Send comment Iteration is not fully understood before geometric iteration is sorted out. To understand why the Feigenbaum fractal looks like without knowing what geometric iteration is all about, is practically impossible. A starting point is chosen on the x-axis, and the first value in the iteration path is found by drawing a vertical segment up or down to the function in question. This is done on the graph at left.
First step is to compute the first iteration value.
The next iteration value is the functionvalue of the first value that is already found. This reflection transformation property of geometric iteration is simple and yet powerful, taking full advantage of our visual senses. Full understanding of what geometric iteration consists of is really necessary. It is recommended that you try out the technique using a pencil, ruler and a piece of paper if you have never seen geometric iterations before.