Detail of a circuit sculpture in the shape of a lighthouse

Op Amp Contest: This Lighthouse Sculpture Flickers In The Rhythm Of Chaos

Op amps are typically used to build signal processing circuits like amplifiers, integrators and oscillators. Their functionality can be described by mathematical formulas that have a single, well-defined solution. However, not every circuit is so well-behaved, as Leon Chua famously showed in the early 1980s: if you make a circuit with three reactive elements and a non-linear component, the resulting oscillation will be chaotic. Every cycle of the output will be slightly different from its predecessors, and the circuit might flip back and forth between different frequencies.

A circuit sculpture in the shape of a lighthouseA light modulated with a chaotic signal will appear to flicker like a candleflame, which is the effect [MaBe42] was looking for when he built a lighthouse-shaped circuit sculpture. Its five differently-colored LEDs are driven by a circuit known as Sprott’s chaotic jerk circuit. A “jerk”, in this context, is the third-order derivative of a variable with respect to time – accordingly, the circuit uses three RC integrators to implement its differential equation, along with a diode to provide nonlinearity.

The lighthouse has three chaotic oscillators, one in each of its legs. Their outputs are used to drive simple pulse-width modulators that power the LEDs in the top of the tower. [MaBe42] used the classic LM358 op amp for most of the circuits, along with 1N4148 diodes where possible and 1N4004s where needed – not for their higher power rating, but for their stronger leads. As is common in circuit sculptures, the electronic components are also part of the tower’s structure, and it needs to be quite sturdy to support its 46 cm height.

[MaBe42] used 3D printed jigs to help in assembling the various segments, testing each circuit before integrating it into the overall structure. The end result is a beautiful ornament for any electronics lab: a wireframe structure with free-hanging electronic components and randomly flickering lights on top. Want to learn more about circuit sculpture? Check out this great talk from Remoticon 2020.

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Chaos Theory In Practice: Chua’s Circuit

Chua’s circuit is the simplest electronic circuit that produces chaos—the output of this circuit never repeats the same sequence, and is a truly random signal. If you need a good source of randomness, Chua’s circuit is easy to make and is built around standard components that you might have lying around. [Valentine] wrote a comprehensive guide which walks you through the process of building your own source of chaos.

The chaos of Chua’s circuit is derived from several elements, most importantly a nonlinear negative resistor. Unfortunately for us, this type of resistor doesn’t exist in a discrete form, so we have to model it with several other components. This resistor, also known as Chua’s diode, can be created with an op-amp configured as a negative impedance converter and a couple pairs of diodes and resistors. Other variations such, as the schematic above,22`01 model Chua’s diode using only op-amps and resistors.

The rest of the circuit is quite simple: only two capacitors, an inductor, and a resistor are needed. [Valentine] does note that the circuit is quite sensitive, so you might encounter issues when building it on a breadboard. The circuit is very sensitive to vibration (especially on a breadboard), and good solder connections are essential to a reliable circuit. Be sure to check out the Wikipedia article on Chua’s circuit for a brief overview of the circuit’s functionality and a rabbit trail of information on chaos theory.

Generating Truly Random Sequences

Your brain can’t generate random numbers, and computers can’t either. Most of the ‘random’ numbers we come across in our lives are actually pseudorandom numbers; random enough for their purpose, but ordered enough to throw statistical analyses for a loop. [Giorgio] thought generating random sequences would make for an excellent project, so he whipped up a random sequence generator out of a few Opamps, resistors, and a handful of caps.

[Giorgio] used a Chua Circuit – a circuit that models nonlinear equations – to create a chaotic system. When pairs of points from these systems of equations are plotted on a graph, a fabulous and chaotic ‘double scroll’ pattern (seen above) can be found. After taking oscilloscope probes to different points on his Chua circuit, [Giorgio] watched chaos magically appear on his ‘oscope screen.

The double scroll pattern isn’t exactly random, but since the Z signal of his circuit chaotically varies between positive and negative, the only thing needed to create a random sequence of 1s and 0s is sending the Z signal through a comparator.

After calibrating and sampling his circuit [Giorgio] captured thousands of samples at a rate of 5 samples per second. From a cursory glance, it looks like [Giorgio]’s circuit is at least as good as flipping a coin, but proper tests for randomness require many more samples.

A very, very cool piece of work that is much, much more elegant than getting random bits from a Geiger counter.