← Back to the archiveSHORT / 030
A Tiny System Builds a Storm in 3D
Chaos & dynamics

A Tiny System Builds a Storm in 3D

BEHIND THE WORK

A tiny system of three differential equations builds a storm in 3D.

One point begins at (0.1, 0, 0). Its x, y and z coordinates keep updating because each rate of change depends on the point's current position. The path never becomes random: the same starting point and equations always create the same Aizawa attractor. Yet nearby motion stretches, folds and circles through a nested three-dimensional vortex.

The completed form rotates so the inner core, outer orbit and vertical depth can be seen clearly.

Artismathic turns equations into visual art—one function at a time.

Music: 'Moonlight Magic' by Asher Fulero

#MathArt #ChaosTheory #AizawaAttractor

THE MATHEMATICAL RULE

dx/dt=(z−0.7)x−3.5ydx/dt = (z − 0.7)x − 3.5ydy/dt=3.5x+(z−0.7)ydy/dt = 3.5x + (z − 0.7)ydz/dt=0.6+0.95z−z3/3dz/dt = 0.6 + 0.95z − z³/3−(x2+y2)(1+0.25z) − (x² + y²)(1 + 0.25z)+0.1zx3 + 0.1zx³start:(x,y,z)=(0.1,0,0)start: (x, y, z) = (0.1, 0, 0)
Watch the drawing↗

WATCH IT COME TO LIFE

Watch the drawing

YouTube loads only after you press play.