Mandelbrot

I found the math board!
/b/ or /g/ didnt help.
So therefore, please help ^^

Copypasta from my prev posts:

Mathfags get in here!
Due to the fact we dont have a math board, imma making this thread hero-o.

ITT I will answer all questions I know myself about mandelbrot, but the real reason im making this thread cause I need some help with certain things.

So if you're some math wonder or just know a lot about fractals and specifically Mandelbrot... Get in here!

My questions:
-How can the main Cardiod of the Mandelbrot be explained? And the perfect circle left of it?
-What kind of self-similarities does the mandelbrot exactly have? Is it safe to say its exact similarity?
-How can fractal dimensions best be explained?
-Can you proof that the antenna of the mandelbrot has infinite amounts of secondary Mandelbrots? (eg mandelbrots in mandelbrots on antenna dont count)
-Almost same: can you proof that the Antenna doesnt have straight lines at all, anywhere?

Thanks :D

Also dont forget, if ur interested I'll answer all of ur beautfiul questions

Mandelbrot is obviously not exactly self-similar.

There are a many fractal dimensions including: similarity dimension (not applicable to Mandelbrot), box-counting dimension, Hausdorff dimension (the most powerful). Box counting dimension is easy to grasp, Hausdorff is not too hard to grasp once you have understood box-counting.

Mandelbrot has Hausdorff dimension 2, which equals its topological dimension (so technically one might say it's not a fractal). The boundary of the Mandelbrot set is a fractal however (it has topological dimension 1, but Hausdorff dimension 2, an interesting fact - sorry to the guy who said MB is boring).