Edmund Harriss and Roice Nelson

Clinical Assistant Professor (EH); Software Developer (RN)
University of Arkansas (EH)
Fayetteville, AR, USA (EH); Austin, TX, USA (RN)

Edmund is a Mathematician, Teacher, Artist and Maker. He likes to play with the ways that the arts can reveal the often hidden beauty of mathematics and that mathematics can be used to produce interesting or beautiful art.

Roice is a recreational mathematician who draws inspiration from higher dimensional and non-euclidean geometry, and applies related ideas to digital art, permutation puzzles, and 3D printing. He appreciates software's ability to realize geometrical structure not physically possible in our 3D universe.

P-adics in Motion
P-adics in Motion
Interactive Animation on a Tablet (tapping the screen in different places explores a wide world of animations).

This animation of nested rotating circles is an illustration of addition on the p-adic numbers. The p-adic numbers start from the familiar whole numbers, but with a different method of measuring distance. Under this p-adic distance two numbers are close, not if their difference is small, but if their difference is a large power of a prime p. So 1 and 9 are quite close in the 2-adics, as 9 -1 is 2 cubed, and 81 is close to 0 in the 3-adics as 81 - 0 is 3^4. As a result any pair of integers lie at a distance of at most 1 from each other, and so all integers lie within the largest circle. The meaning of the other circles and the motion is left as an exercise for the viewer.

We believe this is the first artwork featuring the p-adics.