May 12, 1997: Seven Magnificent Minibrots | May 11 | May 13 | 1997 | FOTD Home |
Fractal
visionaries:
Over the past 7 years, I have probably written and deleted thousands of
formulas. Most of these were discarded because they produced
either a blank screen or duplicated figures that were more easily drawn
with simpler formulas. Only a few survived to find a
permanent
home in my formula file. Today's
formula, Test15, is one of the survivors. I've yet to get
around
to naming it.
I thought of the formula today because I've been reading lately of
formulas that draw multiple midgets in a circle. One thing
today's formula does, among many others, is to draw any number of
midgets of any order, facing either in or out, in a circle around the
origin. Today's picture, seven_up, shows seven midgets of
order
two, arranged in a circle facing outward. To
have them face inward, change the +0.35 assigned real p2 to -0.35.
I'll leave it to the intrepid fractal explorers to discover how to
change the number of midgets, or how to change their shape to midgets
of a different order. I'll give only the caution that
it's easy to get hopelessly lost. But even if you get lost,
you'll see some strange sights.
It's a tricky process involving several parameters that must be changed
and coordinated at the same time. (OK, if anyone
really wants to know, I'll send the method along, but be warned that
the description of the method is mathematically convoluted and will
make rather tedious reading.)
To atone for today's fractal, which is much math and little art, I'll
post a great piece of fractal art tomorrow.
Jim Muth
jamth@mindspring.com
START COMBINED FILE FOR 19.6====================================
Seven_Magnificent { ; time=0:00:02.91-SF5 on P4-2000
reset=2004 type=formula formulafile=jim.frm
formulaname=Test15 center-mag=-0.00126273/0/0.51461
params=0.25/4/0.35/-3/2/1 float=y maxiter=90
inside=0 outside=tdis symmetry=xaxis periodicity=10
colors=000000eJ`_ESU9JO4AMIBLVCJgDItEzeLzURzzXzzSz\
zOzzsrTsQu8Qu8Qt8Qt9Qs9Qs9Qs9QrAQrAQqAQqAQqBQpBRpB\
RoBRoCRnCRnCRnCRmDRmDRlDRlDRlERkERkERjERjFRjFRiFRi\
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j9gn8gq7hw8gt8gr9gp9gnAflAfjAfgBfeBecCeaCe_CeYDdVD\
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`aNbbMccLddLfdKgeJifIjgIkhHmiGnjFokFqlErmDtnCuoCvp\
BxqAyqAzoDwmFukHriJpgLmeNkcQhaSf_UcYWaWYZU_XSbUQdS\
OfPMhNKjKGmGHlHIlIJlIJkJKkKLkKMjLMjLNjMOjNPiNPiOQi\
PRhPShQShQThRUgSVgSVgTWfUXfUYfVXiWYhVYgVYfVZfUZeUZ\
dUZdU_cT_bT_aT_aT``S`_S`_S`ZRaYRaXRaXRaWQbVQbVQbUQ\
bTPcSPcSPcROcQOdQOdPOdONdNNeNNeMNeLMeLMfKMfJLfILfI\
LgHLgGKgGKgFKhEKhDJhDJhCJ }
frm:Test15 {; Jim Muth
z=pixel, a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), k=real(p3), f=imag(p3), g=f*(pixel):
z=((a*(z^b))+(c*(z^d)))^k+g,
|z| <= 100 }
END COMBINED FILE FOR 19.6======================================
END VERSION 19.6 FORMULA-PARAMETER FILE=========================