Ian Sammis
Translating mathematics into art, and making that art as aesthetically pleasing as possible, seems to be the best way to for me understand the mathematics itself. The process of trying to make the art look the way I intend forces me to think in very different ways about the underlying mathematics.
The Moore curve is a closed space-filling curve. By placing an infinite line of Moore curves on the complex plane and applying exp(z), one fills a series of annuli. This work illustrates the effect for one of the curves in the sequence whose limit is the Moore curve. I have colored the interior of each curve by angle from the curve's center, to make the effect of exp(z) more obvious.
This Peano Curve, unlike the Moore curve, does not close on itself. By placing along a Möbius strip, though, one can make the final point fall adjacent to the initial point, forming a single closed loop.