Chaos Lab

Discrete map · 2D · dim 2

Ikeda map

Ikeda's 1979 model of light in a ring cavity. The complex form makes its strange attractor compact and beautifully self-similar.

Ikeda attractor at u = 0.9.

Equations

z_{n+1} = A + B · z_n · exp(i (φ − γ / (1 + |z_n|²)))

At a glance

ParametersA, B, γ, φ (typical: A = 1, B = 0.9, γ = 6, φ = 0.4)
Chaotic forbroad parameter window
HistoryKensuke Ikeda (1979); explained experimentally observed optical chaos.

Try it

Open the interactive playground at /tools/ikeda.

See also

Quick quiz

Test yourself on ikeda

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

  1. Q1.The Ikeda map describes:

  2. Q2.What gives the map its characteristic banana-curl attractor?

  3. Q3.At u → 0 the Ikeda map becomes:

  4. Q4.Kensuke Ikeda introduced this map in:

  5. Q5.The complex z in the iteration represents:

  6. Q6.Standard parameters for the canonical Ikeda attractor are:

  7. Q7.Ikeda was the first map clearly demonstrating:

  8. Q8.Experimental Ikeda chaos has been observed in:

0 of 8 answered