Clifford Alpha — Strange Attractors mathematical physical art

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Clifford Alpha

Strange Attractors

Clifford attractor with a=-1.4, b=1.6, c=1.0, d=0.7.

Price

$29.00

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Format Art Print
Size 18 × 24 in
Material Enhanced matte paper · 200gsm · archival · unframed
Resolution 300 DPI · rendered at 5400 × 7200 px
Production Professional print-on-demand · ships from nearest facility
Shipping Most countries · calculated at checkout
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The mathematics

About this system

The Clifford attractor is a two-dimensional discrete iterated map popularized by Clifford A. Pickover: x' = sin(a·y) + c·cos(a·x), y' = sin(b·x) + d·cos(b·y). The trajectory never escapes a bounded region of the plane, but it also never repeats, filling out an intricate invariant measure that depends sensitively on the four parameters. Each image is the density map of millions of iterates, colored by how often each pixel was visited — a portrait of the attractor's hidden probability distribution.

In the Strange Attractors collection

A strange attractor is a region of phase space toward which a dynamical system evolves over time — but unlike a fixed point or a periodic orbit, the trajectory never repeats. It folds and stretches forever inside a bounded volume. The Lorenz attractor, discovered by Edward Lorenz in 1963 while modeling atmospheric convection, is the canonical example: three coupled differential equations whose solutions trace a butterfly-shaped manifold that has become a symbol of deterministic chaos. The Clifford and Aizawa systems extend this idea with different nonlinear couplings, producing scrolls, shells, and toroidal sheets. What you see in these images is not a sketch or a stylization — each line is the literal trajectory of a point obeying the equations, rendered at full numerical precision over millions of integration steps.

dx/dt = σ(y−x), dy/dt = x(ρ−z)−y, dz/dt = xy−βz