About 50 years ago MC Escher created his four "Circle Limit" patterns, which were repeating patterns in the Poincare circle model of hyperbolic geometry. They were based on the regular tessellations (6,4) and (8,3) of the hyperbolic plane. In general, (p,q) represents a tessellation by regular p-sided polygons with q of them meeting at each vertex. About 30 years ago two students and I came up with an algorithm to draw hyperbolic Escher patterns. Also we will discuss special cases of a more general algorithm not based on regular tessellations. Dr. Doug Dunham is from University of Minnesota-Duluth.