These artworks are based on a generalization of Lucas sequences for complex numbers, defined as:
Z(0) = 1
Z(1) = 1 or i
Z(n) = shrink( e^(iθ)·Z(n-1) + Z(n-2) )

Where shrink() is a function which decreases a complex number into the two-unit square or the unit circle centered at the origin. In these works I use three different versions, based on taking out the integer part of the real and imaginary parts (or the integer part minus 1), or of the modulus of the number in polar form.

Figure 1 depicts the 128 values walk using θ = π/5 and Z(1) = i, and the shrinking function which takes out the integer part of the real and imaginary parts.

In the three artworks that follow, the lines connecting successive values toggle between being drawn or not. See the alt text for more information related to the artworks.
#mathart #math #algorithmicArt #AbstractArt

Still rewriting the algorithmic art library I wrote in #CommonLisp during the height of COVID. I can't say I've managed to make it too much faster, but it *is* easier to use. The canvas mottling code is so much shorter now, and ready to go.

Drawing on a flat canvas can be boring.

The mottled texturing is managed by just doing a bunch of random walks until the pen leaves the scene. Each one has a color *close* to the original canvas background.

#AlgorithmicArt