Larry Crone

For the past thirty years I have been using color to display complex valued functions. Such plots clearly show features such as zeros, poles, and branch cuts. I have also long been interested in the inverse Schroeder function, which is related to functional commutivity and the iteration of functions. I soon put the two together and discovered that it is particularly straight forward to plot the inverse Schroeder function corresponding to rational functions with a repelling fixed point at zero. Although these are all meromorphic, they are extremely complicated and their plots are often mistaken for fractals. I have investigated the plots of many inverse Schroeder functions, and have been overwhelmed by the beauty and variety of the images.