Analogue Chaos Generator PCB

What it is

This is a personal project I made because I wanted to see strange attractors running in real hardware, not just simulated. The board implements four different chaotic dynamical systems — the Lorenz attractor, Chua attractor, Rössler attractor, and Duffing oscillator — all in pure analogue electronics. Plug two of the outputs into an oscilloscope in X-Y mode and you get the classic strange attractor shapes tracing out in real time.

No microcontrollers, no DACs, no lookup tables. Just op-amps, resistors, capacitors and a couple of analogue multipliers doing maths continuously.

The circuits

Each attractor is its own self-contained sub-circuit on the board. They can be switched on and off independently.

Lorenz attractor — the classic one. Three coupled differential equations with two nonlinear terms (XY and XZ). Those nonlinear terms are implemented with AD633 four-quadrant analogue multipliers, and the integration is done with TL074 op-amp integrators. The σ, ρ and β parameters are set by resistor ratios, with potentiometers for live tuning. Watch the butterfly appear.

Chua attractor — produces a double-scroll pattern. This one’s interesting because it uses a gyrator network (op-amps arranged to behave like an inductor) instead of actual inductors. The nonlinear resistor element that makes the Chua circuit work is built from op-amps and diodes. It’s a slightly awkward circuit to get stable but the double-scroll it produces is very satisfying.

Rössler attractor — simpler than the Lorenz, only one nonlinear term so it only needs one AD633. Single-scroll output. Easier to tune and a good one to start with if you’re new to this kind of thing.

Duffing oscillator — a nonlinear driven oscillator rather than an autonomous system. You drive it with an AC signal and the cubic nonlinearity in the feedback produces chaotic behaviour above certain amplitudes. The frequency and Q factor are adjustable.

A lot of the op-amp building blocks here — the integrators, summing amplifiers, and gyrator construction — came directly from circuit patterns in The Art of Electronics by Horowitz and Hill.

Why analogue?

The short answer is that it’s more interesting and harder. A microcontroller running the Lorenz equations in software is a solved problem you can find on any Arduino forum.

Doing it in analogue means you’re implementing the actual differential equations directly as physical circuits — the current through a capacitor is literally integrating a voltage over time. The chaos is real, not computed. Noise, component tolerances, and temperature all affect the behaviour in ways that simulation doesn’t capture.

It also means every parameter change — tweaking a pot, swapping a resistor — is an immediate physical change to the system rather than a line of code. That’s a nice way to build intuition for how these systems work.

Power

The board runs from a single 12V DC input and generates ±15V analogue rails internally using an LTC3265 charge pump. This was the main alternative to using a dual-rail bench supply or a big linear transformer, and it keeps everything self-contained. The ±15V gives the op-amps enough headroom to swing the signal amplitudes I wanted without clipping.

There’s also a 3.3V LDO for the control logic side.

Signal routing & outputs

A rotary switch handles signal routing between the attractor outputs and the board’s coaxial output connectors. Each circuit has test points on all three axes (X, Y, Z) so you can probe intermediate signals without having to touch the circuit directly — useful for debugging and also for feeding into a scope without clip leads flopping around everywhere.

There are 34 test points total across the board. Probably overkill but I’d rather have too many than spend time hunting signals with a probe tip.

Component notes

The AD633 analogue multipliers are doing most of the heavy lifting for the nonlinear terms. They’re not cheap (~£8 each, 3 on the board) but there’s not really an alternative if you want four-quadrant multiplication with decent bandwidth and accuracy. The TL074 quad op-amps handle everything else — integration, summing, buffering, the gyrator in the Chua circuit.

Potentiometers let you tune the chaos parameters in real time. If you push the Lorenz too far off its nominal parameter values it stops being chaotic and settles into a limit cycle or diverges — exploring that boundary live is genuinely interesting.

Manufactured by PCBWay, submitted July 2025.