July 22, 1997: Bullet | July 21 | July 23 | 1997 | FOTD Home |

Fractal
visionaries:

Today's fractal looks like a burgundy bullet caught by a stop-action
camera. Even the shock wave is visible, so I named it
"Bullet". Actually, it's a midget in the XW plane, where
everything resembles a parabola with the open end in the positive
direction. Don't let the maxiter of 3,000,000 worry you; all
the
open areas are periodic, and the picture draws in under 2 minutes.

The picture raises an interesting question -- what feature is to be
considered the entire midget -- the bullet-shaped central area, or the
vertical band partially obscured yet still clearly visible through the
parabolic chaos? This band must be part of the midget because
it
forms part of the midget's boundary.

The breaks in the overlying chaos, where this dark band shows through,
represent all the perturbed Mandelbrot sets with purely imaginary
starting points, where parts of this particular midget are
visible. Here again, we have an example of the totally
different
behavior of the low and high iteration parts of the fractal.
This
different behavior demonstrates that regardless of where a point
starts, if it doesn't escape first, it will eventually settle into the
same orbit as a point that started at 0,0.

And right now, I'm going to settle into my favorite chair to watch the
evening news on TV. Today's finished product has been posted
to
a.b.p.f. and a.f.p. as always. For tomorrow -- I don't
know. We'll see when the time comes.

Jim Muth

jamth@mindspring.com

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

Bullet
{ ; time=0:00:13.40-SF5 on P4-2000

reset=1960 type=formula formulafile=jim.frm

formulaname=XY-XWrotation passes=1

center-mag=-0.00594679/0/3.26976/5.4395

params=89.99/0/0/0/-1.7545/0 float=y

maxiter=3000000 inside=0 logmap=yes periodicity=10

colors=000OFFNFELFCKFBIE9HE8FE6DE5AF3CF4DE5FE6HE7I\

E8KD9MDANDBPDCRCDSCEUCFWCGXBHZBI_BJaAKcALdAMfANh9O\

i9Pk9Qm9Rn8Sp8Tr8Uv3Qs7TqCXnG_kKbiPffTicXl``oZesWi\

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TUlUUlUVlVWlWWlWXlXYlXYlYZlZ_lZ_l_`lAPC8PA7P98OAbI\

T`IS_IQYHPXHNVHMTHKSGJQGH }

frm:XY-XWrotation {; Jim Muth, thanks to Benno Schmid

; p1 = rotation angle in degrees, p2 = parallel planes

; p3 = point of rotation and parallel planes

z=sin(p1*.01745329251994)*flip(imag(pixel))+p2,

c=cos(p1*.01745329251994)*flip(imag(pixel))+real(pixel)+p3:

z=sqr(z)+c

|z| <= 16 }

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