Chaos Equation Visualization

About This Visualization

This visualization demonstrates a chaotic system based on the equations:

x' = -x² + xt + y

y' = x² - y² - t² - xy + yt - x + y

Code: _______

Current t = 0.0

Mathematical formula for X coordinate evolution
Mathematical formula for Y coordinate evolution
Load a saved equation using its code
Starting X value (dimensionless)
Starting Y value (dimensionless)
Starting time parameter (dimensionless)
How fast time evolves per iteration (0.001 - 0.1)
1 (slow, ~1 calc/frame) to 100 (fast, ~12 calcs/frame)

Keyboard Controls

How It Works

For every time t, a point (x,y) is initialized to (t,t). The equation is applied to the point many times, and each iteration is drawn in a unique color.

The equations use 18 parameters to combine x², y², t², xy, xt, yt, x, y, and t terms.

You can save interesting patterns by noting their equation code.