Zaslavsky Web Map

The Zaslavsky map models a kicked oscillator: p → p + K·sin(q), q → q + p (mod 2π·r). At resonance it creates beautiful web-like stochastic structures.

Web r=4

Web r=5

Hex r=6

Triangle

Chaos r=4

Full chaos

K (kick strength)0.9

r (resonance)4

Trajectories100

Steps500

For rational r, KAM tori form webs with 4-fold symmetry. Increasing K breaks tori and creates stochastic layers. Discovered by Zaslavsky (1985) in plasma physics.