My "Mutant Stars" and ribbon designs are based on tilings of the hyperbolic plane . Such figures are usually shown in a circle, as made famous by M.C.Escher's Circle Limit prints. For the mugs and cases, I stretched the circle into an infinite strip. (The circle model is akin to stereographic projection of the sphere; the strip model is akin to a Mercator map.)
The "Dragonbushes" design uses a binary representation of complex numbers in base -1±i; a high-order bit becomes the high bit of the green channel, the next lower bit becomes the high bit of red, and so on down. I think the result looks like foliage on another planet. The fractal S is called a twindragon curve.
"Fun with Refraction" is made by ray tracing . Each virtual bead in the picture is made of a different kind of glass; the index of refraction varies smoothly between 0 at the "east" (so the bead reflects all light), 1 at the "north" (so the bead is invisible), infinity at the "west" (so light reflects endlessly inside the bead), and negative at the "south". The beads reflect (and refract) a multicolored sky.