FOTD -- July 04, 2008 (Rating 8)
Fractal visionaries and enthusiasts:
In a recent letter to the Fractint list, JoTz noticed that the
parent fractal of the "Order Septemdecem" FOTD image, which
resembles a Mandelbrot set and was posted on June 27, has a bit
of unexpected detail in its interior. I have known about this
extra stuff since I started working on the DivideBrot formulas.
The extra detail in the parent of the septemdecem fractal is
actually the fragmentary remains of a Z^17+C Mandeloid, which
appears when the imag(p1) parameter is set very close to but not
exactly at zero. (I usually use the number 0.0000000001 instead
of zero. In this case, the exponential form [1e-010] inserted
in the formula does not work. This will be corrected in version
number 5.)
When imag(p1) is set to virtually zero, the resulting fractal is
the normal Z^17+C Mandeloid. But as imag(p1) is increased, this
Mandeloid gradually grows in size and morphs into the tradition-
al Mandelbrot set, leaving order-17 debris to dissolve in the
interior of the forming M-set. Some of the intermediate steps
are quite interesting, but due to the size change, an animation
with consistently sized elements would be difficult.
The basic rule is: the smaller the value of imag(p1) the smaller
the size of the resulting fractal and the more prominent the
higher order shape, while at the same time, the greater the
value of imag(p1) the larger the size of the resulting fractal
and the more prominent the classic Mandelbrot-set shape.
Today's scene takes advantage of the dissolving high-order
debris in the center of the main bay of the parent 'almost-a-
Mandelbrot set'. The scene is located in what first appears as
a tiny dot, but when blown up reveals itself as an entire
fractal universe.
Due to the unusually large magnitude of the image, an outzoom
to the parent fractal is quite a trip, but very interesting.
But be sure to turn off the logmap feature before taking the
backwards trip.
BTW, the DivideBrot4 formula will soon be superseded by the
DivideBrot5 formula, which will be used for all future fractals
of today's type.
I rated today's image, which shows an unusually well-defined
cubic minibrot, at an 8. It's worth it. I named it "Perfectly
Cubic" for the same reason.
The calculation time of 47 seconds will cause no pain to those
with computers that are not over-qualified. Those with machines
that can surf the web in a flash but cannot run Fractint may
still see the image by visiting the FOTD web site at:
<
http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
and enjoying there the image that Paul calculated.
Lots of clouds, only a little sunshine, high humidity, a tempera-
ture of 84F 29C, and a threat of rain followed by actual rain,
made Thursday less than ideal here at Fractal Central. Not
concerned with weather, the fractal cats spent a good part of
the day trying to catch a fly. When one of them eventually
caught it, the exhausted duo settled down to sleep.
My day was busy, mostly because tomorrow is a holiday. The FOTD
does not take time off for holidays however, and will be posted
on schedule in 24 hours.
Jim Muth
jamth@???
jimmuth@???
START PARAMETER FILE=======================================
Perfectly_Cubic { ; time=0:00:47.85-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot4 passes=1 center-mag=-0.606\
3981173832952/+0.006169462807566/5.040456e+012/1/\
-83.80/0 params=3/3/3/0 maxiter=1000 logmap=58
float=y inside=0 periodicity=9 mathtolerance=0.05/1
colors=00097UAAWBDYCG_DJaEMcFPeGSgHViIZkKbmMfoOkqQ\
rsroumpsllqkhnjfliejgcheaec`caZa_Y_XWXUUVRSTOQROO_\
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do_znazmczmdzq_ztVzwQzzLzzIzzFzzDzzAzz7bz5azHazTaz\
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fzzfzzhzzjzzkzzmzzozzpzzrzzszzdJzQIz4Cz36z21z2Lz3d\
z4zz5zz6zz7zz7zz8zz8zz9zz9zzAVzASzBPzBMzCJzCGzBDzA\
BzA8z96z93z81z87zEDzJJzOPzTVzY`zbfzglzlqzqrzsszttz\
vuzwvzywzzrztnzniziezcQzk }
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=========================================
