Fractals
No idea what I'm talking about? Here's one picture of a
Julian Set
(generated by Fractint)
The 4 dimentional set consisting of all Julian sets, and including the Mandelbrot.
The concept is not so completly new, but I havn't seen it rigorously treated yet.
It's a fairly simple idea: for the formula Z = Z^2 + C, there are (in a way,) 2 variables (Both of which are complex): C, (Which is varied to produce the M-set, letting Z(0) be (0,0) each time,) and Z(0) (Which is varied to produce a J-set, holding C at one value.)
So... it seemed clear to me, that all these together make up ane big set. So, I wanted to look at some other planes intersecting the space. On paper, I worked out that,(taking the pixel to be x,y)
Z(0)= x+ iy | C= 0 + i0
will be a circle.
Z(0)= y+ i0 | C= x + i0
will be something like the space between two Parabolas, opening left.
"So," thought I, "What would it look like if I smoothly rotated from a circle to a M-set?" shouldn't it be enchanting? To see a gradual development from total simplicity to, well, ordered chaos?
Well... I was EVER so excited when I downloaded
FractInt
and fount that there was a 3-D J-set... but limited to being regular J-sets, layered an top of one onother. There IS the possibility to define your own formula for generating a fractal.
My problem is, that I don't have a C-Compiler which functions. So... I'm still immagining what it could look like. If you are interested, and are able to compile the C-Code, let me know! I am quite interested, (to say the least,) in exploring the possibilities.
Back to Assorted |
The Main Index