Mandelbrot Definition and 25 Threads

This is wild. I was always fascinated with the Mandelbrot set, as well as the bifurcation diagram. I had no idea the Mandelbrot diagram was a different visualization of the bifurcation diagram. Question: is this video accurate? I always question the veracity of YouTube science videos.

Is there a code for the mandelbrot set that creates an image with an high resolution so that we can zoom and see the fractal over and over again ?

Okay, so I'm working with a rather frustrating problem with a calculus equation. I'm trying to solve a calculus equation which I conceptualized from existing methods involving complex number fractal equations. I'm very familiar with pre-calculus, while being self-taught in portions of calculus...

When asked about his work, Mandelbrot wrote his equation as such: z -> z^2 + c Is it permissible to also write it as: z = z^2 + c and / or f(z) = z^2 + c

f(z) = z2 + c

Does anyone here know much about these topics? I understand they surround the absence of normally distrubted returns, excessive kurtosis. Fat tails somehow disprove the EMH? Can anyone explain this argument? I've been advised that there are links to turbulence in fluid dynamics, joined by the...

As a mathematician, what may you say are the beauties that you see in the Mandelbrot set??

Homework Statement . I am trying to solve two exercises about complex sequences: 1) Let ##\alpha \in \mathbb C##, ##|\alpha|<1##. Which is the limit ##\lim_{n \to \infty} \alpha^n##?, do the same for the case ##|\alpha|>1##. 2) Let ##\mathcal M## be the set of the complex numbers ##c## such...

This is certainly not "breaking" news, but I saw this article a few years ago and happened upon it again, and wanted to share it here: THE MANDELBROT MONK It seems that what is perhaps the most iconic image of fractal geometry was known before its discovery by Benoit Mandelbrot. (Sun)

Assuming that we could interpret the imaginary axis in the complex plane as the output of a relation, how would we find the equation of the curve that bounds the main cardioid of the M-set? Is there a way to find the equation of the main cardioid on a "minibrot" (e.g. if I zoom in on the fractal...

Hi, I have been working on some Mandelbrot wallpapers for some time but have so far only visualized the whole set i.e. no zooming. I think that it could be nice with wallpapers visualizing a zoomed in part of the border of the set. Does anyone know coordinates to interesting places for zooming...

Homework Statement Note: This is not for homework. I'm trying to teach myself programming and this looks like a fun project. I want to plot the Mandelbrot set using a computer. Homework Equations Z_{n+1}=Z_n^2+c for some constant c The Attempt at a Solution Given: Z_0=0, maximum of...

Hi! The Mandelbrot set is defined as a fractal set of points c of the plan for which the sequence defined recursively by: Zn+1 = Zn.^2c with z 0 = 0 does not tend towards infinity (in module). useful property If there exists an integer N such that | zN |> 2, then the sequence diverges...

Anyone ever watch this? Catchiest math themed song I've ever heard. IE, it's actually goodish.

Can someone explain the Mandelbrot set to me? I know the equation is zn+1 = zn2 + c But what does this mean? Whats its basically saying here? All I know about it really is the existence of fractals, but why are fractals so mathematically important?

Not sure if others have heard, but Benoit Mandelbrot, the father of fractal geometry, passed away this week, as confirmed by the New York Times: http://www.nytimes.com/2010/10/17/us/17mandelbrot.html https://www.youtube.com/watch?v=ES-yKOYaXq0 And now the line "Mandelbrot's in heaven, at...

I'm not sure if this is the correct section to be posting in. I'm writing a summary of the mandelbrot set and I'm not sure I understand how the points are calculated. I've got the equation: z = z^{2} + c This means each value is squared, and then a constant value c is added, to get a...

1a: show w = -i is in the mandelbrot set show that -1-i is not in the mandelbrot set is w= -0.1226 + 07449i in the mandelbrot set, first show that z2 =0 don't know how to do any of them i tried, -(squareroot-1) ^2 = --1, + squareroot -1 idk

Hi, What exactly is the importance of the Mandelbrot set in general? From what I've read, it seems more of a mathematical play thing than anything else.. there must be more to it than the disturbing pictures, no? Also, is there an easily understandable proof anywhere showing that the...

I am currently studying the Mandelbrot set, and have a question about one of the statements on http://mathworld.wolfram.com/QuadraticMap.html" . It says the recurrence for the Mandelbrot set "is not in general solvable in closed form." What does this mean?

I found this image on wikipedia: http://en.wikipedia.org/wiki/Image:Mandel_zoom_00_mandelbrot_set.jpg and i have seen this image like many times, but i have never understood as to how it is plotted. How is the value of the color decided? Plus, if it is a complex plane, how are the axes...

For those of you not familiar with the mandelbrot set, it is the set of all complex numbers c for which the following transform remains finite for an infinite number of iterations: z --> z^2 + c z is 0 for the first iteration My question is this: How can I conclusively determine...

Don't know if this is the right subforum, but here goes: The Mandelbrot set is formally defined as the values of a complex constant c for which the Julia Sets of the iterative function: f(z)=z^2+c are connected (i.e. consists of a single figure) Recall that the Julia sets are the launch...

What is the Lebesgue measure of the Mandelbrot set?

I am sure the same goes for you lot, I am fascinated by the complex patterns of fractals and recently found out it is generated by extremely simple algorithms (which takes weeks to run). What do I actually need run some algorithms that generates fractals?