Larry Crone
"Red and Blue"
digital print, 20"x18", 2005
Larry Crone
Department of Mathematics and Statistics, American University, Washington, DC
For the past twenty 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 multiplier greater than one. Although these are all meromorphic, they are extremely complicated and their plots are frequently mistaken for fractals. I have investigated the plots of hundreds of inverse Schroeder functions corresponding to quadratic rational functions, and have been overwhelmed by the beauty and variety of the images.
To see more images of complicated as well as simple complex valued functions go to
http://www.american.edu/academic.depts/cas/mathstat/People/lcrone/ComplexPlot.html
email:lcrone@american.edu