Chuanna

Chuanna wires up five parts on her breadboard, and out spills a ribbon that loops around two points and never repeats.

The Physics

Leon Chua designed a simple autonomous electronic circuit in 1983: two capacitors, an inductor, a resistor and one piecewise-linear nonlinear resistor, the Chua diode. It oscillates chaotically. The orbit loops around two unstable equilibria and jumps irregularly between them, tracing the “double scroll”.

With the classic parameters a = 15.6, b = 28, m0 = −8/7 and m1 = −5/7, the dimensionless equations below give the double-scroll attractor.

dx/dt = α(y − x − f(x)), dy/dt = x − y + z, dz/dt = −βy
f(x) = m₁x + ½(m₀ − m₁)(|x + 1| − |x − 1|)

• x, y, z: dimensionless capacitor voltages and inductor current
• α, β: dimensionless circuit parameters (a, b on the shirt)
• m₀, m₁: inner and outer slopes of the Chua diode
• t: dimensionless time

Chua 1983; Matsumoto, IEEE TCAS 31, 1055 (1984) found the attractor in simulation; Chua, Komuro & Matsumoto, IEEE TCAS 33, 1072 (1986) proved chaos in the double scroll family.

Honest caveat: The Chua diode is itself built from op-amps or diodes in practice, so “five parts” counts it as one. Chaos was proved in 1986, not 1983.

On the shirt

Front: Chuanna, the pixel-art character, with “THE DOUBLE SCROLL”. Back: the three equations, the diode function, the classic parameters and the 1983, 1984 and 1986 sources. Printed on a unisex tee.