Tool

Standard map

K: 0.9716

K_c ≈ 0.9716 (global chaos).

Seeds: 30

Steps per seed: 1500

Rule (Chirikov standard map)

p_{n+1} = p_n + K sin(θ_n)
θ_{n+1} = θ_n + p_{n+1}     (mod 2π)

Each color is a separate trajectory. Below K_c the phase plane is a mix of KAM tori (closed curves) and resonance islands. Above K_c the chaotic sea fills more and more area; at large K it is essentially everywhere.

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