Gingerbread Man Map

The "gingerbread man" map: xₙ₊₁ = 1 − yₙ + |xₙ|, yₙ₊₁ = xₙ. It creates bounded, symmetric orbits with fractal basin boundaries — and the attractor resembles a gingerbread figure!

Single orbit
Basin map
Density plot
3.1
4.5
3000
Discovered by R. Devaney (1984). The map is volume-preserving (area-preserving in 2D) and reversible. The "figure" has 6-fold symmetry and contains nested KAM-like structures.
Click canvas to start orbit from that point