M.C. Escher used the Poincar´e model of hyperbolic geometry when he created his four “Circle Limit” patterns. The third one of this series, Circle Limit III, is usually considered to be the most attractive of the four. In Circle Limit III, four fish meet at right fin tips, three fish meet at left fin tips, and three fish meet at their noses. In this paper, we show patterns with other numbers of fish that meet at those points, and describe some of the theory of such patterns.