Ian Fritz designed an awesome hyperchaos circuit and gave me the go ahead to let it loose on Eurorack. You can read the discussion on this design on the muffwiggler thread and find the module on ModularGrid .
This is Ian's introduction in his article on the circuit: The Hypster is an electronic fourth-order hyperchaos generator for use in modular electronic music systems.
Hyperchaos is chaos on steroids, with the mathematical divergences being generated in more that the usual single dimension. The module is a unique, original design featuring voltage control of the main system parameters.
In synthesizer applications this module can produce signal waveforms varying from simply periodic to complicated multiperiodic to extremely dense and complex, both in the low frequency control range as well as up into audio frequencies. With an eight-signal output it can simultaneously control a large number of synthesizer parameters or generate multiple audio waveforms for individual processing.
The circuit is built around four voltage-controlled integrators connected in a ring, similar to the configuration of an oscillating ladder filter. But that is where the similarity ends. Each integrator includes damping, making the system more like the 6/8 phase oscillator described on my website. Most importantly, special circuit elements between the four integrators provide the nonlinearities required to produce chaotic oscillations. The gain and resonance of one of the stages may be varied. Varying these parameters produces a wide range of periodic and chaotic signals. These parameters, along with the overall oscillation rate are under voltage control.
It is very wide ranging, from approx 3kHz down to 5 minute orbits, capable of a huge variety of patterns and is particularly partial to being controlled by various CV signals.
Power: 40mA per rail
As the U output runs much hotter than X, Y and Z, the U LED is also much brighter. To balance this, it is a good idea to use a larger valued resistor for U LED's RL (current limiting resistor). typically 2-3 times the value of the other three. For red/blue bi-polar LEDs, usually 4k7 is a suitable value for RL, so for U's RL try 12k or even 15k. Which RL is the one for the U lED? It is the one near the left edge of the PCB (power pins at the top), next to the two 270k resistors.
The Hypster consists of four integrator (chaos) stages connected in a ring. The four outputs are taken at different points in the ring after their respective bit of chaos and signal amplification have been added.
Adding chaos to each stage produces four different outputs, each with slightly different character.
The primary controls on chaos in the module are Damping and Gain.
Damping keeps the circuits in the range of useful, somewhat regular modulation signals. As we'll see later, more damping leads to more regular sine-like oscillations.
There is a fixed Damping value “d” between U, Z, Y, and X.
There is variable Gain and variable Damping before U, so the full damping picture is
~G ~D - (U) - d - (Z) - d - (Y) - d - (X)
In order to understand how each output is different, you can set the module to have full Damping and zero Gain. In this state, the module produces different offsets at each output and the signals are not modulated.
The following screen shots are of a Mordax Data. Flatline scope readings are the values when U is locked into positive or negative ranges.
Zero Gain keeps the U (Yellow) oscillating in either the positive or negative troughs.
X and Z are the same polarity as U, so if U is locked to the positive trough, X will tend positive and modulate in the -1 to +4 range. Z tends to have slightly more amplitude.
Z is similar to X, however Y has an inverted signal (the -Y output is closer to the value on the X output).
In fact, if you monitor +X -Y +Z and -U, in the Curly + Mild position at low Rate, you will get four modulations that are roughly in sync and moving in the same direction (though U has a negative offset).
On the top row, Rate is exponential. Gain and Damp knobs are linear.
The second row of knobs are attenuators on the CV inputs. CV input response is 0 to 10v
3 CV Inputs:
Fine adds to Gain and is about 1/4 the the response of the Gain pot. Once full CW, Gain is not affected by Fine.
There are two switchable Shape parameters, both affecting X and Y outputs.
Squirrelly or Curly
Mild or Wild
Following screen shots of a Mordax Data were taken with a constant rate and no damping. Even if no controls are changed, the chaos circuits will vary the wave shape slightly over time. These screenshot were made in quick succession to show differences between the outputs as controls are changed. These are meant as general guidelines of how the parameters work.
In the Curly + Mild position, with 0 Gain, you get a rather normal sine wave modulation on X.
Y is a little more squared off and Z appears folded or rectified.
In the Curly + Wild position with 0 Gain, the amplitude of U has increased and X has a bit of a ramp.
Back in the Curly + Mild position, raising the Gain to 1/4 knob (or full turn of Fine), the U starts to pass through zero and cause more variance in X and Y. This leads to a pass through zero every other cycle.
The overall Rate affecting U has not changed.
In Curly + Wild position 1/4 Gain looks similar to the Mild position.
Curly + Mild position at Full Gain, 0 Damp, X becomes squared off and Y to becomes folded.
U clips some at +-10V.
However Curly + Wild position at full Gain it appears as if the rate slowed, but in this case it has not. The phasing has just elongated the cycle.
Here is Squirrelly + Mild full Gain no Damp, and the phasing becomes more irregular.
And finally here's crazy Squirrelly + Wild at full Gain no Damp. Looks pretty similar to Squirrelly + Mild.