I think I found a new way to extend Mandelbrot set to 3D. I read twinbee's article about the Real 3D Mandelbrot set. The idea is brilliant! But I think it contains a little mistake: when you square a complex number ((a,b) vector) its angle with x-axis doesn't change to 2 times bigger. The relation between original and new angle is: original tangent=b/a, new tangent=2ab/(a^2-b^2).
In my formula I also used 2 following rotations and calculated angle in this way. I squared z=(x,y,u): z^2=Z=(A,B,C) ; where B/A=2xy/(x^2-y^2), C/B=2Bu/(B^2-u^2), and abs(Z)=abs(z)^2.
The iterative function is (yes, in pascal...
dim1:=x; dim2:=y; dim3:=u;
while zabs<4 do
if (abs(x)<null) and (abs(y)<null) then
sqrx:=sqr(x); sqry:=sqr(y); sqru:=sqr(u);
if (0<=denom) and (denom<null) then denom:=null
else if (-null<denom) and (denom<0) then denom:=-null;
The formation contains the 2D Mandelbrot set, and this 3D extension seems very logic to me: line at head changed to plane, and form has more and more smaller furrows like 2D Mandelbrot has more and more smaller circles. As the standard 2D Mandelbrot called Appleman I call this form Orangeman
I took some pics. Last 5 made with 7 iterations only. Unfortunately I am not a graphic artist yet, but I hope you will render some nice pics
(For anaglyph pics put red-cyan glasses on!)