kx^2 - 1

Type: Module

Category: Source

Updated: Mar 23, 2020

Manufacturer: Benard

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This module is a chaotic generator implementing the simple discrete mapping kx^2 - 1, as described in Ian Steward's classic book "Does God Play Dice? The New Mathematics of Chaos".

The k parameter controls the behavior of the system, which can go from cyclic to chaotic, going through period doubling transitions along the way and points of stability.

The polarity switch allows you to quickly adjust the range of the signal for different uses. You can also adjust the range with the scale and offset controls on the right, and then with the out level knob. The signal is scaled in the above order.

The inject button sends a new random value to the system to restart it.

You can use this module to produce chaotic melodies at slow rates, or noise and FM textures at higher clock rates. Experiment with settings of k to find interesting points, and adjust it to move between order and chaos.

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

For more details about the equation, have a look here: https://www.annanardella.it/chaos.html#chaos