Chaos Lab

Discrete map · 2D · dim 2

Hénon map

Hénon's 1976 reduction of the Lorenz system. The Hénon attractor at a = 1.4, b = 0.3 is the most-studied 2D strange attractor, with Hausdorff dimension ≈ 1.261.

Hénon attractor at classical parameters (a = 1.4, b = 0.3). Hausdorff dim ≈ 1.26.

Equations

x_{n+1} = 1 − a · x_n² + y_n
y_{n+1} = b · x_n

At a glance

Parametersa, b ∈ ℝ (classic: a = 1.4, b = 0.3)
Chaotic fora ≈ 1.4, b ∈ (0.21, 0.32)
Lyapunov exponentλ₁ ≈ 0.42 (classical)
HistoryHénon (1976), 'A two-dimensional mapping with a strange attractor'.

Try it

Open the interactive playground at /tools/henon.

See also

Quick quiz

Test yourself on henon

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

  1. Q1.The Hénon attractor at (a, b) = (1.4, 0.3) has Hausdorff dimension approximately:

  2. Q2.Hénon's two-equation map came from reducing which system?

  3. Q3.Which version has a rigorous proof of being a strange attractor?

  4. Q4.Hénon's map preserves area when:

  5. Q5.Hénon was an astronomer at:

  6. Q6.Hénon's λ₁ at (1.4, 0.3) is approximately:

  7. Q7.Hénon-like maps include:

  8. Q8.Hénon's seminal 1976 paper is titled:

0 of 8 answered