Thomas Attractor

This module is based on the Thomas attractor, a 3D strange attractor originally proposed by René Thomas. This is a 1-parameter system of 3 differential equations with 3 continuous output values, which are calculated using a forward Euler solver. The system behaves chaotically under certain values of b, and the output is cyclically symmetric in its simple form.

The b knob controls the behavior of the system. It can be CV controlled with the input below it.

The dT knob controls the increment used at every sample step to numerically solve the equations. You can think of this as the step size, but keep in mind that this is a continuous system. You can use a sample and hold or a quantizer after the output if you want to use discreet values.

Pressing the inject button will introduce new random values into the system to reset it, but some combinations of values will always return to a steady state after a few iterations.

The cap toggle modifies the values in the system to keep them within a restricted range, causing a different kind of behavior in the process. The switch next to it lets you select between two different algorithms for restricting the values, each of which will result in a slightly different behavior (this switch only takes effect when the cap toggles is engaged). Experiment with the cap toggle and switch to find interesting of b. Both the toggle and the switch can be CV controlled by sending triggers to them to change the state.

The respective scale and offset knobs allow you to easily adjust the range of produced values for musical purposes. Keep in mind that if the scale knobs are set to zero there will be no output.

The module has 4 outputs: X, Y and Z, and a mix of the three. These all have their own attenuator to control the output levels, which multiply the signals after the scale and offset.

It is usually a good idea to connect the outputs to oscilloscopes, to have a clearer idea about what's going on, especially regarding ranges.

This system can produce a wide range of behaviors and noise types when controlling oscillators. Use your ear and experiment to find sweet spots and interesting settings.

This module is part of the Benard Mega Bundle Vol. 3.

For an animation of the Thomas attractor, have a look here: https://www.cake23.de/thomas-attractor.html