0))

classmethod ar(freq=None, a=1, b=1.9, xi=0)¶

class CuspL(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.CuspN

class GbmanN(*args, **kwargs)¶

Bases: sc3.synth.ugens.chaos.ChaosGen

x1 = 1 - y0 + abs(x0) y1 = x0

classmethod ar(freq=None, xi=1.2, yi=2.1)¶

class GbmanL(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.GbmanN

class HenonN(*args, **kwargs)¶

Bases: sc3.synth.ugens.chaos.ChaosGen

x2 = 1 - a * (x1 ** 2) + b * x0

classmethod ar(freq=None, a=1.4, b=0.3, x0=0, x1=0)¶

class HenonL(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.HenonN

class HenonC(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.HenonN

class LatoocarfianN(*args, **kwargs)¶

Bases: sc3.synth.ugens.chaos.ChaosGen

x1 = sin(b * y0) + c * sin(b * x0) y1 = sin(a * x0) + d * sin(a * y0)

classmethod ar(freq=None, a=1, b=3, c=0.5, d=0.5, xi=0.5, yi=0.5)¶

class LatoocarfianL(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.LatoocarfianN

class LatoocarfianC(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.LatoocarfianN

class LinCongN(*args, **kwargs)¶

Bases: sc3.synth.ugens.chaos.ChaosGen

x1 = (a * x0 + c) % m

classmethod ar(freq=None, a=1.1, c=0.13, m=1.0, xi=0)¶

class LinCongL(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.LinCongN

class LinCongC(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.LinCongN

class StandardN(*args, **kwargs)¶

Bases: sc3.synth.ugens.chaos.ChaosGen

x1 = (x0 + y1) % (2 * pi) y1 = (y0 + k * sin(x0)) % (2 * pi)

classmethod ar(freq=None, k=1.0, xi=0.5, yi=0)¶

class StandardL(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.StandardN

class FBSineN(*args, **kwargs)¶

Bases: sc3.synth.ugens.chaos.ChaosGen

x1 = sin(im * y0 + fb * x0) y1 = (a * y0 + c) % (2 * pi)

classmethod ar(freq=None, im=1, fb=0.1, a=1.1, c=0.5, xi=0.1, yi=0.1)¶

class FBSineL(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.FBSineN

class FBSineC(*args, **kwargs)¶: Bases: sc3.synth.ugens.chaos.FBSineN

class LorenzL(freq=None, s=10, r=28, b=2.667, h=0.05, xi=0.1, yi=0, zi=0)¶

Bases: sc3.synth.ugens.chaos.ChaosGen

Lorenz chaotic generator.

Rates

ar (default)

Parameters

freq – Iteration frequency in Hertz, defaults to SampleRate.ir() / 2
s – Equation variable, defaults to 10
r – Equation variable, defaults to 28
b – Equation variable, defaults to 2.667
h – Integration time step, defaults to 0.05
xi – Initial value of x, defaults to 0.1
yi – Initial value of y, defaults to 0
zi – Initial value of z, defaults to 0

Notes

A strange attractor discovered by Edward N. Lorenz while studying mathematical models of the atmosphere. The system is composed of three ordinary differential equations:

x' = s * (y - x)
y' = x * (r - z) - y
z' = x * y - b * z

The time step amount h determines the rate at which the ODE is evaluated. Higher values will increase the rate, but cause more instability. A safe choice is the default amount of 0.05.

classmethod ar(freq=None, s=10, r=28, b=2.667, h=0.05, xi=0.1, yi=0, zi=0)¶