The logistic map is one of the simplest equations to produce chaos. As the parameter increases the behavior changes, from going to to finding a fixed point, to a periodic orbit. That goes through a period doubling cascade, from an orbit of elements to and at the Feigenbaum point it becomes chaotic, never returning to the original value.
Each vessel in the series corresponds to a range of values for . The orbits translated into a path for the machine to follow, as a helix going up the vessel. The clay 3D printer placing a trace as the surface. The increasing disorder apparent in the pots themselves.
One aspect we were not able to explore was to get the material form to not just show the chaos, but to collapse into it. We are still working on a method where this genuinely emerges from the underlying mathematics and its representation.
The bifurcation diagram, shown alongside, gives a different view of the behavior and acts as a map for the whole process with the individual pots becomeing locations. An accompanying 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 Creation: Between Art and Mathematics at the Institut Henri Poincaré, Paris (April–July 2026).
