FOTD -- December 09, 2012 (Rating 5)
Fractal visionaries and enthusiasts:
Today's image of a strange spiral is located in the Scepter
Valley area of the Z^2+C Julibrot. It is sliced in a direction
halfway between the Oblate and the Rectangular, and has been
stretched and skewed to a rather large extent to bring it to a
recognizable shape.
The name "Broken Hyperspiral" refers to the infinitely divided
nature of the features in the image. This unlimited division,
known as 'Cantor Dust', is typical of the Julia sets of points
outside the Mandelbrot set, but as today's image shows, it also
exists in the odd planes and angles.
The image consists totally of points, with no two points being
connected. A zoom into one of the sub-spirals will reveal a
never-ending chain of similar broken spirals, and this series
continues all the way to infinity, which is not an end point or
a very large number, but an abstract idea that can never be
reached.
The rating of a 5 is pretty pathetic by FOTD standards, but it's
all I could give the image, which has little more than a bit of
pop-math interest going for it. More effort on the coloring
might have raised the rating a point or two.
The calculation time of 1-3/4 minutes is about average, but
perhaps a bit slow for an image with so little reward. The
situation is resolved on the web sites.
The completed image is posted for instant viewing at:
<http://www.crosscanpuzzles.com/Archives.html>
with high-definition variations at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The back images are online at:
<http://www.Nahee.com/FOTD/>
Clouds ruled the sky today here at Fractal Central, while the
temperature of 45F +7C kept things feeling seasonal. The
forecasted rain held off until sunset however. Both the cats
and humans had a typical uninteresting day.
The next FOTD will be posted when it is ready. Until whenever,
take care, and if humans ever populate the galaxy, how will they
agree on a universal galactic time? (IMO, we will never
populate anything but planet earth, so there is no problem.)
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Broken_Hyperspiral { ; time=0:01:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 passes=1
center-mag=+0.03264445237728411/+0.172536526663781\
00/8438.382/0.1402/79.9353442340639617/73.17794208\
35490413 params=45/90/0/90/-1.25/0/0/0/2/0 float=y
maxiter=2200 inside=255 logmap=-126 periodicity=6
colors=000knUknUloUloTmpTmpSmqSmqRmrRmrRmsQmsQmtPm\
tPmuOmuOmuNmvMmvLkvKiwKhwJfwIdxHcxGaxG_yFZyEXyDVzC\
ayIcyMeyQgyUiyYky`mydoyhqylpykoyjmygjxdhxafxZcwWaw\
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MhaNiaOiaQjaRkaTlaUl`Wm`Xn`Zo`_o``p`bq`cq`er`fs`ht\
`it`ku`lv`nw_nw_mw`mw`lwalwakwbjwbjwczzczzdzzdzzez\
zezzfzzfzzgzzgzzhzzhzzizzizzjzzjzzkzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:SliceJulibrot4 {; 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=========================================
While Albrecht Niekamp is on vacation and away
from a computer, he has asked me to put some
of his images onto my server.
Here is a link to his "Inside View"
fractal created using his multifractal_10 formula:
http://www.emarketingiseasy.com/Albrecht/1536704E.GIF
Click the image in your browser for its full size:
1600 x 1200 pixels, and to prevent its being
resampled by your browser.
Albrecht's "Inside View" has muted and darker tones
predominating. The dark intricate patterns on the
light background make me think of back-lit suspended
metal filigree.
The somber colors in Albrecht's fractal are created by
this color map: The more colorful hues are essentially
not used at all by his fractal.
http://tinyurl.com/1536704E-map
or:
http://www.emarketingiseasy.com/Albrecht/1536704E_map.jpg
The Fractint parameter set is below.
The full parameter file for the fractal, including
the multifractal_10 formula, is here:
http://www.emarketingiseasy.com/Albrecht/1536704E.par
- Hal Lane
########################
# hallane(a)earthlink.net
########################
===== Start of par file ==============================
1536704e { ; Inside_View
; secant-mmods-bees-phoen-newt
; time 0.33.55 XP Dos shell
; Fractint Version 2004 Patchlevel 11
reset=2004 type=formula formulafile=mfr.frm
formulaname=multifractal_10
function=sin/exp/exp/sin passes=t
center-mag=-1.50145147245682100/+0.100169185289958\
60/843407.3/1/74.9999999981563263/2.46247487678541\
432e-009
params=-0.05825983458967864/0.3785210730307932/153\
67.64595767025/14235.4911030602/152048.0404808048/\
384.1604894048/384.00482000595/256.1007683001/512.\
1007683001/768.1007683001 float=y maxiter=3071
inside=maxiter outside=tdis periodicity=0
rseed=-2436
colors=000<3>000000304<8>X0a_0dc0h<3>p0w<4>_0dX0aU\
0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<11>2TG2RE3OC<3\
>4D3<17>kkammcpoe<3>zwm<6>cYO`UKYQG<3>KA0000<43>00\
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>A08004000<26>000
}
==== End of par file ============================
I had forgotten to post this "investigation" into Jim
Muth's FOTD for November 10th. It had been marked
on my web page as "soon..." The fractal is up there
now, and a direct link to it is below.
It's not especially artistic, but rather interesting.
It's a spike that has another, apparently independent,
spike embedded within it.
Interestingly, the internal spike wanders from one side
to the other within the containing spike, but doesn't
seem to leave it -- at least at the magnifications I
used. It seemed to stay inside at 4k x 3k also.
Anti-aliased. Click the image to prevent resampling
by your browser, and to see its actual size:(1200x900).
http://www.emarketingiseasy.com/TESTS/FOTD/F121110V.jpg
- Hal Lane
########################
# hallane(a)earthlink.net
########################
While Albrecht Niekamp is on vacation and away
from a computer, he has asked me to put some
of his images onto my server.
Here is a link to his "The Big Ball"
fractal created using his multifractal_10 formula:
http://www.emarketingiseasy.com/Albrecht/1536705D.GIF
Click the image in your browser for its full size:
1600 x 1200 pixels.
"The Big Ball" is a very "busy" fractal containing a
great variety of sunny features -- including (at the
very center of the ball) a sort of smiling clown face
wearing green goggles.
The cheery colors in Albrecht's fractal are created by
this color map:
http://tinyurl.com/1536705D-map
or:
http://www.emarketingiseasy.com/Albrecht/1536705D_map.jpg
The Fractint parameter set is below.
The full parameter file for the fractal, including
the multifractal_10 formula, is here:
http://www.emarketingiseasy.com/Albrecht/1536705D.par
- Hal Lane
########################
# hallane(a)earthlink.net
########################
===== Start of par file ==============================
1536705d { ; The_Big_Ball
; secant-mmods-bees-phoen-newt
; time 0.02.44 XP Dos shell
; Fractint Version 2004 Patchlevel 11
reset=2004 type=formula formulafile=mfr.frm
formulaname=multifractal_10
function=sin/exp/exp/sin passes=t
center-mag=-0.0231296/0.0288228/0.5500051/1/92.499\
9999999409539/2.09411585294638769e-011
params=-0.05825983458967864/0.3785210730307932/153\
67.64595767025/14235.4911030602/152048.0404808048/\
384.1604894048/384.00482000595/256.1007683001/512.\
1007683001/768.1007683001 float=y maxiter=3071
inside=maxiter outside=tdis periodicity=0
rseed=-2436
colors=000000oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>M\
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}
==== End of par file ============================
Dear All,
.. or slightly out of the orbit of our fractals? Click start an move the bar (l/r)..:
http://static.flabber.net/files/scale-of-the-universe-2.swf
Cheers,
Guy
#####################################################################################
Scanned by MailMarshal - Marshal's comprehensive email content security solution.
#####################################################################################
While Albrecht Niekamp is on vacation and away
from a computer, he has asked me to put some
of his images onto my server.
Here is a link to his "Beauty Contest"
fractal created using his multifractal_10 formula:
http://www.emarketingiseasy.com/Albrecht/1536706E.GIF
Click the image in your browser for its full size:
1600 x 1200 pixels.
The rainbows pierced by the prickly spikes in
Albrecht's fractal are created by this color map --
that appears to have its rainbow sequence repeated
twice:
http://tinyurl.com/1536706E-map
or:
http://www.emarketingiseasy.com/Albrecht/1536706E_map.jpg
The Fractint parameter set is below.
The full parameter file for the fractal, including
the multifractal_10 formula, is here:
http://www.emarketingiseasy.com/Albrecht/1536706E.par
- Hal Lane
########################
# hallane(a)earthlink.net
########################
===== Start of par file ==============================
1536706e { ; Beauty_Contest
; Secant-mmods-bees-phoen-newt
; Time 0.35.31 XP Dos Shell
; Fractint Version 2004 Patchlevel 11
reset=2004 type=formula
formulafile=multifra.frm
formulaname=multifractal_10
function=sin/exp/exp/sin passes=t
center-mag=-1.44852915023346500/+0.004606349313312\
62/4400.041/1/-65.000000000068539/2.73531544636718\
138e-011
params=-0.05825983458967864/0.3785210730307932/153\
67.64595767025/14235.4911030602/152048.0404808048/\
384.1604894048/384.00482000595/256.1007683001/512.\
1007683001/768.1007683001 float=y maxiter=3071
inside=maxiter outside=tdis periodicity=0
rseed=-2436
colors=000<9>000000000<3>000<9>bbbfffjjj<3>zzz<4>I\
zz9zz0zz<7>0Rz0Nz0Iz<3>00z<5>V0z_0zd0z<3>z0z<3>z0e\
z0`z0V<3>z0Bz06z00<5>zV0z_0zd0<3>zz0<3>ez0`z0Vz0<3\
>Bz06z00z0<5>0zV0z_0zd<3>0zz<3>0ez0`z0Vz<3>0Bz06z0\
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0Gz0<3>0z0<9>0zb0zf0zj<3>0zz<9>0Oz0Kz0Gz<3>00zzE0z\
D0
}
==== End of par file ============================
FOTD -- December 06, 2012 (Rating 7)
Fractal visionaries and enthusiasts:
Not another 7-rated image? Yes, another 7-rated image. This
one lies in the parent fractal that results when 0.1 part of
Z^(2) is subtracted from 0.2 part of Z^(1.5) and straight C is
added on each iteration.
This parent is an oversized thing resembling a Mandelbrot set
rotated 180 degrees so that its west parts face east. Both the
west and east parts of this parent are split into two, and
today's scene lies in a valley of a sub-bud of the southern main
bud.
The name "Seeing Double" does not refer to someone with eye
problems. It refers to the doubling of many of the elements in
the image.
The calculation time of 4-1/2 minutes is more than the image is
worth. But thanks to the web sites, the image may be seen
without the need of calculating it.
The completed image is posted at:
<http://www.crosscanpuzzles.com/Archives.html>
High-definition variations are at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The back images are online at:
<http://www.Nahee.com/FOTD/>
Total sun prevailed here at Fractal Central today, though the
high temperature of only 41F +5C kept a mild chill in the air.
Both the cats and humans had an uneventful day. (It's boring
but true.) The next FOTD will be posted when it is ready, most
likely about 24 hours from now.
Until whenever, take care, and in the quantum world, not only is
it (apparently) possible to receive information from the future,
it is also (apparently) possible to change the past. Of course,
the qualifier 'apparently' must be added to these two demonstra-
ted facts because in our common-sense world they are impossible.
This means that, when we try to describe quantum things, we are
doing little more than mental gymnastics.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Seeing_Double { ; time=0:04:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=ident passes=1
center-mag=+20.38865970233759/-1.853988362389582/\
2.089299e+009/1/177.5/0 params=0.2/1.5/-0.1/2/0/\
1000/0/0 float=y maxiter=1800 inside=0 logmap=358
periodicity=6 mathtolerance=0.05/1
colors=000KERIHRGKRDMQBPQ9SQ7VQ5XQ9ZOC`NFbMIdLMfJP\
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zzdzz`zzYzzVzzZzzbzzfzzjzznzzazzQzzEzzKzzQzzWzzazz\
gzzmzzszzmzzgzzazzWzzQzzK }
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=========================================
While Albrecht Niekamp is on vacation and away
from a computer, he has asked me to put some
of his images onto my server.
Here is a link to his: "Platinum Riddle"
fractal created using his multifractal_10 formula:
http://www.emarketingiseasy.com/Albrecht/16731A.GIF
Click the image in your browser for its full size:
1600 x 1200 pixels.
A copy of the color map that creates the gold and
silver colors is here:
http://tinyurl.com/16731A-map
or:
http://www.emarketingiseasy.com/Albrecht/16731A_map.jpg
The fractal appears to be intricate gold and silver
filigree executed by a master jeweler -- in a somewhat
forceful overall design.
The Fractint parameter set is below.
The full parameter file for the fractal, including
the multifractal_10 formula, is here:
http://www.emarketingiseasy.com/Albrecht/16731A.par
- Hal Lane
########################
# hallane(a)earthlink.net
########################
===== Start of par file ==============================
16731a { ; Platinum_Riddle
; Time 0.05.37 1600/1200
; sec-phoen-newt-bees-sec
reset=2004 type=formula formulafile=mfr_10.frm
formulaname=multifractal_10
function=sin/exp/exp/sin passes=t
center-mag=-0.516993/-0.00123494/0.7928157/1.1324/\
-90/3.88578058618804789e-016
params=-0.05825983458967864/0.3785210730307932/167\
31.32595752213/25234.0311099861/151024.0204808192/\
384.32768524288/384.00482000595/128.2007683001/256\
.2007683001/384.8007683001 float=y
maxiter=3072 inside=maxiter outside=tdis
logmap=4 periodicity=0 rseed=-2436
colors=000<21>000000000<2>000111333<27>oooqqqsss<2\
>xxxzzzyyy<25>CCCAAA888<2>222000000<56>000000000<2\
>000111332<23>ldTnfUpgV<3>xn_<27>A8687565444322200\
0<30>000
}
==== End of par file ============================
FOTD -- December 04, 2012 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image lies in the same parent fractal as yesterday's,
but at a far different location. It is located in the valley of
a mandel-bud some distance south of the large minibrot that held
yesterday's image.
I named the image "Wheel of Destiny". The reason for the
'wheel' part of the name is made clear enough in the 'spinning'
minibrot at the center of the image. It is up to the individual
viewer to interpret the 'destiny' part.
The rating of a 7 is once again merely average. Average and
below-average images are easy to create, which is why we see so
many of them. Finding the above average ones is the challenge.
The calculation time of 1-1/4 minutes is a fair price for an
average fractal. The time will pass quickly enough once the
image gets a good start. The pre-calculated image is posted and
available for free on the FOTD web sites.
Avoid calculation by viewing the finished image on the official
FOTD web site at:
<http://www.crosscanpuzzles.com/Archives.html>
High-definition variations of the image are online at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The entire FOTD library is available at:
<http://www.Nahee.com/FOTD/>
Light rain fell overnight here at Fractal Central. The day
dawned with fog that hung around for a while, but things
improved markedly at mid-morning, when the sun broke through.
The sunny afternoon temperature reached a very spring-like high
of 64F 18C. The fractal cats enjoyed the sun coming in the
southwest window, while the humans enjoyed a day with nothing
major going wrong.
Most likely, the next FOTD will be posted soon. Until whenever,
take care, and fortune tellers claim to be able to see into the
future. At first hearing, this claim seems preposterous, but
some rational scientists now claim that at the sub-atomic level,
information can actually travel backward in time. I guess it's
another of those curious but supposedly meaningless quantum
coincidences, and rationalists can still consider fortune
tellers to be charlatans.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Wheel_of_Destiny { ; time=0:01:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip
center-mag=+1.039956082615642/-0.6873303266486848/\
4.176185e+010/1/35/0 params=-9/-1.9/-1/-9.1/0/0/0/0
float=y maxiter=1800 inside=0 logmap=150
periodicity=6 mathtolerance=0.05/1
colors=0002002002002002002012022032042052062072082\
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QlLSlIVlsblqaloalm`lk`li`lg_le_yc_yaZy_ZyYZyWYyUYy\
SYyQXyOXyLXyJWyHWyUEySHyQJyOMyLOyJRyHUyGZyFYyFYyFY\
yFYyFYyFYyFYyFXyFXyFXyXRy }
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 -- December 05, 2012 (Rating 7)
Fractal visionaries and enthusiasts:
The string of perfectly average 7-rated images continues today,
with a scene in the parent fractal that results when the formula
Z^(2.05)+C is iterated 11 levels down the hyperladder with no
function applied. This parent resembles a distorted Mandelbrot
set rotated so that its west end faces east. A mysterious
axeman appears to have taken a slice out of its main bud.
Today's scene is located where the axe appears to have sliced
through Seahorse Valley.
The name "Star Light Star Bright" refers to the star-shaped
pattern of elements surrounding the central minibrot. It is
also the first line of a well-known children's poem.
The rating of a 7 is a fair appraisement of the image, which
takes a mere 1-3/4 minutes to finish on one of today's speed
demons. And as always, all the hassle of setting up and running
the parameter file may be avoided by checking the FOTD web sites.
The finished image is online at:
<http://www.crosscanpuzzles.com/Archives.html>
Variations are available at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
Thousands of back images are posted at:
<http://www.Nahee.com/FOTD/>
A mix of sun and clouds with a brisk northwest wind and a
temperature of 48F +9C made today seem more seasonal here at
Fractal Central. The fractal cats would have preferred more sun
and less clouds, or at least steadier sun. The humans made it
through the day with ease. Preparing the next FOTD will mean
less ease however, and if all goes well, it will be posted in a
day or so.
Until whenever, take care, and the confirmation of Bell's
Theorem (that there can be no hidden variables in quantum
mechanics and information must get around faster than the
velocity of light) is the only time in the history of science
when a brilliant theorist made a prediction, brilliant
experimentalists pushed the boundaries of their art to test it,
the theory was resoundingly confirmed, and every rational
thinker was miserable.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
StarLiteStarBright { ; time=0:01:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident
center-mag=+0.735201305568/+0.032356486996/2.2e+07\
/1/40/0 params=2.05/0/-11/0 float=y maxiter=2000
inside=0 logmap=221 periodicity=6
colors=000FAKC8G96C6483245cT4WN3OH2GB185EtwBhk8Y_5\
MO2BCZunSicLYUENK7BA9hV6UK3FA3GV2CN18F047iGtWGwQDm\
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028sgSeYdVPULHKA8ABrr7__3IIihfLtQGhKCYF8MA4B5HrfEk\
`CdWAYQ8RL6KGUDAU65UllU8jU6bU5VUANUKFUK7UKscKecKSc\
KEcYhcU`cUUcUMcUFmU7mU5mU2miOzbczWczQczJczDcz6czCm\
zAmz8mz6mz4mz2mz0zzbzzJzzFzzCzzAzz8zz6zz4zz2zz5zz4\
zz3zz2zz2zz1zz0zzGzzEzzCz }
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=========================================
