What is mandelbrot made of?

[kubinator4321]

Today a though occured to me, and I decided I'd share it.
Theoretically, if you zoom in deep enough anywhere on the mandelbrot set, wouldn't you find a minibrot somewhere way down there? If you would, wouldn't that mean, that anywhere on the mandelbrot set you point, there's a minibrot? And if that would be true, wouldn't that mean, that the mandelbrot set is built in its' entirety of minibrots?
Not sure, if the first statement is true though, as I'm not experienced in this kind of stuff, but if it's true, the mandelbrot set just appeared to be even more awesome.

[Adam Majewski]

Mandelbrot set is a part of parameter plane. Parameter plane is infininite so one can find many places were there is no points belonging to Mandelbrot set. See also this question .

If you ask if there are points in the Mandelbrot set which do not belong to hyperbolic components the answer is yes :
* Misiurewicz points
* Feigenbaum points

See also this question

HTH

[Dinkydau]

In a way, yes, the mandelbrot set is built in its entirety of minibrots, in another way not every point of the mandelbrot set belongs to a minibrot. There are infinite spirals, for example. The centers of such spirals are points that dwell bands are closing in on, so they themselves require infinitely many iterations and belong to M, but you will not find a minibrot at the center of a spiral because it is infinite. You could consider such points to be points where minibrots become inifinitely small, some kind of limit point.

Edit: investigate for example 0 + i.

[kubinator4321]

Mandelbrot set is a part of parameter plane. Parameter plane is infininite so one can find many places were there is no points belonging to Mandelbrot set.

Actually, I pointed out a few times that I'm talking about pointing on the MANDELBROT SET, not on the parameter plane.

[claude]

There are minibrots everywhere in the boundary of the Mandelbrot set, by which I mean: any circle with radius > 0 that contains a point of the boundary of the Mandelbrot set will also contain minibrots.  See Adam's answer for circles with radius = 0 (ie, points).

Minibrots are not everywhere in the Mandelbrot set, just pick a circle completely inside a hyperbolic component (aka solid region resembling cardioid or disc), and there will be no minibrots in it.  Example circles: center 0 radius 0.2, center -1 radius 0.1.

[quaz0r]

sorry for needlessly bumping this thread, i stumbled across it and i must say, you guys are incredibly (intentionally?) thick.  the guy was obviously talking about the boundary, not inside or outside points.     i think you guys were just punishing him for not articulating himself perfectly...