Tool
0-1 test for chaos
Gottwald and Melbourne's 2004 binary chaos test. Maps any scalar time series to a 2D random-walk-like trajectory; linear MSD (output ≈ 1) means chaos, bounded (output ≈ 0) means regular.
Gottwald-Melbourne 0-1 test
p_n(c) = Σ φ_j cos(j c), q_n(c) = Σ φ_j sin(j c)
M_n(c) = mean square displacement of (p, q) walk after n steps
K(c) = correlation(n, M_n(c)) — ≈ 1 for chaos, ≈ 0 for regular dynamics.
K (averaged over many c): 0.916
verdict: CHAOTIC (K → 1)
The (p, q) random-walk-like trajectories are diffusive (linear MSD)
when φ is chaotic, bounded when φ is regular.FAQ