July 7, 1997: Point of Attraction | July 6 | July 8 | 1997 | FOTD Home |

Fractal
visionaries:

We're entering the summer doldrums, (at least here in the northern
hemisphere), and things are slowing down all around. In honor
of
the occasion I've posted a hot fractal. I named it "Dawning"
because it vaguely reminds me of a sunrise. But it looks like
no
sunrise I've ever seen on Earth. Perhaps it's a sunrise on
Mars.

Actually, it's a scene in a four-dimensional Mandelbrot set.
This
is not the four-dimensional julibrot figure I talk about so much, but
an actual 4-D Mandelbrot figure, where if the Julia sets are
considered, we have an eight-dimensional figure.

No, I am not able to picture this object in my mind; I'm not even going
to try. The 4-D julibrot monster is hard enough.
But at
least by taking that figure one 3-D slice at a time I'm making progress.

The formula is a slightly modified version of the Hypermandel formula
in Fractint. Being as obsessed as I am with the julibrot
figure,
I haven't done much exploring of the HyperSquare formula, but I do know
that it's full of surprises. Maybe one of these days I'll
really
dive down deep into it and find something entirely unexpected.

Today's image has been honorably posted to a.b.p.f. and
a.f.p.
Tomorrow's fractal will be a surprise I found in the XZ plane.

Jim Muth

jamth@mindspring.com

START 19.6 FILE=============================================

Point_of_Atraction { ; time=0:00:56.24-SF5 on P4-2000

reset=1960 type=formula formulafile=jim.frm

formulaname=HyperSquare passes=t center-mag=+0.011\

68689983424549/+0.1087448950599747/71.4165

params=0/0.9993/10/0/1e-010/0 float=y maxiter=1600

bailout=100 inside=0 logmap=yes periodicity=0

colors=000O`LQ_KSZJVYIXXHZWG`VFcUEeTDgSCiRBlQAnP9p\

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zzzzzzzzzzzzzzzzzzzzzzzzz }

frm:HyperSquare {; Jim Muth

a=(p1),b=(0,0):

q=sqr(a)-sqr(b)+pixel

b=p2*a*b+p3

a=q,

|a|+|b| <= 100 }

END 19.6 FILE===============================================