Chaos Lab

Discrete map · 2D · dim 2

Tinkerbell map

A 4-parameter discrete dynamical system whose attractor is dragon-like and notoriously sensitive to parameters.

Tinkerbell attractor at (a, b, c, d) = (0.9, −0.6013, 2, 0.5).

Equations

x_{n+1} = x_n² − y_n² + a x_n + b y_n
y_{n+1} = 2 x_n y_n + c x_n + d y_n

At a glance

Parametersa = 0.9, b = −0.6013, c = 2, d = 0.5 (classic)
Chaotic fordepends on parameters; classical values are chaotic
HistoryIntroduced as a study object in nonlinear dynamics in the 1980s.

Try it

Open the interactive playground at /tools/tinkerbell.

See also

Quick quiz

Test yourself on tinkerbell

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

  1. Q1.The Tinkerbell map is a:

  2. Q2.At the classical Tinkerbell parameters (0.9, −0.6013, 2, 0.5):

  3. Q3.Why is the Tinkerbell map notoriously sensitive?

  4. Q4.Its attractor's nickname:

  5. Q5.The Tinkerbell map's Jacobian determinant is:

  6. Q6.Tinkerbell map first appeared in:

  7. Q7.Trying initial conditions far from (−0.72, −0.64):

  8. Q8.What category of dynamical system is the Tinkerbell map?

0 of 8 answered