ComplexMap Package

CartesianMap[f,{xmin,xmax},{ymin,ymax}] produces a pair of graphics. The left shows a grid in the complex plane covering the region from xmin to xmax, and ymin to ymax. The right graphic shows the images under f of the intersection points of the grid, with these points joined by line segments. The horizontal and vertical grid lines (and their images) can be colored with the options XLineStyle and YLineStyle. Set these options to a graphics directive (or to a list of graphics directives). The number of grid lines (20 in each direction by default) can be adjusted in two ways: set the option GridSize to a positive integer (or to a list of two positive integers if you want different numbers of horizontal and vertical lines); or change the iterators to {xmin, xmax, dx} and/or {ymin,ymax,dy}. CartesianMap will also accept any options accepted by Graphics.

CartesianMapMovie[f,{xmin,xmax},{ymin,ymax}] produces an animation based on CartesianMap. The option Progression may be set to any one of LR, RL, BT, or TB. These stand for (Left to Right), (Right to Left), (Bottom to Top), and (Top to Bottom), respectively, and control the direction in which the red line segment moves. Other options include the options of CartesianMap, and any options accepted by Graphics.