Attractors — Jerry Guo

System

Attractor

A flow with three lobes and cyclic symmetry.

Changing parameters can produce periodic or escaping trajectories. Reset restores the preset.

Samples Time step

Initial state & burn-in

x₀ y₀ z₀

Discard transient

Appearance

Palette

Background Gradient

Gradient strength 78% Line width 0.95 px Glow 42%

Camera

Zoom 100% Perspective 18%

Export

3840 × 2160

Long edge

Exports include every sample and use the current view. Larger images take longer to save.

Model equations

ẋ = −ax − 4y − 4z − y²

ẏ = −ay − 4z − 4x − z²

ż = −az − 4x − 4y − x²

A numerical approximation using fourth-order Runge–Kutta integration. Small changes to the starting point can lead to very different trajectories (the decimal places are doing actual work here).

Sprott: A Symmetric Chaotic Flow

Trajectory preview