Chaos Lab

Discrete map · 2D · dim 2

Gingerbreadman map

A piecewise-linear area-preserving 2D map whose iterates trace out a gingerbread-man silhouette around a regular pattern of fixed points.

Iterates of the gingerbreadman map: mixed regular/chaotic phase space.

Equations

x_{n+1} = 1 − y_n + |x_n|
y_{n+1} = x_n

At a glance

Parameters(no free parameter)
Chaotic foralways (mixed regular/chaotic phase space)
HistoryDevaney's 'introduction to chaotic dynamical systems' textbook.

See also

Quick quiz

Test yourself on gingerbreadman

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

  1. Q1.The gingerbreadman map x_{n+1} = 1 − y_n + |x_n|, y_{n+1} = x_n is:

  2. Q2.The map's name comes from:

  3. Q3.Number of fixed points of the gingerbreadman map:

  4. Q4.Phase space of the gingerbreadman is:

  5. Q5.Devaney popularised this map in:

  6. Q6.The absolute-value term |x| makes the map:

  7. Q7.Compared to Hénon, gingerbreadman is:

  8. Q8.Iterates of the gingerbreadman seeded near the fixed points trace:

0 of 8 answered