Kaplan-Yorke Dimension Explorer

D_KY = j + (λ₁+…+λⱼ)/|λⱼ₊₁| — fractal dimension from Lyapunov exponents

Attractor

Lyapunov Spectrum

λ₁ (largest)
λ₂
λ₃ (smallest)
Σλᵢ
D_KY

About D_KY

The Kaplan-Yorke conjecture (1979) relates Lyapunov exponents to the fractal dimension of a chaotic attractor.

Sort exponents λ₁≥λ₂≥…≥λₙ. Find j where Σᵢ₌₁ʲ λᵢ ≥ 0 but Σᵢ₌₁ʲ⁺¹ λᵢ < 0.

D_KY = j + (λ₁+…+λⱼ)/|λⱼ₊₁|

For Lorenz: D_KY ≈ 2.06
For Rössler: D_KY ≈ 2.01

D_KY = Lyapunov dimension — numerically equals the information dimension (Ledrappier-Young theorem).