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)