Frolic.md

Frolic

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

Mathematical basis

Frolic is based on the Rucklidge Attractor, a system of three differential equations

$$ \frac{\mathrm{d}x}{\mathrm{d}t} = -2 x + a y - y z $$

$$ \frac{\mathrm{d}y}{\mathrm{d}t} = x $$

$$ \frac{\mathrm{d}z}{\mathrm{d}t} = -z + y^2 $$

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, Frolic 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 $a$ ranges from 3.8 to 6.7, which was experimentally determined to give a wide range of orbital behavior: from highly ordered to highly chaotic. In other words, when the CHOAS knob is set all the way down (−1), the value of $a$ is set to 3.8, resulting in a simple repeated loop. If CHOAS is all the way right (+1), the value of $a$ is set to 6.7 and the output of Frolic will be more chaotic.

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 Frolic. If you place a Frolic immediately to the left of a Tricorder, Frolic will start to feed data into Tricorder, which will plot a 3D graph: