Fractal visionaries:

For today's fractal I turned to the classic Mandelbrot set.  But I did a few tricks with it, so don't expect just another Mandelbrot fractal.  To begin, I sliced the Mandelbrot-Julia figure in the XZ plane.  In relation to the M-set as it usually appears on the screen, this is the orientation of the surface of your desktop.  The area displayed is deep inside the right valley at the mouth of the top bud of the M-set.

The second trick was exaggerating the vertical distances in my picture by a factor of 10,000.  If I didn't do this, nothing but a few thin horizontal streaks would be visible.  In the XZ plane, the features stretch out as one nears the XY plane.  This is because the features are actually curved around the origin of the four-dimensional Julibrot figure, and are being sliced at a very sharp angle.

I have heard it said that the slices of the Julibrot figure other than the classic Mandelbrot and Julia sets hold little of interest.  As you can see, my explorations are proving otherwise.

Tomorrow, I'll extend my explorations to the oblique slices of this 4-D object, and see what kind of a fractal I can turn up.

Jim Muth
jamth@mindspring.com


START COMBINED FILE FOR 19.6===============================

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  formulaname=Man-YZ-XZ passes=1
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  params=0/0.65/1/0 float=y maxiter=50000 inside=255
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frm:Man-YZ-XZ {; Jim Muth
; p2 = 0 = Julibrot YZ plane
; p2 = 1 = Julibrot XZ plane
; p2 = >0 <1 = Oblique planes
z=real(pixel)+flip(real(p1)),
c=imag(pixel)+flip(imag(p1)),
a=p2, b=flip(cos(asin(p2))):
z=sqr(z)+((a+b)*c),
|z| <= 25 }

END COMBINED FILE FOR 19.6=================================