Logistic Equation Chaos Patch

At the Danskmodular meet-up in Copenhagen last week Konstantine got into explaining how one might approach creating a chaos patch on an analogue modular system without using a random/chaos module.

He demonstrated how the logistic equation k*x*(1-x) might be reformulated as k*(x-x^2) so as to make it easier to patch. (Some source reading on the equation can be found here.)

I had a go at putting it together in Audulus, both using the expression node as well as simply using the multiplication and addition nodes.

It turns out to be a simple way of achieving something similar to the kind of chaos spectrum Rob Hordijk achieves with his Rungler. The logistic equation outputs a constant value when k is smaller than 3, followed by a period of doubling with a second bifurcation at 3.5, chaos shortly after 3.577, and 3-step period around 3.83.

It also reminded me of @biminiroad’s look at the difference between chaos and randomness in one of his Audulus live streams almost exactly two years ago.

Logistic Chaos Patch.audulus (35.6 KB)


Very interesting read and illustration patch, thank you!

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