I use pencil, pen, pastel, paper, cardboard, scanner, camera, computer, and printer to achieve my desired effects. I usually think of mathematics as just another part of the creative process, even though there usually is a mathematical way of looking at the finished product.
This piece began as a doodle sketched on the agenda for a math department meeting. I implemented an algorithm involving rotations, reflections, a tiling scheme, and cropping. Finally, I incorporated a Strange Loop in the sense of Hofstadter. The viewer is invited to attempt retrieving the original sketch or to visualize a looping animation composed of the three frames.
This piece began as an oil pastel drawing on paper. I thoroughly deconstructed it and then systematically reassembled the pieces to form the resulting image. There is an 8x8 array of boxes in the foreground. Although the process of arranging the boxes was done very carefully, no pattern is intended. Do you see one?
This piece began as a pencil sketch on cardboard. There are 18 copies of that sketch in this image, and they are all interconnected. In the end, we have a view of 18 vertices of a graph, all but three having degree 4. There is also a vertex at infinity whose degree is at least eight.