A "Circle Limit III" Calculation

Douglas Dunham
Bridges Donostia: Mathematics, Music, Art, Architecture, Culture (2007)
Pages 395–402


M.C. Escher’s Circle Limit III is usually thought to be the most appealing of his four “Circle Limit” patterns. Two artistic/mathematical questions seem to arise: (1) what angle do the white backbone lines make with the bounding circle, and (2) are other such patterns of fish possible? H.S.M. Coxeter answered the first question and I described a 3-parameter family of possible fish patterns in my 2006 Bridges Conference paper. In this paper, I combine those questions by calculating the intersection angle for any such fish pattern.