FOTD -- January 02, 2003 (Rating 8)
Fractal visionaries and enthusiasts:
For the second day of the second year of the third millennium we
have a fractal image that rates a much-above-average 8. It is
one of my 'evaporated' scenes, where I take an image that
contains a negative power of Z, find something interesting, and
then raise the bailout radius to one-googol, which causes the
screen to go blank. Next, I apply one of the non-flat inside
fills to the image, which now consists totally of 'inside'
points. Sometimes, nothing much happens, but usually, the
inside fill reveals the 'ghost' of the scene that originally was
there. Thus, today's image is a ghost, a thing which in the
world of fractals certainly does exist.
I was a bit puzzled when the time came to give a name to the
image. It reminded me of something...but what? Then, after
pondering for several minutes, I thought of a jellyfish. This
was it. The image, with its appearance of transparency, reminds
me of a jellyfish drifting gently in a warm ocean current. Of
course, no real jellyfish is so symmetrical. It is the effect
of transparent elements before an infinite blue background that
earns the name.
The warhorse MandelbrotMix4 formula calculated a critical plane
of the expression 45Z^(-0.8)-36Z^(-0.9)+(1/C) to create the
parent fractal of today's image. When calculated with the
default bailout radius, this parent is little more than a circle
filled with great blobs of fractal glop. But a small bud of
Mandel-material lies on the X-axis, and today's image is located
at the tip of a filament stretching from a sub-bud of this bud
into an open area, where it finally dies out.
The 37-minute render time of the attached parameter file is
slow. Those with other things to do as the normal work routine
resumes will want to download the completed GIF image from
Paul's web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
or from Scott's site at:
<http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
With the temperature hanging in the middle 40'sF (around 6C), it
rained steadily all day Wednesday here at Fractal Central, some-
times quite heavily with occasional claps of thunder. Some
minor flooding was reported around the area, but F.C. remained
dry. The dynamic cats were very depressed however as they sat
at their window, watching the rain and wishing they could go
out. An evening treat of tuna helped ease their depression, but
they still ended the day in a sullen mood.
Though today is starting cloudy, at least the rain has ended,
which is a good sign. Now, if the mud in the yard would dry,
the dynamic ones might have a pleasant day. It will take more
than a dry yard to make my day pleasant however. This will not
happen until the design work is finished, and it will not be
finished until I begin. So until tomorrow, take care, and be
kind to your fractals.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START 20.0 PAR-FORMULA FILE================================
Jellyfish { ; time=0:30:23.25--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=t
center-mag=-0.4004091333751482/+0.0215282924423132\
/3.080974e+007/1/80/-1.5530640837951859e-007
params=45/-0.8/-36/-0.9/0/1e+100 float=y logmap=yes
maxiter=1200 inside=fmod proximity=1 periodicity=10
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rP7pTAoXDn`GmdJlhMklPjpSi }
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END 20.0 PAR-FORMULA FILE==================================
Hi folks!
Grateful for all your answers which I've enjoyed - all
of them interesting attempts to reduce such a complex
subject to a simple definition. Special thanks to Jos
H.'s for having been particularly entertaining, giving
me enough food for reflection :)
Cheers all!
Anna
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FOTD -- January 01, 2003 (Rating 7)
Fractal visionaries and enthusiasts:
It's a new year here at Fractal Central, and we start it off
with a sudden switch to an optimistic outlook and a trip to the
Z^(sqrt(2))*(0.6(C))+C fractal to find an image that rates a 7.
The parent fractal was drawn by the JimsCompMand formula, which
is simply a generalization of the cmplxmarksmand formula of
Fractint.
The strange little midget in the image lies in the East Valley
area of the largest midget on the main stem of the Z^(1.4142)+C
Mandeloid. Yes, I can already hear the voices telling me that
the Z*(1.4142)+C Mandeloid has no main stem, that the stem
vanishes as the exponent of Z is dropped to a value less than 2.
This is true, but the parent Mandeloid of today's image is not
exactly the Z*(1.4142)+C figure. In the JimsCompMand formula,
Z^(1.4142) was multiplied by 0.6(C) before (C) was added. This
multiplication causes the fractal to split apart along the
negative X-axis, and this splitting causes the non-existent
negative stem to emerge from never-land into the world of
fractal reality, where it can be examined as though it had never
vanished.
The prominent midget is still there on the revealed stem,
grossly distorted of course, with its East Valley still easily
recognizable. The stem itself still zig-zags down into the
center of the valley, and it still has midgets strung along it,
though at such a low power of Z, the midgets are rather
difficult to pick out along the zig-zagging and branching stem
filament.
Today's scene lies quite deep, so deep in fact that it actually
shows signs of breaking up, and needed the mathtolerance reset
to /1 to reach the magnitude. I have included the mathtolerance
setting in the parameter file so that the image will draw at the
correct magnitude at all resolutions.
I named the image "Broken Symmetry" because of the spectacular
discontinuity that, along with the coloring, spoils (or makes)
it. This is the one of the greatest degrees of disorder that I
have yet come upon, though undoubtedly an infinity of midgets
with even more disorder do exist and are waiting to be found.
The 13-minute render time is a bit trying, and may be avoided by
visiting Paul's FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
or Scott's site at:
<http://sdboyd.dyndns.org/~sdboyd/fotd/index.html>
and downloading the completely rendered image from there.
The weather was much improved Tuesday here at F.C., with mostly
sunny skies, light breezes, and a temperature of 55F 13C. The
small amount of dampness remaining in the yard did not deter the
dynamic ones from enjoying a 2-hour romp, which helped their
moods immensely. In fact, they ended the day in such a pleasant
mood that they were satisfied with their normal diet.
But today is rainy, and I doubt that their pleasant moods can
weather the storm. Check tomorrow to see how they make out. As
for me, I'll probably do little more than watch football on the
TV. Until next FOTD, take care, and here we go again with
another whole year to get through.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START 20.0 PAR-FORMULA FILE================================
Broken_Symmetry { ; time=0:13:24.99--SF5 on a P200
reset=2002 type=formula formulafile=jim.frm
formulaname=JimsCompMand passes=1 mathtolerance=/1
center-mag=-1.36389419716712900/+0.671782211838532\
70/1.326342e+013/1/102.501354055520352/3.885780586\
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zzdzzczzbzzbzzazz`zz7zz7z }
frm:JimsCompMand {; Jim Muth
z=c=pixel:
z=z^p1*(c^p2)+c,
|z| <= p3+100 }
END 20.0 PAR-FORMULA FILE==================================
