Misshapen Chaos: of Well Seeming Forms
A series of six clay 3D-printed vessels on walnut bases, each encoding a different parameter of the logistic map as the equations are transformed into machine toolpaths for the printer. The surface of each vessel — from regular coiled rows at the base to chaotic bumps at the rim — traces the period-doubling cascade as the map bifurcates toward chaos. Created with Vincent Edwards and Jean Schmidt. Exhibited at Bridges 2025 (Eindhoven) and at the Création: Between Art and Mathematics exhibition at the Institut Henri Poincaré, Paris (April 2026).
The logistic map xn+1 = rxn(1 − xn) is one of the simplest equations to produce chaos. Vary the parameter r upward and the long-run behaviour changes: a single fixed point, then two alternating values, then four, then eight — each doubling happening faster than the last — until at the Feigenbaum point the orbit becomes fully chaotic.
Each vessel in the series corresponds to a value of r at one of those doublings. The equations do not merely illustrate the map — they become machine code, controlling a clay 3D printer whose layer-by-layer deposition traces the orbit directly onto the surface. Where the map oscillates with period two, two distinct coil patterns alternate; where it bifurcates to period four, four patterns interleave; in the chaotic regime the surface texture becomes genuinely disordered.
The work exposed an honest limitation: we anticipated seeing order visibly give way to chaos as a gradient. No such gradient emerged from the mathematics alone. The bifurcation diagram — shown alongside — makes the transition explicit in a way no single form can. The sonification adds a further dimension: the rhythmic patterns of the period-doubling cascade are audible as well as visible. Together the three representations offer a richer experience of the logistic map than any one provides alone.
Made with Vincent Edwards and Jean Schmidt. Exhibited at Bridges 2025 (Eindhoven, July 2025) and at Création: Between Art and Mathematics at the Institut Henri Poincaré, Paris (April–July 2026).
