Background--Simple iteration from a Specified Boundary Condition

ExplFun[0,0.25] = π/4 above serves as an initial value for the function. The initial value and α determine the value at any later time.  The initial value can be expressed as another parameter for the function. We use a recursive method to define the function and store computed values in memory.

One might as well write a function to calculate a vector representing `trajectory', here is an implementation to compute a trajectory vector of specified length.  We use AppendTo to grow an initially empty list.  We will do the same thing with another method (Nest) below.

We define a function, Evolve, producing  an interactive tool with input : Initial values and α.

Created by Wolfram Mathematica 6.0  (06 November 2007)