Mortgages and Sea Shells: A Dynamic Approach

This column focuses on iterating linear functions of both a real and a complex variable and shows that there is some interesting geometry underlying the process. Here is a quick overview of how to iterate a linear function. (If you are unfamiliar with the process, [1] has a good introduction to iteration.) Start with a linear function in the form f(x) = ax + b and a value x0 and then calculate the sequence x0, x1 = f(x0), x2 = f(x1) = f(f(x0)), x3 = f(x2) = f(f(f(x0))), . . .