4
votes
0answers
51 views

Why does the Mandelbrot shape show up in other fractals?

In the pictures below, the Collatz map fractal includes parts resembling the Mandelbrot set. Why? Do other fractals do so? The Mandelbrot set From Wikimedia Commons Part of the Collatz map fractal ...
1
vote
1answer
85 views

From 'The Joy of x' book: John Hubbard and problems with multiple roots

My math skills are super rusty. In an effort to get some vigor back I started some reading and picked up The Joy of x based on its rave reviews.. I just couldn't make any sense out of the following ...
6
votes
1answer
209 views

Why is the bailout value of the Mandelbrot set 2?

For the past few days I've been studying the Mandelbrot set, and many say that if the iterations of a point stay within a magnitude of 2, the point converges. A very natural question of "why is the ...
42
votes
2answers
2k views

A new kind of fractal?

http://www.gibney.de/does_anybody_know_this_fractal Is this some known kind of fractal? Update: This one got a lot of great feedback from around the net. I summarized it here: ...
1
vote
1answer
332 views

Complex Numbers in Fractal Algorithms

I am a high school freshman who is undertaking a small development project on fractals. I do not want to get too in depth, but I would love to blow my math teacher's socks off. Having looked through ...
4
votes
2answers
129 views

Quick Julia/Mandelbrot Testing

I have successfully implemented a realtime Julia/Mandelbrot set generator on the GPU. Primarily out of curiosity, what I'm looking for now is a faster test algorithm. Ideally, I want a boolean ...
5
votes
1answer
343 views

Is a 3D Mandelbrot-esque fractal analogue possible?

I understand that (unlike complex numbers) there's no consistent 3 dimensional number system (even 4D loses some nice properties). Regardless, I'm wondering if there might be a 'trick' to create a 3D ...
2
votes
2answers
371 views

Undiscovered fractal sets?

I'm interested in the topic of fractals, such as those created by the borders of the Mandelbrot and Julia sets. My question is if there are other, not yet discovered fractal sets, which one could ...
0
votes
1answer
94 views

rearrange $z \mapsto z^2 + c$

Mathematics, some of its magic is that a lot is known about how to rearrange its statements (equations). Given the Mandelbrot Set: $z \mapsto z² + c$ (or more precisely) $z_{i+1} = z_i ^2 + c$ ...
18
votes
4answers
829 views

Mandelbrot fractal: How is it possible?

I'm a programmer and have recently played around a bit with rendering Mandelbrot fractals / zooming into them. What I can't grasp: How can such infinite, complex shapes come out of somewhat 10 lines ...