Glee.md

Glee

Glee is a low frequency (and ultra-low frequency) chaotic oscillator.

Mathematical basis

Glee is based on the Aizawa Attractor, a system of three differential equations

$$ \frac{\mathrm{d}x}{\mathrm{d}t} = (z - b)x - d y $$

$$ \frac{\mathrm{d}y}{\mathrm{d}t} = d x + (z - b)y $$

$$ \frac{\mathrm{d}z}{\mathrm{d}t} = c + a z - \frac{z^3}{3} - (x^2+y^2)(1 + e z) + f z x^3 $$

The right sides of these equations are all linear functions of $x$, $y$, and $z$. The left sides are all rates of change of these variables with time.

The equations above convert the current location of a particle into a velocity vector that points in the direction the particle must move. No matter where the particle is, Glee calculates its velocity vector and uses it to update the particle's position vector.

Outputs

The outputs are available in two different forms, for convenience:

1. Three separate monophonic output ports for X, Y, and Z respectively.
2. A polyphonic port P that represents the vector (X, Y, Z) using 3 channels.

Knobs

SPEED: This knob allows varying how fast the simulation runs. The default speed is 0, but speed may be set anywhere from −7 to +7. Each unit on this knob's scale represents a factor of 2. That means when you change SPEED from 0 to +3, it will be $2^3=8$ times faster. Thus the speed can made $2^7=128$ times slower than the default by turning the SPEED knob all the way to the left, or 128 times faster than the default by turning it all the way to the right.

CHAOS: This knob controls the value of the $a$ parameter in the first equation. The value of $c$ ranges from 0.5941 to 0.6117, which was experimentally determined to give a wide range of orbital behavior while remaining stable.

CV input

The SPEED and CHOAS knobs have associated attenuverters and CV input ports. Both can be operated over the full knob range using a wide enough attenuverter setting.

Graphing with Tricorder

Tricorder is a 3D oscilloscope designed for compatibility with Glee. If you place a Glee immediately to the left of a Tricorder, Glee will start to feed data into Tricorder, which will plot a 3D graph: