Clifford Strange Attractor

Overview

This piece shows the Clifford attractor, a type of chaotic system defined by just four parameters and two equations. I used a = −1.4, b = 1.6, c = 1.0, and d = 0.7. From an initial point at the origin, the values of x and y evolve using the formulas: x = sin(a·y) + c·cos(a·x), and y = sin(b·x) + d·cos(b·y). Even though each update uses only sine and cosine, repeating this calculation one million times generates motion that looks unpredictable and organic. The equations are symmetric, so I mirrored the full dataset by appending −x and −y to create additional texture and balance.

To build the image, I plotted over two million points with a twilight shifted colormap. I calculated an intensity for each point using the square root of x² + y², then normalized it between 0 and 1. This value controlled the color and helped bring out the overlapping density patterns. I added multiple transparent layers using alpha values from 0.02 to 0.15 to soften the glow and blend the curves. The final result has a smoky, folded shape that hints at hidden order beneath the surface.