In article <D6368981A5754454B8FB422FB07A9ECC@charlie>, "David M Fisher" <sunfish8@verizon.net> writes:
I was going through my fractal files and asked myself a question to which I don't know the answer: Exactly what am I seeing when I view a fractal?
Depends on the fractal. With complex plane iterated formulas, what you are seeing is the visualization of stable orbits as the inside of the set and unstable orbits as the outside of the set. With IFS or L-system fractal types, you're seeing something else. Bifurcation diagrams and some of the other fractal types in fractint (ant, cellular) are different visualizations of chaotic systems.
What is the relationship of the display to the <z> axis?
Nothing standard, really. Some iterated equations in the plane are slices of higher dimensional structures and for those it makes sense to think of the Z axis being something relevant.
Is it possible to rotate any fractal so that any axis becomes any other axis? Or is the computed display all there is? Is it possible to begin parsing with different axes? Basically, imagine a rectangle the ratios of which (x, y, z) are 2:4:1 (of any magnitude). Where on, or in, this rectangle is the position of the fractal? And if it were observed from the smallest axis (z), what would it look like?
Well, most iterated plane equation fractals don't have a volume or a Z, so I'm not sure what you mean by this. You can artificially consider Z to be the number of iterations before behavior (stable or unstable) of the orbit is determined. However, this interpretation of "Z" isn't part of the fractal itself and is just a visualization trick. -- "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download <http://legalizeadulthood.wordpress.com/the-direct3d-graphics-pipeline/> Legalize Adulthood! <http://legalizeadulthood.wordpress.com>