Chaos Lab

Discrete map · 2D · dim 2

Baker's map

A simple model of mixing: bake the dough by stretching and folding. Conjugate to the Bernoulli shift on bi-infinite binary strings, the cleanest example of measure-theoretic chaos.

Baker's map applied to a horizontally striped image: stretch, cut, stack.

Equations

Stretch the unit square 2× horizontally, cut, and stack.

At a glance

Parameters(no free parameter)
Chaotic foralways
Lyapunov exponentλ = ln 2
HistoryStudied since the 1960s as a paradigm of ergodic theory.

Try it

Open the interactive playground at /tools/arnold-cat.

See also

Quick quiz

Test yourself on baker

9 multiple-choice questions. Pick an answer for each, then submit to see explanations.

  1. Q1.The baker's map acts on the unit square by:

  2. Q2.Its Lyapunov exponent is:

  3. Q3.Why is the baker's map a fundamental example?

  4. Q4.On bi-infinite binary strings the baker's map acts as:

  5. Q5.The baker's map is:

  6. Q6.Topological entropy of the baker's map equals:

  7. Q7.Why is it called 'baker's'?

  8. Q8.The baker's map is:

  9. Q9.What variant gives the 'asymmetric baker'?

0 of 9 answered