"Rational Circles"

Digital Print, 24” by 15.6”, 2009.

detail

This image consists of a large number of circles. To describe the set of circles let [a,b,c,d] represent the circle whose points are the zeros of the bivariate polynomial
p(x,y)=a(x²+y²)+bx+cy+d. If a, b, and c are relatively prime integers then I call the circle a "reduced rational" circle. The drawing then consists of reduced rational circles such that a²+b²+c²≤9², as viewed through a rectangle whose lower left is (0.01,0.21667) and whose upper right is (0.395,0.46667). (The view box was mostly chosen for aesthetic reasons.) The darkness of each circle depends inversely on its radius and on the term a²+ b²+c².


Stephen Schiller, Principal Scientist, Adobe Systems Inc.
Oakland, CA

"Most of my mathematical art has its origins in images I make to help me understand the solution to some problem I am facing in my work as a computer scientist. There is great power in mathematical theorems that help us understand a complex set of objects. But sometimes such theorems hide, or at least allow us to temporarily ignore, the true complexity of a subject. This duality often comes up when one tries to actually implement a mathematical idea. Thus, I find myself interested in images that are a manifestation or rediscovery of the complexity that is inherent in even simple mathematical areas."