s_{i} = a,-a,…; a = -i.

Center: i; Zoom = 0.3

This one starts part III. Mainly because Part II was getting too long, and I called the last post the “grand finale”. However the basic formula has not changed. I have not tired of the desert color scheme yet. But I will convert to the more traditional rainbow colors with black insides so part III looks different compared to part II.

I had planned to base part III on the general two-step sequence, s_{i} = a,b,a,b,… However some of the first few picture I generated looked very familiar. For example 0,1… is the same as -.5,.5,…. At first I thought I got the picture files mixed up. It turns out all that matters is the difference a-b. The picture for general a,b,… is the same as 0,b-a,0,b-a… translated a units. It is easy to see that c’=c-a is a conjugation of both steps in the sequence fractal.