Chua's circuit is the canonical chaotic circuit: the simplest electronic system for which chaos has been mathematically proven rather than just observed. It needs one inductor, two capacitors, a handful of resistors, and one component you cannot buy: the Chua diode, a resistor with a negative-slope region in its current-voltage curve.
Building the impossible resistor
Nothing passive has a negative resistance region, so the Chua diode is synthesized: two op-amps and six resistors arranged as a pair of negative impedance converters. Ours used half of a TL082 for each converter, powered from a pair of 9V batteries to keep the supplies clean and floating.
Tuning into chaos
With the values from the classic recipe (18 millihenries, 10 and 100 nanofarads) the behavior is set by a single 2 kilohm trimmer. Winding it slowly walks the circuit through the textbook route to chaos: a steady oscillation first, then the waveform doubling its period, doubling again, and then dissolving into the aperiodic scribble that never repeats. On the scope in X-Y mode, the two capacitor voltages trace the famous double scroll attractor.
The part that makes it worth building rather than simulating: breathing near the inductor visibly shifts the attractor. A chaotic system this small is sensitive enough that the bench itself becomes part of the circuit, which is the entire lesson.