SYSTEM_PARAMETERS
PARAMETERS
3000
1
CONTROLS
x(n+1) = 2x(n) mod 1
y(n+1) = (y(n) + floor(2x(n))) / 2
LIVE_RENDER // CANVAS_2D
ITERATION: 0
LIVE_RENDER
DATA_LOG: BAKERS_MAP
The Baker’s Map is the simplest model of chaotic mixing. Each step stretches the unit square horizontally by a factor of two, cuts it at the midpoint, and stacks the right half on top of the left. The map is measure-preserving, so a uniform distribution stays uniform forever — but points colored by their initial height interleave into ever-finer horizontal bands, making the stretch/cut/stack mechanism visible. This is the same kneading action that gives chaotic systems their mixing property: after enough folds, any two nearby points end up far apart.