Logo by mjk1093 - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Visit us on facebook
 
*
Welcome, Guest. Please login or register. March 28, 2024, 12:27:37 PM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: [1]   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: What is mandelbrot made of?  (Read 586 times)
0 Members and 1 Guest are viewing this topic.
kubinator4321
Forums Freshman
**
Posts: 18


« on: January 17, 2015, 09:38:40 PM »

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.
Logged
Adam Majewski
Fractal Lover
**
Posts: 221


WWW
« Reply #1 on: January 17, 2015, 09:50:44 PM »

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
Logged
Dinkydau
Fractal Senior
******
Posts: 1616



WWW
« Reply #2 on: January 17, 2015, 10:15:47 PM »

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.
« Last Edit: January 17, 2015, 10:26:02 PM by Dinkydau » Logged

kubinator4321
Forums Freshman
**
Posts: 18


« Reply #3 on: January 18, 2015, 12:58:34 PM »

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.
Logged
claude
Fractal Bachius
*
Posts: 563



WWW
« Reply #4 on: January 18, 2015, 01:10:47 PM »

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.
Logged
quaz0r
Fractal Molossus
**
Posts: 652



« Reply #5 on: March 29, 2016, 12:50:16 AM »

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.   roll eyes   i think you guys were just punishing him for not articulating himself perfectly...  snore
Logged
Pages: [1]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
We are all made of Stars FractalForums.com Banner Logos Cyclops 0 1935 Last post November 05, 2010, 05:49:21 PM
by Cyclops
made with bones Mandelbulb3D Gallery miguelnpg 0 766 Last post May 02, 2011, 06:42:16 PM
by miguelnpg
Finally made it! Meet & Greet PheonRa 0 825 Last post June 01, 2011, 07:57:52 PM
by PheonRa
just some pictures I made Images Showcase (Rate My Fractal) thom 0 1601 Last post August 07, 2011, 06:38:10 PM
by thom
a map I made of the Mandelbrot Set Images Showcase (Rate My Fractal) « 1 2 ... 5 6 » billtavis 89 10946 Last post October 05, 2016, 03:35:03 AM
by stardust4ever

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.277 seconds with 24 queries. (Pretty URLs adds 0.014s, 2q)