The Rössler Band

Plate 84 speaks for itself: “Stretch, fold, repeat.”

The Physics

Rössler built the simplest smooth chaotic flow he could. Trajectories spiral outward, then the z term lifts and folds them back, making a single folded band.

ẋ = −y − z, ẏ = x + a y, ż = b + z(x − c)

• x, y, z: state variables, dimensionless
• a, b, c: parameters, dimensionless

a = b = 0.2, c = 5.7. A single folded band.

Sources

• O. E. Rössler, Phys. Lett. A 57, 397 (1976).

On the poster

Plate 084, “The Rössler Band”: the pixel-art plate with its slogan “Stretch, fold, repeat.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.