FOTD -- June 28, 2008 (Rating 7)
Fractal visionaries and enthusiasts:
Today's formula, DivideBrot4, is another new one -- the final
version of the DivideBrot series. The only change from
DivideBrot3 of the series is in the real(p1) parameter, where
the number 2 is subtracted from the entered value before
iteration begins. This change permits the order of the
minibrots to be directly defined by the value entered as
real(p1).
The real(p2) parameter defines the escape radius. The imag(p2)
parameter is not used. The imag(p1) parameter controls the
prominence of the higher-order elements in the resulting
fractal. A smaller value of imag(p1) results in a greater
prominence of the higher-order elements. A larger value gives
more prominence to the underlying order-2 Mandelbrot set, while
at the same time enlarging the size of the fractal, which makes
the real(p2) parameter necessary to expand the bailout radius so
that the entire fractal fits within it.
Today's image is named "No Fault Lines". I gave it this name
because the central minibrot is of the order 3.5 and such
fractional-order minibrots are always surrounded by discontinui-
ties, which spoil the surrounding patterns of the minibrots.
Today's minibrot however is a horse of a different color. Its
surrounding pattern consists of seven elements, and these
elements are intact. Seven, of course, equals two times 3.5,
the order of the minibrot. The name refers to the lack of
discontinuities.
The image is located on the west side of the northern branch of
the Seahorse Valley of the oversized Mandelbrot set that is its
parent fractal. The Seahorse Valley characteristics are very
prominent throughout the image. The order-3.5 characteristics
are obvious only in the shape of the minibrot.
I rated the image at a 7. It consists of too much mathematics
and not enough artistic value for a higher value. Rendering the
scene with the outside set to 'tdis' helped a little, but not
enough to grant the image a rating of 8.
With its calculation time of 1-3/4 minutes, the job of running
the included parameter file should offend no one. But in this
modern day and age, some computers have forgotten the old ways
and don't know what to do with DOS programs such as Fractint.
Those with such new-fangled instruments may still see the image
however by going to the FOTD web site at:
<
http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
and viewing it there.
Warm temperatures, high humidity and showers prevailed here at
Fractal Central on Friday. The fractal cats dislike a tempera-
ture of 86F 30C, so they were not too happy with the conditions.
But cats are cats, and before long the feline duo had found a
cooler place in which to sleep.
My day was kept busy by a customer of the worst kind -- one who
needs his job at once, but doesn't know what he wants, and as a
result, keeps calling in changes. In the end, common sense won
out. I refused to answer the phone after the fifth call. The
last I heard, he was satisfied. The next FOTD fractal will be
posted in 24 hours. Until then, take care, and look up.
Jim Muth
jamth@???
jimmuth@???
START PARAMETER FILE=======================================
No_Fault_Lines { ; time=0:01:44.21-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot4 passes=1
center-mag=-7.662916327120194/+1.181354355289796/\
3.256997e+007/1/-98.25/0 params=3.5/10/1000/0
float=y maxiter=5000 inside=0 outside=tdis
logmap=110 periodicity=10
colors=000JP3UgDP0DK99FH65zX7mN9`DhsH_kDRcAIW6NwsH\
rbFjUDcLBWCW8Nor4ah3OZ331vtV3My`IlPE`EnHocJbULRKNF\
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LDhI9PL6XCTPHKHLBBMvANhAOVAPHKeFBadAXSATFERCCQ7AI5\
Ac4Ac4Ac34cR6mJ8mBOmr4m36m3zz3zzuzzgzzUzzGzzRzzFzz\
jzzWzzHzzezzWzzMzzCzz2zz3 }
frm:DivideBrot4 { ; Jim Muth
z=0, c=pixel, a=real(p1)-2,
b=imag(p1), d=real(p2)+100:
z=sqr(z)/(z^(-a)+b)+c
|z| < d }
END PARAMETER FILE=========================================
