Four New Ways to Make Chaos with Caudal
- Leonardo
- 5 hours ago
- 5 min read
If you have been following the Caudal story, you know that the module started as a simulation of a four-segment pendulum. Over time, I added the Planets and Fish Tank models, and later the Fluctuations mode inspired by the Buchla Source of Uncertainty. With this update, I'm adding four new operation modes that I've been developing over the past months.
When I designed the original Caudal models, I focused on continuous physical systems: things that move smoothly through space, like pendulums and planets. For this update, I wanted to explore a different territory: systems that exhibit more structured forms of chaos, including oscillator synchronization, feedback loops, discrete-time processes, and nonlinear dynamics.
One thing I find fascinating about these models is where they come from. None of them were originally designed for music; they were developed by scientists trying to understand phenomena in biology, physics, and engineering. The fact that they produce such musically interesting signals is, in a way, a happy accident.
Coupled Oscillators
The first new mode is based on the Kuramoto model, originally developed to study how biological oscillators spontaneously synchronize. One of the early motivations was explaining a spectacular phenomenon: in parts of Southeast Asia, thousands of male fireflies gather in trees at night and flash on and off in perfect unison. The model has since been applied to everything from brain activity to chemical reactions.
In Caudal, the mode features 8 oscillators that can either lock in synchrony or interfere with each other. The Energy control determines the coupling strength. What I find interesting about my implementation is that the oscillators don't lock in phase, they settle with a 1/8 period offset between them. As you change the energy, they may find different stable points with different phase relationships. It's one of those models where small changes in parameters can lead to very different behaviors.
Feedback Dynamics
The second mode is based on the Mackey-Glass system, which was originally developed to model the variation in the relative quantity of mature cells in the blood. The researchers Mackey and Glass were investigating whether chaotic dynamics could exist in physiological systems and whether they might play a role in the complex rhythms observed in hematological diseases. The key insight was that there is a significant delay between the body detecting low cell concentration and the bone marrow producing and releasing new cells, and that delay can produce chaos.
In Caudal, I use coupled delay differential equations with nonlinear feedback. The resulting signals have a distinctive character, sharp transitions mixed with smooth curves, that sounds quite different from the other modes. The Energy control affects the amount of feedback, so you can dial in anything from gentle modulation to full chaos.
Analog Shift Register
This mode is inspired by Tom Whitwell's Turing Machine, one of the most popular Eurorack DIY projects. At its core, the Turing Machine is a binary sequencer built around a 16-bit shift register, a sequencer you can steer rather than program precisely.
My implementation uses 8 analog shift registers to create pseudo-random signals that can be locked. One important difference from the original Turing Machine is that my register values are not binary but analog, which allows for more gradual mutations. The Energy control determines how likely the values are to change, so you can find a sweet spot between repeating patterns and pure randomness.
Since this is a discrete-time model, it needs a clock. The module generates one internally based on the Speed parameter, but you can also feed an external clock through the Sample and Hold input. When you do, the Speed knob becomes a clock divider/multiplier, from dividing by 4 at the lowest setting to multiplying by 4 at the highest.
Kicked Rotors
The last new mode is based on the Chirikov Standard Map, introduced by Boris Chirikov in 1969 at the Institute of Nuclear Physics in Novosibirsk. His work emerged from Soviet research in plasma physics and particle dynamics, where understanding chaotic behavior was essential for magnetic plasma confinement. The physical system it describes is surprisingly simple: a stick rotating frictionlessly around a pivot, receiving periodic kicks, hence the name "kicked rotator." This same principle applies to how circular particle accelerators work, accelerating particles through periodic kicks as they circulate in the beam tube.
In Caudal, the Energy control determines the kick strength, creating a transition from regular to chaotic motion. If you're familiar with the Feigen module, you can think of this as an extended version. Like the Analog Shift Register, it's also a discrete-time system that accepts an external clock.
Why These Four?
Over the years, I have evaluated many different chaotic systems. Some looked interesting on paper but didn't translate well into useful or interesting modulation sources. Others were too similar to what I already had. These four made the cut because each one brings something genuinely different to the table. The Coupled Oscillators give you synchronization phenomena. The Feedback Dynamics produce a unique evolving character. The Analog Shift Register bridges the gap between chaos and sequencing. And the Kicked Rotors offer a different flavor of discrete chaos.
Proper Manual
When I released the first version of Caudal, the manual was a brief description of the controls and modes. It did the job, but it didn't really explain what was going on under the hood. For this update, I decided to rewrite it from scratch.
The new manual is more in the style of the Freak manual, and, if I'm being honest, closer to the scientific papers style I used to write when I was a student. Each mode now includes a description of how the model works, what the energy parameter does to it, and any quirks you should be aware of, like which modes are not perfectly reversible or how the discrete-time models use the Sample and Hold inputs as clock inputs.
You can find the manual on the Caudal product page alongside the firmware.
Caudal in VCV Rack
Caudal was originally released for VCV Rack. Then I ported it to hardware. The next natural step was to port the hardware back to VCV Rack. Now you can try a complete replica of the hardware module as part of the Vult Compacts package.
Getting the Update
You can download the latest firmware from the Caudal product page:
The update process is the same as before: enter bootloader mode by holding HIT and RECALL while pressing Reset, then play the firmware file through the SPEED input jack. If you need a refresher on the process, check the manual on the product page.
I hope these new modes inspire your patches. If you come up with something interesting, I'd love to hear about it.
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