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.
 

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