where is a two cycle sequence.

There are many ways to combine sequences and fractals. When I started on this adventure I made a list of several methods to investigate. probably qualifies as the simplest way to incorporate a sequence. Also a two-cycle sequence, (two repeating numbers a,b,a,b,a,b…) is perhaps the simplest non-trivial sequence.

Already with this simple setup, it is clear that we are not looking at your father’s Mandelbrot set.

I think it is obvious, but just in case. is the i^{th} number in the sequence. The i^{th} step in the fractal calculation is