Hénon Map

This module is a generator based on the Hénon map, which for some parameter values exhibits chaotic behavior. It can also converge to a periodic orbit, or diverge into infinity if the values are not constrained.

The Alpha and Beta parameters control the system, which outputs X and Y values. Under some parameter settings the system can get stuck. 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 scales the values to keep them within range, causing a different kind of behavior in the process. This does not directly affect the range of the output, but only the values within the system, before they're scaled and offset (see below). Experiment with the Cap Values knob to find interesting behavior (this knob only takes effect when the cap toggles is engaged).

The Rand button sets the Alpha and Beta knobs to random values for quickly exploring different combinations. But keep in mind that you may also need to inject new values in some cases when the system gets stuck, using the inject button. The small R toggles next to the Cap Values knob determine whether or not it will be randomized.

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.

There are 3 outputs: for the X and Y values, and for the difference between the two. These have an additional attenuator to control the output level, which multiply the signal 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. Sometimes the output values are in the negative range, so you may need to scale by negative numbers to use the output as control voltage.

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.