FOTD -- October 23, 2011 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image is a scene in the East Valley of the large
minibrot on the main stem of the Mandelbrot set. The parent
fractal is in fact a Mandelbrot set that takes on order-9
characteristics in its depths.
The minibrot at the center lies near a larger minibrot, which in
turn lies near an even larger minibrot . . . At this point I
lose count of the minibrots, but I think there are about four of
them in the ladder-chain up to the surface.
The name "A Sheep in the Deep" has no connection at all with the
image. It simply popped into my head when I made my mind a
blank, a task I find quite easy to accomplish.
The rating of a 7 includes a full point for the coloring, which
took over twice as long as calculating the image. The
calculation time of 3 minutes entered into the parameter file is
an educated guess of the time the calculation would have taken
on the faster but now dead machine. (The image actually took
12-1/2 minutes to finish on the slow unit.)
The finished image may be viewed on the official web site at:
<http://www.crosscanpuzzles.com/Archives.html>
without the need to calculate it.
The high-definition version is posted at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original, now classic web site may be accessed at:
<http://www.Nahee.com/FOTD/>
The morning fog cleared off by 11am here at Fractal Central
today, leading to a sunny afternoon with a temperature of 59F
15C. The fractal cats, still on watch for a possible return of
the fighting tomcats, spent the first part of the day in the
window facing the back yard. But the fighters have apparently
moved on, and by the afternoon the fractal cats shifted their
watch to the sunny shelf in the southwest window, which faces
the front sidewalk.
The humans spent the day doing nothing, which is quite enjoyable
when it is done in moderation. The next FOTD will be posted in
24 hours. Until then, take care, and would this country's real
savior please put in an appearance.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
A_Sheep_in_theDeep { ; time=0:03:00.00-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=FinDivBrot-2 function=recip passes=1
center-mag=-1.749083935595091/+0.00000124195835773\
/1.4056e+013/1/-42.5/0 params=9/500000000000000.0/\
0/0 float=y maxiter=2600 inside=0 logmap=333
periodicity=6 mathtolerance=0.05/1
colors=00000200300401502603613724835846956A67A78B8\
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bzzezzhzzkzznzzdzzVzzLzzBzz1zzxzzpzzizzbzzWzzTzzQz\
zOzzKzzGzzDzz9zzbzzbzzXzz }
frm:FinDivBrot-2 { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }
END PARAMETER FILE=========================================
FOTD -- October 21, 2011 (Rating 8)
Fractal visionaries and enthusiasts:
In these FOTD discussions I often mention the parent fractal of
an image. In most cases, this parent fractal is the image that
appears on the screen when the formula parameters are entered
and nothing is changed. My default settings are: a magnitude of
0.66..., the default color palette, a maxiter of 1500, a
periodicity of 6 and a logmap of zero.
Sometimes an outzoom is needed to fit an entire oversized parent
onto the screen, or an inzoom is needed to enlarge an undersized
parent to fill the screen. In other cases, there is no limited
fractal that could be called a parent fractal. The entire
parent fractal appears to be of unlimited size. Today's image
is one of these misfits.
Today's image lies in the apparently infinite fractal that is
created by the MandNewt06 formula. This can be demonstrated by
repeatedly outzooming from the image until the limit of Fractint
is reached. Even way out here, there is no sign of the fractal
coming to an end.
As for the image itself, it reminds me of blue clouds caught
evaporating away to reveal a universe of brownish spheres
loosely arranged into nets and spirals. I rated the image at
an 8, a full point of which is a bonus for the coloring effort
needed to get reasonable smoothness from 256 colors.
The name "Evaporation" refers to the bluish clouds, which to me
appear to be clearing away, perhaps after a fractal storm. The
calculation time of just over a minute will bring grief to no
one if, in their opinion, the image lays an egg.
For a little fun, try changing the exponent part of the real(p4)
parameter a few orders of magnitude in either direction and
watch the blue cloud totally evaporate or thicken.
The already-calculated image is available on the official FOTD
web site at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition version is at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
Typical October weather prevailed here at Fractal Central today,
which made for a not too pleasant afternoon. The sun was
blocked most of the time by dark lumpy clouds scudding from the
west, (stratocumulus), which dropped occasional sprinkles, while
the temperature remained stuck in the mid 50's F around 12C, and
the wind gusted to 20mph, 30kph. Not being weather wise, the
fractal cats ignored the marginal conditions and concentrated on
deciding who would own the new chair. FL put a heavy afghan
over the chair to thwart their scratching efforts while they
bickered for ownership.
The next in the apparently unending series of fractal images
will be posted in 24 hours. Until then, take care, and if I
don't exhaust the supply of fractals in this world, I'll keep
finding them in the next. But I still wonder how I'll continue
posting them to the list.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Evaporation { ; time=0:01:08.27-SF5 on P4-2000
reset=2000 type=formula formulafile=basicer.frm
formulaname=MandNewt06a passes=1 float=y
center-mag=-0.0587134/0.29352/32.89674/1/-135/0
params=-1.82/-1.79/2.48/-1.18/1.28/1.63/1e-030/0
inside=bof60 logmap=yes periodicity=0 sound=off
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frm:MandNewt06a {; Jim Muth
z=c=(pixel*p1):
a=z^3+(c-p2)*z-c
b=p3*z^2+c-1
z=z-1*a/b
p4 < |a| }
END PARAMETER FILE=========================================
FOTD -- October 22, 2011 (Rating 7.5)
Fractal visionaries and enthusiasts:
The October 22 image is late because I spent extra time today
trying to get the 2000mhz fractal computer to run. The machine
has always been questionable, and this morning, when it came on
with a blue 'something's wrong' screen, I decided to try only
one more time to get it running. Reseating all the cards did
nothing, so I said farewell to the 9-year-old 2000mhz unit,
stored it in the closet, and brought the 13-year-old 200mhz
machine out of retirement.
The older machine booted up perfectly, and now has the position
of honor on the fractal desk top, where it will remain until
replaced by the next currently active machine to be retired.
The failed machine will live on however through its video card,
which handles the Fractint DOS video modes perfectly, and which
I will install in the replacement machine.
Today's image is a quickie that I found on the old fractal
computer after the newer unit stopped working. The very fast
image is a mixture of Z^2 and Z^5 created by the FinDivBrot-2
formula. The rating of a 7.5 includes an unusual 1.5-point
bonus for my coloring work. The basic fractal shape has
appeared several times previously as FOTD's, but I did devote a
considerable time to achieve the slate-gray effect, which was
only inspired by the program and needed much hand work.
The central shape is filled with quintic minibrots, all of which
are virtually identical and not worth the trip down. The parent
minibrot is one of those deceptive Mandelbrot sets that at first
glance appears normal, but develops more quintic-like features
the deeper one dives into it.
The name "Platinum Oxide" refers to the overall color cast.
The calculation time of 35 seconds is an estimate. The image
actually took 2 minutes and 13 seconds on the 200mhz unit. On
the 2000mhz machine, which runs 4 times, (not 10 times}, as
fast, I assume it would finish in 35 seconds.
The already-calculated image is available on the official FOTD
web site at:
<http://www.crosscanpuzzles.com/Archives.html>
The high-definition version is at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original, now classic web site may be accessed at:
<http://www.Nahee.com/FOTD/>
Today's weather here at Fractal Central was a repeat of
yesterday's, with more dry but dark clouds, raw winds and a
temperature of 52F 11C. The fractal cats took the day in
stride, and were distracted only by a major cat fight that broke
out in the back yard when two prowling tomcats crossed paths.
The humans had a routine day, though I became quite annoyed when
the 2000mhz fractal computer went on the blink again.
The next FOTD will be posted in 24 hours. Until then, take
care, and the most qualified does not always win.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Platinum_Oxide { ; time=0:00:35.00-SF5 on a P2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=FinDivBrot-2 function=recip passes=1
center-mag=+0.3596259397545952/+0.6447633584097521\
/3515559/1/-30/0 params=5/100000/0/0 float=y
maxiter=1500 inside=0 periodicity=6
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oTsoTupUvpYeS_dQadPcdOddN }
frm:FinDivBrot-2 { ; Jim Muth
z=(0,0), c=pixel, a=-(real(p1)-2),
esc=(real(p2)+16), b=imag(p1):
z=(b)*(z*z*fn1(z^(a)+b))+c
|z| < esc }
END PARAMETER FILE=========================================
FOTD -- October 20, 2011 (Rating 8)
Fractal visionaries and enthusiasts:
Today we return to the warhorse formula, the MandAutoCritInZ,
where we check the parent fractal created when 3 negative parts
of Z^(neg(sqrt2)) are combined with 1.5 negative parts of
Z^(2*(neg(sqrt2))) and (1/C) is added on every iteration.
This parent consists of two large bays, one on each side of the
X-axis, with a large minibrot-filled field of debris scattered
to the east. Today's image lies in a smaller patch of chaos
just south of a large bud on the east side of the large north
bay.
Two tricks were involved in creating the effects in the image.
To begin, I reduced the bailout radius to an unusually small 7,
then I rendered the resulting image and its ballooning elements
with the 'outside' set to 'tdis'.
The name "Fantasia in Blue" was inspired by the overall blue
cast of the image, though I have toned the blue down a bit since
naming the image. The rating of an 8 is what I felt the image
was worth at the time I rated it. The calculation time of 3-1/2
minutes is well within reason.
To avoid all calculation hassle, view the finished image on the
official FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
And view it in high definition at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original, now classic, web site may be accessed at:
<http://www.Nahee.com/FOTD/>
Saturday was ruled by heavy clouds here at Fractal Central,
though the rain for the most part stayed to the west. The
fractal cats, who pay far less attention to the weather than the
humans, ignored the temperature of 57F 14C and had a lazy day,
taking turns sleeping on the new chair instead of fighting for
it.
The humans, FL and I, had an uneventful day also. With the
graphic design work slowing down, more and more days are
becoming uneventful. The one thing not slowing down however is
the FOTD, which I now have more time to work on. The next FOTD
will be posted in 24 hours. Until then, take care, and if the
climate changes, will the change be for the better or worse?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Fantasia_in_Blue { ; time=0:03:37.29-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=+1.300193586061464/+0.4252430675353652/\
2.728e+011 params=-3/-1.4142/-1.5/-2.8284/0/-93/0/0
float=y maxiter=1500 inside=0 outside=tdis
periodicity=6 mathtolerance=0.05/1
colors=000dD7iG5oJ2uM1uP0uS2uT4rW5qY7m`8kb9idBgfCd\
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00w00z00z0C3HI3EN4CT7BZA8 }
frm:MandAutoCritInZ {; 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)+(p4)),
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l }
END PARAMETER FILE=========================================
FOTD -- October 19, 2011 (Rating 8)
Fractal visionaries and enthusiasts:
For today's image I turned to a built-in Fractint formula, the
type=manzzpwr, a formula I rarely if ever bring up, which on
every iteration raises Z to the power of previous Z then adds
Z^(n). In today's image 'n' equals -12. After a few minutes of
tweaking and experimenting with the formula, I turned up today's
image, which for obvious reasons I named "Mandala-Head". The
image resembles one of those surreal paintings by Rene Magritte
in which people have things such as apples where their heads and
faces would be expected. Today's image has a mandala instead of
a head.
(A mandala is a devotional symbol representing the eternal
cycles that fill the universe, especially the cycle of birth and
death believed in by most eastern religions but considered
heathen doctrine by the western religions, where the doctrine of
only one chance to achieve salvation is accepted as truth.)
Most of the image's effect was achieved by rendering the scene
with both the inside and outside parts set to 'atan'. The
peach-turquoise color scheme adds to the effect, since the peach
areas somewhat resemble the color of skin.
The rating of an 8 might be a little liberal, but why not, since
today I'm in one of my more liberal moods. And there will be no
trouble at all with the calculation, since the time is a
fireball-fast 25 seconds.
For maximum convenience, the image has already been calculated
and posted to the FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
It is posted in high definition at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
The day began with clouds and mist here at Fractal Central. The
foul weather continued for the rest of the day, never quite dry
and never quite wet. The fractal cats approved of the
temperature of 66F 19C, but Cassie approved a bit too much when
she took her claws to the upholstery of the new chair and got
herself scolded.
The humans had another near normal day, with nothing out of the
ordinary to report. The next FOTD will appear in 24 hours.
I'll leave it to the individual fractalist to figure where it
will appear from. Until then, take care, and if reincarnation
is true, then about half the people on earth hold false beliefs;
if it is false, then the other half hold false beliefs. In
either case, the religious beliefs of at least half the people
on earth are false.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Mandala-Head { ; time=0:00:25.26-SF5 on P4-2000
reset=2004 type=manzzpwr passes=1 params=0/0/-12
center-mag=0.430612/0/0.5657059/1/-90/0
float=y maxiter=1500 bailout=10000 inside=atan
outside=atan logmap=yes periodicity=10
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gAWgeZQeZRe_Sf_Sf`Tf`UgaU }
END PARAMETER FILE=========================================
FOTD -- October 18, 2011 (Rating All Math)
Fractal visionaries and enthusiasts:
Today's image rates All Math. The mathematical interest is just
about all it has going for it. The image itself is little more
than a passing scene in an infinite world of fractals. And the
calculation time of nearly 2 hours is far beyond reason. In
addition, the exponent of Z that created the image is 1.0005, so
close to unity that no one in his right mind would enter it as a
parameter with any expectation at all of finding much more than
smooth and straight band edges.
Questioning my own sanity, I did enter this value as the
exponent of Z, and in addition I felt fairly confident of
finding something of interest. Today's image is what popped up
where nothing should exist.
The scene is neither a Julia set nor a Mandelbrot set, but
something in between. The detail in the image is not the
organized chaos that makes most fractals so interesting. The
detail in today's image consists of countless discontinuities
arranged into half-orderly elements. If any part of the image
is zoomed into, a flat featureless area will ultimately be
arrived at. In ordinary fractal chaos, the chaotic features
continue without limit.
The name "Down in the Boondocks" refers to the exponent of Z,
which is by far the closest to unity of any FOTD fractal so far.
A price must be paid for seeing detail in a fractal so close to
unity however. The price is the need of a very high maxiter,
resulting in a calculation time of 1-3/4 hours, which is tedious
indeed for such an unartistic image. But help has arrived in
the form of the FOTD web sites.
All the tedious calculating may be avoided by viewing the
finished image on the FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
It may be seen in high definition at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original, now classic web site may be accessed at:
<http://www.Nahee.com/FOTD/>
The day began with clouds here at Fractal Central, but the
clouds cleared off before noon, leading to an afternoon of
sunshine, balmy south breezes and a temperature of 70F 21C.
With rain and colder weather forecast, today might have been the
last near-perfect day of the fall.
The fractal cats passed a good part of the day sharing the new
chair. The humans disagreed a bit about politics (as is
standard) but the day passed uneventfully. The next FOTD will
be posted in 24 hours. Until then, take care, and liberal
thinkers know that conservative policies are the cause of the
problems, while conservative thinkers know that liberal policies
are the cause of the problems. Neither side appears able to
recognize that their conflicting views of the solution are also
a part of the problem.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
DownInTheBoondocks { ; time=2:05:44.73-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot5 passes=1 maxiter=120000
center-mag=+2.723099067722828/+0.02123607283229285\
/6919/1/5/0 params=37.5/0/37.5/0/1.1513/0/0/0/1.00\
05/0 float=y inside=0 logmap=-15900 periodicity=9
colors=000zdCzeEzfGzgIzhKziMzjOzkQzmSznUzoWzpYzq_z\
razsbzs_zsXysUwsRurOsqOqpOooNmnNkmNilMgkMfjMeiLdhL\
cgLbfKaeK`dK_cJZbJYaJX`IWZIVXIUVHTTHSRHROGQLGPIHOF\
GNDKMDKLFKKIKJKKINKHPKUKzTKzTKzTKzTKzTKzTKzTKzSKzS\
KzSKzSKzSKzSKzSKzRKzRKzRKzRKzRKzRKzRKzRKzQKzQKzQKz\
QKzQKzQKzQKzPKzPKzPKzPKzPKzPKzPKzOKzOKzOKzOKzOAzOA\
zOAzOAzPAzQAzRAzSAzSAzTAzUAzVAzWAzWAzXAzYAzZ1z_1z_\
2z`2za3zb3zc4zc4zd4ze5zf5zg6zg6zh7zi7zj7zk8Wk8Yl9_\
m8an6co4eq2gr0is0ku0mv0ox0qz0sy0ux0ww0ww0ww0ww0ww0\
ww0ww0ww0ww0ww0uw0sw0qw0ow0mw0kw0iw1gw1ew2ew2ew3ew\
4fw4gw5gw5hw6hw6iw7iw7jw8kw8kw9lwAluAmsBmqBnoComCo\
mDpmDpmEqmEqmFrmEsmFrmFqmFpmGomGomGnmHmmHlmHlmIkmI\
jmIimJimJhmJgmKfmKfmKemLdmLcmMczOazQ`zS_zUZzWXzYWz\
_VzaUzcTzeRzgQziPzkOzmMznLzpKzpJzpIzpGzpFzpEzpDzpB\
zpAzp9zp8zp7zp5zp4zp3zp2zp1zp2zp2zpfzpezpezpdzpczp\
czpbzpazpazp`zp`zp_zpZzpZ }
frm:SliceJulibrot5 {; draws all slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=(-z)^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
FOTD -- October 17, 2011 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image is the third one created with an exponent of
1.05, though today it is positive Z rather than negative Z that
we raise to the power of 1.05. The parent fractal was created
by calculating the expression Z^(1.05)+C at a level of 0.31...
turns down the complex logarithmic hyperspiral with the 'recip'
function applied.
The surprise in the image is the existence of a minibrot. The
minibrot lies at the center of a disorganized spiral, which is
another surprise. Most spirals appear boring because they
continue unchanged all the way down to infinity; today's spiral
however comes to a definite end at the central minibrot.
I named the image "Bare Singularity". I almost named it
'neutron star', but the singularity name has more impact. I'm
not sure a bare singularity could actually exist. Any
singularity would necessarily have an event horizon around it,
and would therefore lie unseen inside a black hole, but it is
fun to try to imagine what a bare singularity might look like.
The rating of a 7 is about what the image is worth. A little
extra effort on the colors might have rased the rating to a
7-1/2.
The calculation time of 7 minutes starts to drag before the
image is finished. Avoid the dragging by viewing the image on
the web site.
The official FOTD web site is at:
<http://www.crosscanpuzzles.com/Archives.html>
where the finished image is posted.
or the high-definition web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original web site may be accessed at:
<http://www.Nahee.com/FOTD/>
Light rain fell during the night here at Fractal Central, but by
daybreak the sky was clear. The rest of the day brought full
sun with only a few passing clouds, and a temperature of 64F
18C. The fractal cats approved of these conditions, at least
during the times when they were not distracted by a large orange
tomcat that wandered onto the back porch. The world of the
humans featured only routine stuff not worth reporting.
The next FOTD is due to be posted in 24 hours. Most likely it
will be posted on schedule. Until then, take care, and if
nothing can escape from an (almost) black hole, how does the
gravity get out?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Bare_Singularity { ; time=0:07:09.90-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=recip passes=1
center-mag=-2.109365353519732/+2.80890231424387/\
1.629783e+011/1/-85/0 params=1.05/0/-0.31034272286\
14155/0 float=y maxiter=5000 inside=255 logmap=700
periodicity=6 mathtolerance=0.05/1
colors=000GWeXmjNdgGWe8Pb0Ha0AZ03X00V00W00W00W00W0\
0W00W00W00X00X00X00X01X01X01X01Z02Z02Z02Z02Z03Z03Z\
03Z03_05_05_05_05_06_06_06a06a07a07a07a07a08a08b08\
b08b09b09b09b09b0Ab0Ad0Ad1Gl1Cd1Cd2Cm2Cd3De3De3De5\
Me5Me6Me6Me5Md6Me6Me6Me7Me7Me7Me7Me8Me8Hl8Me8Gv99u\
9Mu9GuAMuAMuA9uAMuCCuCEuCMuC9uDMuD9uDEuEMuEDuEHuEG\
uGEuGEuGDuGCu8DuHAuHGuC8sH9uGHuDAuEJuDIuDAuCCmAImA\
9o9Fo8Co8Do7Go6Ho6Io5Do2Cp3Do5Eo5EoLJo6GoLQh7Ao8Co\
8Po9Do9IoASoAEoCOmCGmDHjDMjEIhELhGJgGJgHPeHMeLQeIN\
eJNeJPeLPeLQeMQeMSeNSdNTdPTdPVdQVdQWdSVdSWeTWeTWfV\
WfVXgWZgWXgXZhXZhZ_fZ_g_ag_agachabgbegbeidgodglehm\
ejoglqglzhmzhpzjpzjozlozlozmozmozopxopxppxppxrpxrp\
xsrxsrxurxurxvrxvsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxx\
sxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsx\
xsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxs\
xxsxxsxxsxxsxxsxxsxxsxzzz }
frm:MandelbrotBC3 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)+PI-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z|<a }
END PARAMETER FILE=========================================
FOTD -- October 16, 2011 (Rating 8!)
Fractal visionaries and enthusiasts:
How low can you go?
Yesterday's image brought a big surprise when I found actual
chaotic detail in the (-Z)^(1.05)+C Julibrot. Today's image
brought an even bigger surprise when I found chaotic detail in
the (-Z)^(1.0025)+C Julibrot, which is 20 times closer to unity,
and this is exactly what I named it.
The rating of an 8! expresses my surprise at this unexpected
turn of events, and I would not be surprised to find the biggest
surprise as I continue to lower the exponent.
In addition to the unexpected detail, the image shows a
surprising overall pattern of radiating arms and curving loops.
And yes, the background is filled with a large variety of detail.
The calculation price for all this surprise is an unwieldy
15-1/4 minutes. But the web sites will eliminate this problem.
The finished image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
in 640x480x256 resolution.
The hi-def version is posted at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The classic FOTD web site is at:
<http://www.Nahee.com/FOTD/>
A sunny morning was followed by a cloudy afternoon here at
Fractal Central. The temperature settled around a comfortable
66F 19C for most of the day, keeping the fractal cats content
until we brought a new chair into the living room. When we set
the chair in its place, Nicholas checked it, seemed satisfied,
and walked away. Cassie checked the chair and immediately laid
claim to it. She will probably make it her own catsonal chair,
where Nico will be permitted only with her permission.
The next FOTD will be posted in 24 hours. Until then, take
care, and if we took the money from the ridiculously wealthy
one-percent and distributed it evenly among the remaining
99-percent, everyone would have about double what he now has.
The demand for goods and services would then double, which would
cause the prices to double also, cancelling the extra wealth.
The only change would be a lack of ridiculously wealthy people.
My solution to the problem of the unequal distribution of wealth
is to ****** the ******* so that ******* ** ******** **** *****
would be equal. And then everyone would be satisfied.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
A_Bigger_Surprise { ; time=0:15:14.06-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot5 passes=1 center-mag=2.7\
2198/0/3.20013/1/-90/0 params=37.5/0/37.5/0/1.1513\
/0/0/0/1.0025/0 float=y maxiter=32767 inside=0
logmap=-668 periodicity=9
colors=000OG0QI0SK0TN0VQ0XT0XW0YZ0Wa0Ud0Sg0Qj0Mm0O\
p0Qr0Rr0Tq0Up0Wp0Xo0Zo0_n0am0bm0dl0ek0gk0hj0jj0ki0\
mh0nh0pg0qg0nd0lb0j_0gY0eW0cT0aR0ZO0XM0VK0TH0QF0OC\
0MA0J60K80KA0KC0LE0LG0LI0MK0MM0MO0NQ0NR0NT0OV0OX0O\
ZzP`zPbzPdzQfzQhzQjzQkzOizNhzLfzKezIczHbzGazK_zNZz\
RXzUWzXUz`TzcRzgQzjOzmNzmNzmOzmOzmPzmOzmPzmPzmPzmQ\
zmQzmQzmRzmRzmRzmSzmSzmSzmTzmTzmTzmUzmUzmUzmVzmVzm\
WzzYzz_zzazzczzezzgzzizzkzzmzzozzqzzszzuzzwzzxzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzblzc\
mzdnzdozeqzfrzfszgtzhvzhuzixzjwzjzzhvzgwzfuzetzdtz\
cqzbrzaoz`oz_lzZmzXizWjzVfzUgzTdzSdzRazQbzP`zO_zNZ\
zLXzKWzJUzITzHSzGQzFPzEOzDNzCLz8NzBLzDNzGNzIPzLSzN\
UzQXzSZzU`zT_zTZzTYzTYzTXzTWzTVzSVzSUzSTzSTzSSzSRz\
SQzRQzRPzROzRNzRNzRMzRLzRLzQKzQJzQIzQIzQHzQGzQFzPF\
zPEzCizEhzGfzHdzJbzLazN_z }
frm:SliceJulibrot5 {; draws all slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=(-z)^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
FOTD -- October 15, 2011 (Rating ?)
Fractal visionaries and enthusiasts:
Rarely does a parent fractal become Fractal of the Day, but
today is the second consecutive day on which a parent fractal
has been featured.
In yesterday's image we saw that the (-Z)^(1.05)+C Julibrot
apparently holds no interesting semi-chaos, at least not in the
area of Seahorse Valley. In today's image we find that first
impressions are sometimes wrong.
Today, we check the hump that passes for East Valley in the
Mandelbrot aspect of the Julibrot. We check it at an angle
double rotated 37.5 degrees toward the Julia direction, and what
we find is total chaos. While all the edges in yesterday's
image were smooth, today's image shows nothing but chaos in its
eastern parts. To add to the interest, this chaos consists of
discontinuities, which vary widely in character in different
parts of the image, yet have a similar theme in restricted areas.
Such a mixed-up Julibrot surely has many additional curious
slices in this East Valley area. I'll be checking other slices
over the next few days, and I would not be surprised if some
slices achieved FOTD image status.
The name "The Big Surprise" expresses my feelings when I checked
the 37.5,37.5 angle of today's slice through 'east hump'. The
rating of a question mark shows my indecision. The mathematical
interest is certainly there, and would rate about an 8, but take
this math interest away and the artistic value falls short of
FOTD reference standard.
The redeeming feature is the super-fast calculation time of 50
seconds, which will give no one a reason to regret the wasted
time if the image falls flat with them.
To view the image without the bother of calculating it, visit
the FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
To see the image in high-definition, visit:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
To see all the images since April 1997, go to:
<http://www.Nahee.com/FOTD/>
Conditions were windy here at Fractal Central today. The gusts
near 50mph, 80kph kept the leaves swirling. Otherwise the
partly cloudy skies and temperature of 64F 18C were harmless.
The fractal cats were also pretty harmless, sleeping as they did
through a good part of the afternoon.
FL and I stopped by a local 'occupy' demonstration around noon.
Somehow I found myself holding a we're-not-going-to-take-it-any-
longer sign and getting honked at by passing cars. Luckily, no
harm was done to my middle-of-the-road political reputation,
since all sides apparently agree on the same problem, if not the
solution. We then spent the rest of the day on a short
antiquing expedition. The next FOTD will be posted in 24 hours.
Until then, take care, and when the time is right, the answers
will become obvious.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
The_Big_Surprise { ; time=0:00:50.15-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot5 center-mag=1.07545/0/\
0.3427852 params=37.5/0/37.5/0/1.1513/0/0/0/1.05/0
float=y maxiter=15000 inside=0 logmap=yes
symmetry=xaxis periodicity=9
colors=000blYcmXdnXdoWeqWfrVfsUgtUhvThuSixSjwRjzRh\
vQgwQfuQetPdtPcqPbrOaoO`oO_lNZmNXiNWjMVfMUgMTdLSdL\
RaLQbKP`KO_KNZJLXJKWJJUIITIHSIGQHFPHEOHDNGCLG8NHBL\
GDNGGNGIPGLSGNUGQXGSZGU`GT_FTZFTYFTYFTXETWETVESVES\
UESTDSTDSSDSRDSQDRQCRPCROCRNCRNCRMBRLBRLBQKBQJBQIA\
QIAQHAQGAQFAPF9PE9PD9PD9PC9PB8PA8OA8O98O88O77O77O6\
7O57O57P68Q69R7AS7BS8CT8DU8DV9EW9FWAGXAHYBIZBJ_BJ_\
CK`CLaDMbDNcEOcEPdEPeFQfFRgGSgGThHUiHVjHVkIWkIYlJ_\
mIanGcoEeqCgrAis8ku6mv4ox2qz0sy1ux2ww2ww3ww3ww4ww4\
ww5ww5ww6ww6ww7uw8sw8qw9ow9mwAkwAiwBgwBewCewCewDew\
EfwEgwFgwFhwGhwGiwHiwHjwIkwIkwJlwKluKmsLmqLnoMomMo\
mNpmNpmOqmOqmPrmOsmPrmPqmPpmQomQomQnmRmmRlmRlmSkmS\
jmSimTimThmTgmUfmUfmUemVdmVcmWczYaz_`za_zcZzeXzgWz\
iVzkUzmTzoRzqQzsPzuOzwMzxLzzKzzJzzIzzGzzFzzEzzDzzB\
zzAzz9zz8zz7zz5zz4zz3zz2zz1zz2zz2zzfzzezzezzdzzczz\
czzbzzazzazz`zz`zz_zzZzzZ }
frm:SliceJulibrot5 {; draws all slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=(-z)^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
FOTD -- October 14, 2011 (No Rating)
Fractal visionaries and enthusiasts:
The exponent of (-Z) in today's image is 1.05, a value that
would be expected to create little in the way of interesting
fractals. But it is negative Z that we are iterating today, not
positive Z, and when it comes to fractals with an exponent of Z
between 1 and 2, negative Z wins hands down.
The parent fractal, with an exponent only 0.05 above unity,
already has some halmarks of the Mandeloids -- a prominent
period-2 bud on the negative X-axis and a very well-defined
Seahorse Valley.
To produce today's image I found the Julia set of this valley,
which is an empty featureless figure-eight shape, and double
rotated the view 0.5,0.5 degrees. The result is a figure eight
nearly filled with the bloated Mandelbrot valley.
Searching for interesting semi-chaos, I increased the maxiter to
500000, but when I saw that no chaos was to be found, reduced it
to the present 75000, which is still quite large enough.
The name "An Old Smoothie" refers to the smooth edges of
everything in the scene. Since the image is the second similar
one in a few days, I declined to give it a rating. The result
is probably not worth the calculation time of 11-1/2 minutes, so
thank goodness for the FOTD web sites.
The finished image is posted in SF5 resolution at:
<http://www.crosscanpuzzles.com/Archives.html>
and in higher resolution at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original, now classic, FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
A series of heavy thunder-showers plagued Fractal Central
through the night and most of today, with about 3 inches, 7.5cm
of rain falling in that time. The fractal cats checked the
window several times, but when the thunder grew too sharp,
they ducked for cover in the closet. FL simply endured the
conditions, while I rather enjoyed the action. At least, the
temperature of 64F 18C pleased human and cat alike.
The next FOTD will be posted in 24 hours. If an antiquing
expedition arises, it might be late however. Until whenever,
take care, and don't worry about who might be the next U.S.
president. You'll never notice a difference. The international
corporate conglomerate is actually running things and will
continue doing so.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
An_Old_Smoothie { ; time=0:11:29.48-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot5 center-mag=-0.3568/0/1
params=89.5/0/89.5/92/-0.736/0.03/0/0/1.05/0
float=y maxiter=75000 inside=0 outside=tdis
logmap=75 periodicity=9
colors=000Q86R56R26R06Q17Q27Q28Q38Q49Q49Q5AQ5AQ6BQ\
7BQ7CQ8CP9CP9DPADPAEPBEPCFPCFPDGPEGPEHPFHPFHSIFVKE\
XMD_OBbQAdS9gV7jX6lZ5o`3rb2td1qc6obBlaGjaLh`Qe_Vc_\
_`ZcYYaVY_SXYQXWOWUMWSKUQIUOGUMGUKHUIHUGHTEGRDFPCE\
NFDLHCKJBIMAGO9ER8CT8BV9DYAF_BHaBJdCLfDNhEPjERmFTo\
GVqGWsFVqFVpEUoEUnDTmDTlCSkCSjBRiBRhAQgAQf9Pe9Pd8O\
c8Ob7Na7N`6M_6MZ5LY5LX9QTDVQGZNKcJNgGRlDUpAXqB_rBa\
sCdtCftDiuDkvEnwEpwFsxFuyGxzGzzGzu9zp3zm4zj4zj4zk4\
yk4xl4wl5vm5umAtnFsnKroMqoOpoQooSnoUmoWon_rlZtkYvj\
OxiIzh5uf8qdAmbCiaEe_GaYIYWLUVNQTPMRRIPTEOVGMZIKaK\
IdMHgOFjQDmSBpTAsWDqZGo`ImcLlfOjhQhkTfnWepYcs`aub`\
vebvgdvjfvlhvojvqlvtnwwwuuusssqqqooommmkkkiiigggee\
ecccaaa___Y_YW`WUaUU_SUYQUWOUUMUSKUQKUPMUROUTQUVSU\
XTUZVU`XUbZUd_UfaUhcUjeUlfUhhUejUblUZnUWpUTrUQtUbd\
UnQUzBUZVU7mUCdUGWUKNUOYUPWbQV_RUXSTUTSRUROVQLWPIX\
OFYNCZM9_L7_KUE1UD2UD2UC2 }
frm:SliceJulibrot5 {; draws all slices of Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=(-z)^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================
