Iterating Complex Linear Functions

When you iterate a function, you create a sequence. This sequence is called an orbit. Much has been written about iterating real valued linear functions. Not much has been written about iterating complex linear functions. I stumbled on this topic while teaching a Chaos and Fractal Geometry course. If you iterate a complex linear function of the form F[x + yi] = (a + bi) (x + yi) + c + di, where a, b, c and d are real numbers, you create orbits that can be plotted using a spreadsheet.