The 3D chaotic system contains only two nonlinearities:

 dx/dt = α x (1 – y) – β z

 dy/dt = - γ y (1 – x²)                                                                                                     

 dz/dt = μ x

 

For P₀ (α, β, γ, μ) = (3, 2.2, 1, 0.001), and IC₀  = (1, 1, 0), it exhibits an exclusive silhouette:

 

 Graphics: Jos Leys

 

Surprisingly, for the same parameters P₀ but IC₁ = (1.2, 1, -0.02), a new attractor appears overlapping the previous one:

 Graphics: Jos Leys

 

Such phenomenon leads us to revist the Butterfly Effect popularized by Edward Norton Lorenz ( see the paper).