Ooooh Fractals


#1

Hello. This is my large post about fractals. Ignore the posts of smileys below. First,

Some random information on fractals:

A fractal is a self-similar, repetitive shape that yields infinite detail. They are generated by algorithms.

Before computers, fractals were known simply as ‘monsters’, because the didn’t fit in ‘normal’ geometry. For example, the Dragon Curve, Cantor Dust, Koch’s Snowflake… All monsters.

Then this crazy smart man Benoit Mandelbrot used a computer to start computing the Julia set, which is just one of those repeating equation things you do in school (this is a linear equation), except its on the complex plane, which is like the Cartesian plane but with imaginary numbers. Yeah, so he made all these Julia sets, in black in white, and they took overnight to compute. So, he was all like, ‘whoa’, and decided he liked them so much he made the Mandelbrot set. Basically he gathered up his Julia sets and put them in a blender along with a few teaspoons of awesome. Most of those images you just saw are Mandelbrot’s, I might have a few Julia’s mixed in. Well, after he did this he made a few books and this other smart guy found out about them, used them to render mountains, and fractals became big. So, now we have lots of different sets.

Ok. Now, pictures of each set.

We’ll start with monsters. These are repeating patterns that really really annoyed mathematicians.
The most famous is probably the Koch Snowflake.
http://i.pgu.me/3RqfWDcx_original.jpg

This can give you a basic idea of what a fractal is. I think Ill just have one other monster, since they are so boring.
Sierpiniski’s triangle:

Okay, now for the fun stuff. Escape-time fractals. There’s a whole bunch of complicated math behind each one, but if you understand it your a mathematician and if your a mathematician you wouldn’t have read this far anyway, so… no math.

First, the Mandelbrot set. Lots of images for this.






That’s probably enough.

Next, the Julia set. This is different from the Mandelbrot set because it can have many different shapes.




Excellent use of variables, there.

Next, we have the Lyapunov Set. You make these with a short AB pattern. Changeable.

This here’s a burning ship fractal. Also changeable.


A cool video using it:


This makes me laugh. Geek humor.

Then we have these Nova and Newton fractals. Their ugly. If you really want to see them you can go look them up on Wikipedia, I guess, but its not worth it.

Ok, so that’s the majority of 2D fractals. There’s also some weird fractal flame stuff, but its so confusing I’m not going to post anything about it. So, now for 3D stuff. You put your favorite 3D video in the comments, and Ill put it up here.


#2

:smiley:


#3

:smiley:


#4

:smiley:


#5

:smiley:


#6

:smiley:


#7

:smiley:


#8


#9

Fractals are awesome! :slight_smile:


#10

:smiley:


#11

:smiley:


#12

:smiley:


#13

:smiley:


#14

Nope, but this does

:smiley:


(WildCat23) #15

This is like the stuff you see when you close your eyes and lay down for a while without falling asleep.


#16

Really? My second attempt worked on my iPod. Hmm…


#17

I just generated this one this morning.


#18

I made this one this morning too.


#19

:smiley:


#20

:smiley: