FOTD -- April 28, 2014 (Rating A-7,M-6)
Fractal visionaries and enthusiasts:
After yesterday's ultimate image, today's near average one seems
an anticlimax. I named it "Fractal Anticlimax" accordingly.
The scene of the action lies in the distorted East Valley of the
parent Mandelbrot set, which is totally corrupted in its depths
by cubic energies, and even on its surface is starting to show
quite a few cubic tendencies.
The art rates a 7. A little more effort might have raised the
rating a half point or so. The math rates a 6. Corrupted
Mandelbrot sets have been a staple of the FOTD for quite a few
years, so the image holds little that has not been seen before.
The calculation time of 1-1/6 minutes is quite reasonable.
Avoiding the calculation entirely by checking the web sites is
equally reasonable.
Avoid the calculation by viewing the finished image at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Today dawned clear here at Fractal Central, but clouds moved in
as the day progressed, and by mid-afternoon it was totally
overcast, with rain predicted by nightfall. The fractal cats
exhausted themselves tussling with each other all morning, then
slept most of the afternoon. The fractal humans were rather
sullen, but considering the world situation, who can blame us.
The next FOTD will be posted in about 24 hours. Until then,
take care, and let's avoid all the feel-good talk about a bright
side.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Fractal_Anticlimax { ; time=0:01:10.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=FinDivBrot-2 function=recip passes=1
center-mag=+0.1755284019811146/-0.01181651130270\
323/1.785588e+014/1/167.4/0 params=3/-6/0/0
float=y maxiter=750 inside=0 logmap=120
periodicity=0 mathtolerance=0.05/1
colors=000678879A6BC6DE6FG5HI5JK4LM4NO3PQ3RS3TU2VW\
2XY1Z_1_a1`c5aeAbgFciKdkPemUgmZhmcmmhrnmvnoznmvnhr\
ncojZheUbaPXYKRUGLQDFMA9I83E66A3860A30700503A06F08\
K5AMACOCEQCEVBFZAGc9Jh9Mm8Pr7Uz6Zz6czCUmIYcOeRUmMZ\
uHazGczGezGhzFjzFlzFomEqmEsmEjcHaYKUSMLRPDmRGRQJNQ\
MfQPaQShPVjPYVP`WPcWPfaOibOkaOjfOifObfMUcKIcIeciec\
dddddddddddddddddddddddddddddddddddddddddddddddddd\
ddddddddddddddddddddgggggggggggggggggggggiiiiiiiii\
hhhhhhhhhiiiiiijjjjjjjjjkkkkkkkkkkkkkkkhhhhhhhhhhh\
hllllllllllllllllllllllllllllllllllllllllllllllllp\
pppppppppppppppppppppppppppppppppppppppppppppppppp\
tttttttttttttttttttttttttttttttttttttttttttttttttt\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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 -- April 27, 2014 (Rating A-10,M-10)
Fractal visionaries and enthusiasts:
Finally, after all these years, we have a FOTD that rates a
double 10. And it took an invasion of flying saucers from outer
space to earn this astounding rating. My first impulse was to
name the image 'Saucer Invasion', but then I decided to give the
aliens the benefit of a doubt, and not automatically assume they
are war-like creatures. I finally decided that the aliens are
here on nothing more threatening than a galactic convention, and
named the image "Saucer Convention".
The art rates the holy grail of a 10 because after hours of
working on the 48-colors of the palette, I finally got the image
to appear almost 3-D photographic. The math earns the same
rating because I have no idea what is going on with the math,
which appears to have something to do with both Mandelbrot
images and Newton's method of finding roots. This could well be
the only FOTD that will ever be posted rating a double ten.
The flying saucers are all made of some burnished hi-tech
copper-colored metal. Some of them resemble huge flying
kettledrums, while others resemble thin, flattened dish-like
craft, barely able to hold an intelligent alien. It's anyone's
guess what the inhabitants of the saucers might look like.
The saucers must be mother ships carrying fleets of smaller
craft. How else could the many smaller groups flying in
formations be explained?
The image takes 3-1/4 minutes to calculate, which is likely a
lot less than the time it took the saucers to reach the earth
from their home worlds scattered throughout the galaxy, if not
the universe.
See the finished image instantly at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
The partly cloudy sky, chilly north winds and temperature of 57F
14C were fine for spring gardening here at Fractal Central
today, though not quite so good for the fractal cats, who were
unhappy about the chill and waited for the sunshine to become
dependable, which never happened. The fractal humans were in
kind of a down mood. The next FOTD will in all likelihood be
posted 24 hours from now. If not, it will appear in 48 hours.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Saucer_Convention { ; time=0:03:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=mandnewt.frm
formulaname=MandNewt12 passes=1 center-mag=+0.7897\
049206/-0.0284320591/284405/1/107/0 params=-4.3808\
/-0.5139/-1.2595/1.0881/-0.811/2.519 float=y
maxiter=250 inside=bof60 logmap=yes periodicity=0
colors=000yzzyxvxwrwumvshuqctlZshWreRqcQobPnaOm`Nl\
_MkZLjYKiXJhWIgVHfUGeTFdSEbRD`QD_PCZOCYNBXMBWLAVKA\
UJ9TI9SH8RG8PF8OE7ND7MC6LB6KA5J95H84F73D62B5184052\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
0000000000000000000000000 }
frm:MandNewt12 {; Jim Muth
z=g=pixel, a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), e=real(p3), f=imag(p3):
h=z^a+(g-1)*(z-b)
j=c*z^d+g
z=z-e*h/(f*j),
0.0000000000000000000000000000005 <= |h| }
END PARAMETER FILE=========================================
FOTD -- April 27, 2014 (Rating A-10,M-10)
Fractal visionaries and enthusiasts:
Finally, after all these years, we have a FOTD that rates a
double 10. And it took an invasion of flying saucers from outer
space to earn this astounding rating. My first impulse was to
name the image 'Saucer Invasion', but then I decided to give the
aliens the benefit of a doubt, and not automatically assume they
are war-like creatures. I finally decided that the aliens are
here on nothing more threatening than a galactic convention, and
named the image "Saucer Convention".
The art rates the holy grail of a 10 because after hours of
working on the 48-colors of the palette, I finally got the image
to appear almost 3-D photographic. The math earns the same
rating because I have no idea what is going on with the math,
which appears to have something to do with both Mandelbrot
images and Newton's method of finding roots. This could well be
the only FOTD that will ever be posted rating a double ten.
The flying saucers are all made of some burnished hi-tech
copper-colored metal. Some of them resemble huge flying
kettledrums, while others resemble thin, flattened dish-like
craft, barely able to hold an intelligent alien. It's anyone's
guess what the inhabitants of the saucers might look like.
The saucers must be mother ships carrying fleets of smaller
craft. How else could the many smaller groups flying in
formations be explained?
The image takes 3-1/4 minutes to calculate, which is likely a
lot less than the time it took the saucers to reach the earth
from their home worlds scattered throughout the galaxy, if not
the universe.
See the finished image instantly at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
The partly cloudy sky, chilly north winds and temperature of 57F
14C were fine for spring gardening here at Fractal Central
today, though not quite so good for the fractal cats, who were
unhappy about the chill and waited for the sunshine to become
dependable, which never happened. The fractal humans were in
kind of a down mood. The next FOTD will in all likelihood be
posted 24 hours from now. If not, it will appear in 48 hours.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Saucer_Convention { ; time=0:03:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=mandnewt.frm
formulaname=MandNewt12 passes=1 center-mag=+0.7897\
049206/-0.0284320591/284405/1/107/0 params=-4.3808\
/-0.5139/-1.2595/1.0881/-0.811/2.519 float=y
maxiter=250 inside=bof60 logmap=yes periodicity=0
colors=000yzzyxvxwrwumvshuqctlZshWreRqcQobPnaOm`Nl\
_MkZLjYKiXJhWIgVHfUGeTFdSEbRD`QD_PCZOCYNBXMBWLAVKA\
UJ9TI9SH8RG8PF8OE7ND7MC6LB6KA5J95H84F73D62B5184052\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
0000000000000000000000000 }
frm:MandNewt12 {; Jim Muth
z=g=pixel, a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), e=real(p3), f=imag(p3):
h=z^a+(g-1)*(z-b)
j=c*z^d+g
z=z-e*h/(f*j),
0.0000000000000000000000000000005 <= |h| }
END PARAMETER FILE=========================================
FOTD -- April 25, 2014 (Rating A-8,M-7)
Fractal visionaries and enthusiasts:
Today's image lies in the parent fractal that results when 0.01
part of Z^(2) is subtracted from Z^(-2) on each iteration. This
parent is gargantuan in size, though the unlikely escape radius
of today's image cuts off most of it.
This odd escape radius of 99.999 was carefully chosen to bring
the scene of today's action as close as possible to the cutoff
point, where the bubbles created by the 'fmod' outside option
are as prominent as possible.
The name "Koilon Bubbles" describes the bubble-like objects in
the image, and points back to the time when empty space was
assumed to be filled with an invisible substance called aether,
which transmitted light waves. Some people, mostly occultists
who called the aether 'koilon', also assumed that atoms were
actually made of bubbles in this all-pervading substance that
were held open by the creative power. Curiously, now that dark
energy has come on the scene, this idea does not seem quite as
goofy as when it was seemingly disproved by the theory of
relativity.
The art rating of an 8 is thoroughly earned, since I spent over
an hour working up the custom coloring. The math rating of a 7
is earned because the un-truncated parent fractal extends
apparently infinitely in both the outward and inward directions.
The calculation takes 1-1/2 minutes -- fast enough to keep
boredom at bay. And the web sites can avoid all calculation
problems.
Save a little effort by viewing the finished image on any one of
the FOTD web sites at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Morning sun gave way to afternoon clouds and evening rain here
at Fractal Central today. The temperature of 64F 18C was very
near normal. The fractal cats were too busy tussling with each
other to care very much about the outside conditions, though I
did hear Jasmine chattering when a pigeon landed near the
window. The humans, who are becoming ever more disgusted with
politics and the mass media, had an average day. The next FOTD
will be delayed until April 27, two days from now. Until that
time arrives, take care, and beware of manipulative media
exaggerations.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Koilon_Bubbles { ; time=0:01:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=-4.439109860299364/-5.965792592977377/\
2.5e+008/1/-42.5/0 params=1/-2/-0.01/2/0/-0.001/0/0
float=y maxiter=1000 inside=0 proximity=0.5
outside=fmod logmap=yes periodicity=6
colors=000zzzxyzwwzuuzsszrqzqozpmzokznizmgzkeziczg\
aze_zcYzaXz_WzYVzWUzVTzUSzTRxSQvQPqOOoMNnKMlILgGKe\
FKdDIaBHY9FX9FV7DT5BO3BM29K27I07F05D03B03905H27S39\
Z5Bc7Df9Fi9FiDIzFKzHMzIOzKQzKQzKQzKQzKTzKTzKTzKTzK\
VzKVxMVvMVqMXoMXnMXiMXgMYeMYaMY_MYYKX_KX_IXaIXaHXd\
HXdFXeFXeFXgDXgDXiBXiBXl9Xl9Xn9Xn7Xo7Xo5Xq5Xq3Xt3X\
t3Xt5Yq7Yo7Yn9YlB_iB_gD_gF_eF_dHaaIa_IaYKaXKaXMdVO\
dTOdQQdOTeMTeKVeKXeIXeHYgFYgD_gBagBag9di7ei5ei3gi2\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
0000000000000000000000000 }
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, esc=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < esc }
END PARAMETER FILE=========================================
FOTD -- April 24, 2014 (Rating A-7,M-3)
Fractal visionaries and enthusiasts:
There is not much to say about today's image, which is a scene
deep in the east shore line of the north branch of Seahorse
Valley of the Mandelbrot set. Since the magnitude is at the
limit of conventional math, arbitrary precision math will
produce a slightly sharper rendering, but at the same time will
increase the calculation time from 10 minutes to a day or more.
I put some extra effort into the coloring, mainly by setting the
logmap at a higher than proper value, which produces the large
flat areas that I colored black. This earns the art aspect a
respectable 7. The math however is pure Mandelbrot stuff.
There is nothing wrong with this, but the trick is now over 30
years old and hardly worth a rating above a 3.
The name "Return to Basics" reminds us that the Mandelbrot set
is still the most basic of all fractals. The calculation time
of 10 minutes is a rough average. Different machines run
type=mandel fractals at widely different speeds. So avoid all
uncertainty by visiting the web sites.
Check the finished image on the FOTD web sites at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Despite the brilliant sun, the high temperature of 59F 15C and
brisk wind from the north kept a feeling of late winter in the
air here at Fractal Central today. The fractal cats, who now
regularly tussle with each other, were too pre-occupied with
their play to be concerned with the slight chill. The fractal
humans simply got through the day the same as they have done on
countless other days. The next FOTD will be posted in 24 hours.
Until then, take care, and see you soon.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Return_to_Basics { ; time=0:10:00.00 SF5 at 2000MHZ
reset=2000 type=mandel center-mag=-0.7499977505574\
505/+0.00301634025810139/2.177347e+013/1/-40/0
params=0/0 float=y maxiter=750000 bailout=4
inside=0 logmap=-91500 mathtolerance=0.05/1
colors=000000000000xc7xeBxhFwjKwmOwoSwqWmwzrnfpmkn\
lpigidccESw9Tw4Uw5So6Qh7Oa8NV9LOAJHBHABG3SnjQjhOgg\
NdfLaeKZdQOnVEwcBcl8Kt60n96iBCdDI_FOVHUQJ_TBGU8KW6\
OX4SS6NO7JK8FGAAI668C2KQ1Wb1fo1im9lkHojPrhXugcndfh\
ahaZkWXmPUoJRrCOt6MvPbpgsjaaqXKxqc5nc6lK6jc6hc6fc6\
dg6bf6`f6wB5ag4wB5bY6w07jk8wS9p_BwOCqUDrREwLFwPGwU\
HwVIwVJwUKwVLwWMwXNwXOw_Pw_Qw_RwZSwZTwZUw_VpWWqWXr\
WYsWZtW_uW`vWavWbvWcvWdvWewWfwWgwWiwWjwWkwWlwWmwWn\
wcJwc_wcowcjwcewc`wcWwcXwcXwcXwcdwckwcRzcMzcIzcEzc\
Azc6zc8zcUzcOzcJzcEzc9zc4zcBzcHzcOzcUzm`zmfzm`zmWz\
mRzmMzmfzmzzmuzmqzmmzmhzmdzm`zmczmePmhJmjDmlTmggmb\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
END PARAMETER FILE=========================================
FOTD -- April 23, 2014 (Rating A-7,M-6)
Fractal visionaries and enthusiasts:
>From a distance the little minibrot at the center of today's
image may look quadratic, but it certainly is not. It is of
order 1.5 and lies in a parent fractal that resulted when I
iterated the expression Z^(1.5)+C at a level 33 levels up the
hyperladder with no function applied. The name "It's Not
Quadratic" confirms the apparent discrepancy.
This parent is shaped quite like the minibrot in the image, and
is oriented so that the large period-2 bud points out to the
south. Today's scene is located in a sprawling chaotic spiral
just inland from the southeast shore line of the parent's main
bay.
I intentionally set the logmap about 25 levels too high. Doing
this created a flat background that could be given any color I
wished. For various reasons I chose solid black.
The art rates a 7, mostly because of the flat black background.
The math rates a 6, since the math trick is so old that it is
hardly a trick any longer.
The calculation time of 1-1/2 minutes is fast enough. But visit
the web sites for an even faster way to view the image.
The web sites are online at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Lots of clouds with only a few breaks of sun spoiled the day
here at Fractal Central. The brisk north wind and temperature
of only 54F 12C made things even worse. The fractal cats
endured the discomfort with only minor complaints. The humans
had no complaints at all -- we were too busy.
The next FOTD will be posted in about 24 hours. Until then,
take care, and let's avoid discussing religion, politics or
philosophy for a few days.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
It's_Not_Quadratic { ; time=0:01:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident passes=1
center-mag=+0.7796928496537461/-0.5595061592029913\
/3.314487e+008/1/112.5/0 params=1.5/0/33/0 float=y
maxiter=2400 inside=0 logmap=162 periodicity=6
colors=000000SafRWfPQfOKgMEgLGgKKgPPpUUxWZvXcuYhtZ\
ms_or`qqctphwpmznrzjjzgdoddgadeZdUmdUmdUmdKmdKmdKm\
dKmdKzdKzdKzdKzZKzUKzPCzQKzRKzUKzWKzZKz`KzcQzePzfQ\
zgRzgRzhSzhSmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmzcmz\
cmzcmmcmccmUcmKcmIcmLcjOcgRccTc_WcXZcTacPdcMfcIidE\
leBof7qg4kf8eeB_dEVdHTaKR_NPYPOWSMUUKRXIPZHNaFLdDJ\
fBGiAEk8Cn6Ap48s36u5At6Dt7Ht9KsAOsBRsDVsEYrFarHdrI\
hrJkqLoqMrqNuqe_ZwEHpHOiJUbL_WNeQPkTSjWVjYYi`_icbi\
eehhghkjhmmgppgsrguufxxfzzfzzazzWzzR4mMFmPQmS`mVjm\
YlmVnmTocQqcOscMtcJvcHwcFvcGucHtcHscIreJrkJllGflE`\
lCWlAZfC``EccGecIhcKjcMlcN8hxHhyKhhPcbUcXXcVZcTacR\
cePehNhjLjmJloHhoFdoE`oDYoC_nBanBczAezAizAjz9kz9lz\
8mz8nz8oz7pz7qz7rz6sz6tz5uzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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 -- April 22, 2014 (Rating A-7,M-6)
Fractal visionaries and enthusiasts:
Today's image is named "Broken Perfection". The reason for the
name is readily apparent in the image, which shows an almost
perfect ring around a minibrot. The ring resembles a donut-
shaped planetary nebula puffed off from a dying star, but look
closer. The ring is broken on its east side by a discontinuity
that is caused by the fractional nature of the Z^(10.5) exponent
and extends all the way to the central minibrot.
The 9-1/2 bays of the minibrot point to an exponent of 10.5,
while the 10-1/2 elements in the ring confirm the deduction.
The location of the scene is at the edge of a larger but still
order-10.5 minibrot on the main spike of the parent Mandelbrot
set, just east of the prominent large quadratic minibrot.
The art rates a 7, mostly due to the modicum of extra effort I
put into the coloring. I could rate the math aspect no higher
than a 6, especially after noting that we have been exploring
this math trick for over a week.
The calculation time of merely forty seconds makes up for any
deficiencies however. This time will pass faster than Ali
Baba's forty thieves. But there is no danger, since the web
sites will keep the thieves at bay, at least for those who
choose to take shelter there.
The web sites are online at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Heavy clouds and light rain spoiled things here at Fractal
Central today until the sun broke through in mid-afternoon. The
temperature of 68F 20C was mild enough, but with the house heat
turned down, the fractal cats would have preferred more sun.
The humans had a thoughtful day. While I was out walking, I
noticed that the trees in the town square are still as bare and
bleak as in midwinter, and it's only one week until the month of
May, when trees are usually in full leaf.
The next FOTD will be posted in 24 hours or whenever. Until
then, take care, and at this Easter time I hear of a decline in
religious faith. The decline is nothing new, but could it be
driven by the fact that among the over-educated, religious faith
is widely seen as a vestige, which is now little more than a
comforting diversion from reality clung to by the under-educated
and easily disproved by scientific study and rational thought?
Jim (both Theist and Atheist) Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Broken_Perfection { ; time=0:00:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=FinDivBrot-2 function=recip inside=0
center-mag=-1.741394475156175/+0.00000405269130397\
/2.773655e+012 params=10.5/1e+020/0/0 float=y
maxiter=400 periodicity=6 mathtolerance=0.05/1
colors=000zdkzmsznlznezo_zoTzoNzoKzoHzfFzZDzRBzJ9z\
B7z35z4Ez5Mz6Uz7az8izA4z9Ez8Oz7Yz7fzEczKazRZzXXzcV\
ziSzpQzvOzqQzmRzhTzdUz`WzWXzSZzPYzO_zN`zMazLbz5xzD\
mzLczTUzcEz`KzPEzUKzZQzcWzhazmgzrmzwtzvszvrzvqzvpz\
vozvnzvmzzqzyozvlztjzrhzpfzzzzzzzzzzzzzzyzzxuzwrwv\
ouulsthqsbprZoqWlpTkoQjnNimKhlHgkIfjJeiKdhLcgMbeNa\
bO`_PZYQXVRUTSPQQLOLJLJGJGEGDAEB9CA79757725404NA4T\
F4YK4bP4gU4kb4ph4vo4zv4zzcztevtxjowZjwOfwVMbW1IU3K\
S5LQ7NP9ONBQLDRKFTIGUGIVFKXDMYBO_AQ`8Sb6Uc5Vd6Ue6T\
ezSezRezQezPezOezPdzQdzQdzRdzSdzUdzVdzObzSczWdz_ez\
cezgfzkgzohzshzdYzROzDEzJIz2EzOLzgEzhLziSzjYzkdzlk\
zouznszmqzlpzknzjlztnzolzjkzfizahzXfzTezOczKbzO_zR\
YzcFz`JzXNzURzRVzOZzPdzPjzQpzQvzOtzNrzMqzLozKmzJlz\
IazISzIIzFGzDEzBCzKKzTSzzzzX`zS`zN`zI`zD`z8`z4`z5U\
z6Oz7Hz8Bz85zCBzFGzIMzLRzOXzRazUgzXlz0mz7kzEizLhzS\
fzZdzdczSUzGLz4CzELzNUzWb }
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 -- April 21, 2014 (Rating A-8,M-5)
Fractal visionaries and enthusiasts:
Today's brilliant image is a scene on the edge of the main spike
of the Z^(2.0000001)+C Mandeloid. On the surface this parent
fractal appears to be an everyday Mandelbrot set, and most of it
is just that, but as today's image shows, strange things are
happening along its main spike.
The image is located on the northern edge of the spike, which is
infinitely divided. The division of the spike is mirrored in
the network of white filaments surrounding the central minibrot.
And that central minibrot has its own problems. The minibrot is
not a single minibrot. It lies on a discontinuity where it has
been split into two separate minibrots, neither of which are
fully there.
The art rates an 8, even though I posted a very similar image
about 5 years ago. The math rating of a 5 is held down by the
over-familiarity of the divided-spike math trick.
The name "A Split Opinion" refers to the divided spike. The
calculation time of four minutes is slow, but at least in my
humble opinion, is worth the wait. And the web sites are always
there to make life easier.
Regardless of my individual opinion, viewing the image on the
web sites will be far more convenient than running the parameter
file. The web sites may be accessed at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
The glorious sunshine and temperature of 70F 21C here at Fractal
Central today was just what the doctor ordered. I'm not sure
what ailment it cured, but the fractal cats took full advantage
of the sun, as they chased the shifting sunbeams. The fractal
humans simply made it through the day with nothing happening
that was worth reporting.
The next FOTD will be posted in almost no time at all. Tomorrow
is the best bet. Until this great fractal apparition, take
care, and with all the misleading nonsense in the media, people
probably know less than half as much as they think they do.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
A_Split_Opinion { ; time=0:04:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=slices.frm
formulaname=MandelbrotN center-mag=-1.749737348005\
255/+0.0000004927012753/3.447818e+011/1/32.5/0
params=2.0000001/0/0/0/0/0 float=y maxiter=32767
inside=0 periodicity=6 mathtolerance=0.05/1
colors=000pDzqCzm0zsCzyYzzstzzmzzhzzfzzczu_yqXwmUu\
hRsdOq_KpWFmRCkM7jH3hC0f50d00c00a00Y00W10S50PC0MH0\
JK0FP0CS07X03a10dA0hK0mU0pc0tm0zr0yz0wz0tw0qs0oo0n\
k0mh0le0kb0j_0iX0fU0cR0`O0YL0UI0PE0I80D30A00500300\
000500900D00H01K03P05S07W09Y0Ca0Df0Fh0Hk0Jo0Kq0Pz0\
Ow0Mt0Kq0Jo0Jk0Hh3Ff7DcCD_DCXH9UK7RO5OR5KS3HW1DY09\
a00d03c05c57cD9aJDaOFaUH_YJ_cM_gO_mPYqRYuUYzWXzXXz\
YXz_X00N00Q00T10W20X30`43b59e6Bf7Bj8Ck9DkAElAFmAGn\
AHoAIpAJqALrAOsARtAUuBXvC_wGbxKeyPhzUmzZpzctzhzzmz\
zrzzzzzzzzamzahzaczaZzaUzaPzaMz_MzYOzXRzWSzUUzUXzS\
YzR_zPczOdyMfuMhtKjqJkpHomFpkDqhDtgCud9wc7z_5zY0zX\
5zX9zXDyXHwXKuXPsXSqXWoXYmXakXfhXhgXkdXocXsXYqaXpd\
XogWojWmmUkpUjsSptXmuUjuSguPduOWHMaCJeAHh5FlCCoF9q\
J5sM3tP0tS0uW0wY0ya0zd0zg0zh0we0ta0qX0mS1hO5cJ9ZDF\
U7JP1MK7JFCH0HF0KC0P90S70W30_10c00g00j00m00j03g79d\
DFaKKYPPWWUSaYPfcMkgJpkFu }
frm:MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16 }
END PARAMETER FILE=========================================
FOTD -- April 20, 2014 (Rating A-7,M-7)
Fractal visionaries and enthusiasts:
The parameters of today's fractal show that it is located on the
west side of the north branch of Seahorse Valley of its parent
Mandelbrot set. But this parent M-set is not just any old
M-set, it is a set that has been corrupted in its depths by
Z^(11) energies.
The amazingly large imag(p1) parameter of 100000000000000000000
is necessary to keep the corruption down in the depths. I'm not
sure how or why this works, but it does work, so why question
such a useful thing.
The corruption in today's image is of order 11, which is an odd
number. When the M-set is corrupted with odd energies, the
switch from the quadratic to the odd-order level is much more
interesting, since an odd number of elements cannot be
symmetrically melded into an even number of quadratic elements,
and since the corrupting energies are not fractional, there are
no discontinuities to make sudden 'quantum' leaps.
The art and math values of today's image both rate a 7. The
name "Two Full Elevenths" is based on the combination of Z^(2)
and Z^(11) energies.
The calculation time of 2-1/2 minutes will pass. How fast it
will seem to pass depends on the patience of the individual
fractalist. But everyone can have infinite patience by checking
the finished image on the web sites, thereby eliminating the
chore of calculation.
The web sites are at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Total sun and a temperature of 68F 20C gave the fractal cats as
well as the fractal humans the best Easter in several years here
at Fractal Central today.
The next FOTD will be posted in 24 hours. Until then, take
care, and the more a person tries to figure out what's wrong
with the world, the more confusing everything becomes.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Two_Full_Elevenths { ; time=0:02:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=FinDivBrot-2 function=recip passes=1
center-mag=-1.768537043766396/+0.00289078841806103\
/1.482942e+012/1/45/0 params=11/1e+020/0/0 float=y
maxiter=1800 inside=0 logmap=266
periodicity=6 mathtolerance=0.05/1
colors=000RUhQUgPUfOUeNUdMTcLSaKR_JQYIPWHOUGNTFMSE\
LRDKQCJPBIOAHN9GM8FL7EK6DJ5CF4BA3A028416704ASh7Um6\
Wr5Yv5_v4mx3mz3mz2wz2wz6wz9rvCmrFmoImlLniOpfSqcVr`\
YsY`tVcuSfvPiwMlrLhmKchJZcIUZHPUGKPFFKFBFF8AF78F76\
F64F63F6LFAaGDdGGfBTW6eL1rIAsFJsDSsNLzROuURpXTk_Wg\
cZbf`YicTlfPphKskFvnAyp6vm9skBpiDmfFjdHgbKd_MaYOZW\
QXUSWRQVPOUMNTKLSHKRFIQCGPAFO7DN5CQ7HT8MV9RYBW`C`b\
DeZCgWBhTAiQ9kN8lK7mH6nE5pB4q83r52sB5qG8pLBoQEnVGm\
`JleMkjPjocitchrccpc_wcWwcSwhOwcKwZGwUMwUSwWYwYbw_\
hwanwcswemwggwibrkXrmSmoMiqHhsGfuFevEdvEcvDawC`wB_\
wBZxAYx9Xx9WuFVrLUoQTmWSmaRmfQmlPmrOmwQmsRmoSmkTmh\
UpdVs`WwXXoUYfQZZM_PIw_jU9BP37wfjK66KA7PE8UIAUMBZL\
CZMEcNFcOGfOIjPJkPKlPMmPNnPOoPPpQcqQcrRcsSctUhuUhv\
UhwUhxZmyZmzZmzZmzcrzcrzcrzcrzhrzhrzhrzhrzmvzmvzmv\
zmvzrzzrzzrzzrzzvzzvzzvzzvzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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 -- April 18, 2014 (Rating A-8,M-8)
Fractal visionaries and enthusiasts:
Today's image lies in a parent Mandelbrot set corrupted by
Z^(0.9) energies. In this case, the corruption extends all the
way to the parent's surface, where it splits the main spike into
fractal chaos. Today's scene is located very close to the
X-axis in some of this chaos just west of the split-apart large
minibrot.
I named the image "Sandy Scenery" because of the well-defined
area of near total chaos surrounding the minibrot lying at the
center of the scene, well beyond the reach of Fractint .
I have rated both the art and math aspects at an 8. I really
did put extra effort into the coloring. And the math is kind of
a mystery. It is far from obvious why corruption energies less
than two have such a dramatic effect on even the surface of the
parent M-set, and also why the minibrots of the corrupted parent
remain quadratic and do not morph into lower-order ones.
The calculation time of 1-2/3 minutes is fast enough to prevent
impatience or boredom from arising, but life can still be made
simpler by avoiding calculation completely and checking the
finished image on the web sites.
For maximum convenience, the image has already been calculated
and posted to the FOTD web sites at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://www.Nahee.com/FOTD/>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Clouds prevailed all day here at Fractal Central, but they were
thin enough to let a trace of sunlight through. The fractal
cats, who wanted more than just a trace, were spotted crouched
in their cat sulk positions several times during the afternoon.
The humans, who would have preferred a temperature higher than
54F 12C, took what they could get.
The next FOTD will likely not be posted until April 20. Until
the moment of bliss arrives, take care, and it's getting so
confusing that a person can't tell the good aliens from the bad
ones without a program.
Jim (not an alien) Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Sandy_Scenery { ; time=0:01:40.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=FinDivBrot-2 function=recip logmap=-176
center-mag=-1.754416325421651/+0.000014838350617/\
1.726933e+013/1/-15/0 params=0.9/100/0/0 float=y
maxiter=1200 periodicity=6 mathtolerance=0.05/1
colors=00050A50B50C50D50E50F50H50J70L90NB0PD0RF0TH\
0VJ0XL0ZN0`Q6cTCfWIiZOlaUocZqdcsfhuhmwjrzkvzzzzwlz\
wiqxgiwdbwcXvaVr`SmZPfYM_VLSLYJDKC6ABCAAIAANAATAAZ\
AAAAAAAAAAmRGjWGgaFcfF`lErqEpzCmuAhq8cm7ci6Ze5Ua4K\
X3EP49K4DF5HA5LA5PKFSKPVcZYch`gzVbzPczJczDcz7cz1cz\
2cz2cz2cz2cz6cz9cMDcNGcOJcQNcRQcSTcT_UYeUbkUgqPlwQ\
pd`cNjRKkOIlMFmJDmHAnE8oC5p93p77mHAjQDgZBbWAcU9cS8\
cQ7cN6cL5cJ4cHCcMKcRScW_c`gceocjwcoaceGzWHtXHoYHjZ\
HeZH`_HW`HR`LQ_PQ_SQZWPZ_PYbPYcSVcUSdWPdYMe_JeaGec\
EaeQZf`wVYtWUrXQoYNmZJk_Fh`Cfa8db5cpbdtbgegjRkmDom\
GpmIpmKqmNqmPrmRrmUsmWsmYtm`tmbumdumgvmivmkvljrkio\
jikihhhgdggaffZeeVdeScdObcLacH`bE_cBScILcPEcW7cb0c\
i3cf6cd8cbBc`EcYGcWJcUMcSOcPRcNUcLWcJXcLYcMZcN_cO`\
cPacQbcRbcSccUdcVecWfcXgcYhcZic_ic`hcagcbfcceccdcd\
dceccfbcfacg`ch`ci_ciZcjYckXclXcldc_lcNtcBqc9oc8lc\
6jc5hc4dcA`cFXcLTcQQcVMc` }
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=========================================
