z2+c+si
si = -1, 1, -1, 1, …
Center: 0.00555195607569483, 0.796788357586998, Zoom = 8388608000
Summary so far: Comparing to z2+c, the escape set picture for this formula looks surprising normal. There are two main, separated, cardioids. They are surrounded by many little satellites. We have found more and “thinner” Misiurewicz points. However, despite the sparseness, every neighborhood of every M point contains infinitely many minis. (Conjecture supported by many pictures.)
When I first started looking at sequence fractals, my approach was quite random and the early results were nothing like these pictures. I had to dial back to the simplest cases to find familiar territory. We have been exploring in almost familiar territory, in the suburbs just outside of Mandelbrot city. Next let’s take a cautious step into the jungle.