Only 20 years? I've been following this for longer I'm sure... -----Original Message----- From: fractint-bounces@mailman.xmission.com [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Jim Muth Sent: 20 October 2010 20:14 To: fractint@mailman.xmission.com Subject: Re: [Fractint] What? At 09:34 PM 10/19/2010 -0400, D Fisher wrote:
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? What is the relationship of the display to the <z> axis?
When a Mandelbrot fractal is viewed, the two C axes are displayed on the screen, while the two Z axes are perpendicular to the plane of the screen. This nonsense is possible because the formula Z^2+C consists of two complex numbers which have four variables in all. Four variables define a space of four dimensions. (In the Julia sets, the Z axes are on the screen, while the C axes are perpendicular.)
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?
Yes, any Fractal may be rotated through any orientation in the four-dimensional hyperobject called the Julibrot. The SliceJulibrot4 formula that I frequently use does just this.
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?
The Mandelbrot set cuts a two-dimensional slice through the center of the Julibrot, though it does not cut the Julibrot apart. The perturbed M-sets cut other slices in the same orientation, though not through the center. The Julia sets cut slices through the same Julibrot in an absolutely perpendicular orientation. When a Mandelbrot set is viewed from the other 2 axes, nothing of the M-set remains but a single point, but we now see new stuff surrounding the point that we call a Julia set.
This has me baffled, and is mind game that is generating a lot of heat. Any answer would be appreciated, but especially one I could understand. Thx
David M fisher
This is the situation as I see it. Lots of luck understanding it. After 20 years, I'm still not sure I actually understand it. Jim M. _______________________________________________ Fractint mailing list Fractint@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint