0

I'm new to fractals and especially the Mandelbrot Set. I've noticed these never ending and self-similar spirals all around the Mandelbrot set, just like the one below:

enter image description here

At lower max-iterations, there is a black point in the middle of the spiral, which suggests me that there could be a minibrot there.

enter image description here

I've read that minibrots are centered on c values with super-attractive orbits. However, since the spiral never ends, I cannot precisely get the middle point and calculate its orbit.

Is there really a minibrot infinitely small at the end of the spiral?

Yılmaz Alpaslan
  • 103

1 Answers1

1

Spirals have no minibrot at the center, just a single Misiurewicz point, a strictly pre-periodic $c$ value with repelling orbit. Simple examples: $c = -2$, $c = i$.

But if you zoom deep towards a spiral center with $n$ spokes, the minibrots in its arms will be flanked by two similar spirals (one arm of each goes to the minibrot, and the minibrot has two extra arms), which altogether can look a little like a $2n$-armed spiral from a distance (example video: The 22-Legged Ant).

Claude
  • 5,647