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

bump?

Most of that stuff sounds boring or trivial or both.

The Mandlebrot set is a dull bit of maths.

Mandelbrots ? In my Mandelbrots ?

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).

It looks like a fucked up beetle and doesn't afraid of anything.

>>5
That's alright it's still dull, a corollary of a dull fact is still a dull fact.

Specific examples, except in the most pathological of cases, are rarely interesting. Add to that the fact that the mandelbrot set is an example of a pretty useless bit of mathematics and it adds up to nothing.

There are must simpler (and more interesting examples) of things with different topological and hausdorff dimensions, space filling curves or the cantor set, more interesting by merit of being constructions or counterexamples/examples to obvious questions to ask.