Dan Slater's Article in CMJ, and X to the kth power - how do you do it?
costello at seanet.com
Wed Jul 29 04:32:55 CEST 1998
The new Computer Music Journal (Volume 22, Number 2, Summer 1998)
finally hit the stands. Dan Slater has a fascinating article in it -
"Chaotic Sound Systems." Y'all gotta track it down.
Anyway, Mr. Slater describes a hypothetical Buchla module (complete with
an "artist's conception" that points out how truly beautiful the Buchla
200 designs were visually) that would implement a Ueda Attractor. As
described, the Ueda attractor circuit is very similar to a
state-variable filter, but with the inverting stage replaced with an x^3
stage (x cubed) and the signal input connected to the first integrator
stage. Slater's hypothetical module uses an x to the k function, where
the circuit can be converted from a state variable topology to an Ueda
Attractor by changing the value of k (for a state-variable filter, k=1;
for the Ueda attractor, k=3).
How the heck would you do this? Is there some common circuit that
produces an x to the k function, where k can smoothly vary (i.e. by
non-integer values) between 1 and 4? x^1 is simple; x^2 could be a
multiplier where the input is multiplied by itself; x^3 could be created
by a second multiplier multiplying the input by the product of an x^2
stage. But how do you get, say, x^2.74? And how do you vary these
smoothly? Could you use feedback from a multiplying stage, where a
signal is multiplied by the output of the multiplier? Or maybe feedback
in a 2-multiplier configuration?
As always, any and all advice welcome. I think that this would be a
cool circuit to own.
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