This fractal is a cosine based parallel resistor formula with a z^3 minimum
z term. It has 3 way symmetry and a lot of thin filaments that look kind of
like bubbles.
Here is a link to an image:
http://dl.dropboxusercontent.com/u/33642054/image/bubble_links.jpg
The Fractint compatible PAR file for the image is:
Bubble_Links { ; Exported from Fracton.
reset=2004 type=formula formulafile=fracton.frm
formulaname=F_20140217_1620 passes=1 float=y
center-mag=-0.7027677552871285/0/1520405.599721868\
/1/0/0
params=-1/1/0/4/-1.5/0/1.5/0/0/0 maxiter=2000
inside=0 periodicity=6
colors=0BE0NZ0ZsDgzYozlrzSaz7Lz0Cl07T0BE0NZ0ZsDgzY\
ozlrzSaz7Lz0Cl07TA0ES0Yi0qrDxuYxxlwxSqx7kh0YN0H0BE\
0NZ0ZsDgzYozlrzSaz7Lz0Cl07TA0ES0Yi0qrDxuYxxlwxSqx7\
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JS0Vl6dzRlzktzelzLWz0Fy0Be06M0BE0JS0Vl6dzRlzktzelz\
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Wz0Fy0Be06M000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
00000000000000000000000000000000000000000000000000\
0000000000000000000000000 }
frm:F_20140217_1620 {
; Exported from Fracton.
; Similar to the parallel resistance formula
a=real(p1),b=real(p2),d=imag(p1),f=imag(p2),
z=0,c1=pixel-p3,c2=pixel-p4:
z=1/(1/(a*z*(cos(z)-1)+c1)+1/(d*(z^f)+c2)),
|z|<100
}
--
Mike Frazier
www.fracton.org
FOTD -- February 17, 2013 (Rating A-7,M-7)
Fractal visionaries and enthusiasts:
Today's image is named "The Holy Trinity". This has nothing to
do with religion, where the Holy Trinity refers to the three
aspects of one god. It refers to the three obvious minibrots
hidden deeper in the image, which are a sign that the scene lies
in the basin of attraction of a larger minibrot that in turn
lies in the basin of the parent fractal.
The parent fractal came into being when I combined 1 negative
part of Z^(-7.7) with 7 negative parts of Z^(-1.1) and added
(1/C). This parent is a grossly oversized and quite complex
thing consisting of a scattering of oddly shaped bays with fila-
ments extending from them and terminating in circles. Today's
scene lies in a circle southwest of the main field of fractal
activity. The circular theme shows quite strongly in the closed
yellow elements surrounding the trinity.
The art and math aspects of the image both rate a 7. I'm not
sure if this rating justifies the 5-1/2 minutes required to run
the parameter file, but the FOTD web sites are always ready to
deliver fractal calculation justice.
Find justice where it is least expected. 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>
The near total sun today here at Fractal Central was pleasant
enough, but the temperature at sunrise was a very chilly +1F
-17C, and rose no higher in the afternoon than 25F -4C.
The fractal icicles have now grown to nearly 2 meters long and
continue growing. We still have a way to go however if we hope
to set a local record. Some nearby icicles hang over 4 meters
long. The fractal cats are not concerned with ice. What they
want is more food. The fractal humans are preparing to clear
away the next snow, which is expected tomorrow morning.
The next FOTD will be posted in 24 hours. Until then, take
care, and be assured, the climate is changing. This is what
climate does when greenhouse gasses are added to the atmosphere.
The solution is to find a renewable and non-polluting energy
source that does not harm the environment or stifle the economy
with higher energy prices, as wind and solar energy would do.
Fusion energy is years away if it will ever arrive at all, so do
any concerned environmentalists have any world-saving ideas?
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
The_Holy_Trinity { ; time=0:05:30.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=-12.0649323747913/+5.188179127275399/\
1.04e+011/1/-11.62/0 params=-1/-7.7/-7/-1.1/0/0/0/0
float=y maxiter=750 inside=0 logmap=434
periodicity=6 mathtolerance=0.05/1
colors=00038F49G5AH69I7CJ8FK9IMALOBOQCRSDUUGXWJ_TN\
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eQdfVegZehcfiggjlgQH7RE4SG9TIEUKJVMOWOTXPXYRaZTf_V\
k`XpaZua_y`ax`cx`ex_fxl9i }
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 -- February 16, 2014 (Rating A-7,M-6)
Fractal visionaries and enthusiasts:
Today's fractal shows some of the nonsense that results when 4.5
parts of Z(-3) are combined with 9 parts of Z(-1.5) and (1/C) is
added.
The resulting parent fractal consists of a large bay shaped like
a lima bean, with lacy wings extending northwest and southwest
from the bay. Today's image is located on a minor filament near
the eastern extremity of the large bay.
The art rating of a 7 and math rating of a 6 will earn no
medals, but these ratings will make the image an acceptable
'also ran'.
The name 'Real or Unreal" came about when I was overcome by a
spate of philosophizing about the nature of fractals. It has
little to do with today's particular image.
The calculation time of 1-2/3 minutes is near average. Check
the FOTD web sites for a better deal.
The image is posted for public admiration 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>
Today was chilly here at Fractal Central, with variable amounts
of clouds and a high temperature of 25F -4C. These conditions
are ideal for keeping cats happy with their cozy indoor lives,
which might explain why the fractal cats seemed unusually happy
all day. The fractal people, never totally happy, passed the
day pondering the mysteries of life.
The next FOTD will be created and posted probably in 24 hours.
Until the next FOTD appears, take care, and instead of trying to
make ghosts acceptable by demonstrating that they are real,
let's agree with the scientists who imply that the objective
physical world is a mental construct. Both approaches make
ghosts acceptable by considering them to be just as real or
as unreal as the world we appear to see around us.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Real_or_Unreal { ; time=0:01:40.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=+1.179344023051262/+0.3795996886752721/\
3.01722e+008/1/122.5/0 params=4.5/-3/9/-1.5/0/0/0/0
float=y maxiter=1050 inside=0
outside=tdis periodicity=6
colors=000bhheghgghjghlfhoghqfhsghpefnddlbbiaag__e\
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U2AV3CX5DY6F`7Ga8Ib9JcALeCNfDOgEQhFRjGTkHUlJWmKXoL\
ZpM_qNarOboQZmRWWjhZih`ih }
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 -- February 15, 2014 (Rating A-6,M-5)
Fractal visionaries and enthusiasts:
Today's image was done in haste, and it shows in the erratic
coloring, which holds the art rating to a 6. The math trick is
so old that I could rate it no higher than a 5.
The name "Loch Mandy Monster" came to mind when I noticed that
the eight small open areas surrounding the central minibrot are
shaped quite like the monsters that people sometimes claim to
have seen swimming in Loch Ness as well as in other long thin
lakes that were once arms of the open sea. Being a sensible
person when common sense is appropriate, I find it hard to
believe that a breeding population of physical monsters could
thrive and remain undetected in these lakes. As for monsters
from another dimension, I have no comment.
The oversized parent fractal resulted when I combined 4 parts
of Z^(-1.5) with 1 part of Z^(-6) before adding (1/C) on each
iteration. This parent is shaped like a violin lying on its
side. Today's scene is located on a minor filament extending
from a small bud on the shore line of a large critical bud at
the east end of the parent fractal.
The calculation time of only 45 seconds will pass in a flash and
a half. Whether instant satisfaction is found when the flash
subsides depends on the whim of the individual fractalist.
Visiting the web sites will reduce any fractal disappointment.
So avoid great disappointment. Check 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>
The day began with snow here at Fractal Central. By the time it
ended just after noon about 6 new inches or 15cm had piled up.
The fractal he-man leaped into action as soon as the snow ended,
and within an hour the sidewalk was clear. But the sidewalk now
looks like a canyon, with shoulder high cliffs of snow and ice
piled along both sides, totally covering FL's prize rose bushes.
But now there are few places left to pile the snow, and even
worse, the coffee is running low. Luckily, more coffee is
available at the nearby convenience store, which never closes,
but with heavy snow again expected on Monday, the only place to
pile it will be on top of the present piles. The fractal cats,
never ones to worry themselves over human problems, were puzzled
about the strange appearance of the outer world, but soon turned
their attention to play and food.
The next FOTD will be posted in 24 hours, give or take a few.
This is not a guarantee. With nothing else to do however, it is
reasonably assured. Until then, take care, and would fractals
still exist even if the so-called 'big bang' that supposedly
created our universe had never happened?
Jim (Why ask a stupid question?) Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
Loch_Mandy_Monster { ; time=0:00:45.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip float=y
center-mag=+1.808025176460789/+0.3512848505070288/\
3001146/1/141.25/0 params=4/-1.5/1/-6/0/0/0/0
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zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
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 -- February 14, 2014 (Rating A-8,M-7)
Fractal visionaries and enthusiasts:
Today's FOTD image shows one of the infinity of things that
happen when Z^(1.3) is subtracted from Z^(1.2) and straight C is
added on each iteration. This unlikely combination creates a
grossly oversized parent fractal resembling a Mandelbrot set
rotated 180 degrees with flippers on the west side of its main
bay. Today's image lies in the East Valley of a twisted
minibrot on a filament extending from the southwest flipper.
I named the image "The Mysterious East" even though it lies on
the west side of its parent.
The art rating of an 8 reflects the extra effort I put into the
coloring. The math rating of a 7 says little about the math
aspect, which by this time is totally familiar.
The down side of the image is its slow calculation time, which
at 6 minutes will give impatience a chance to arise and might
even cause a fractalist to decide not to do the calculation at
all, thereby missing the pleasure of viewing the image. But
luckily, the web sites are always there to restore pleasure.
Avoid the calculation and experience total pleasure by viewing
the 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>
The day dawned with 1 foot, or 12 inches, or 30cm (make your
choice) of fresh snow on the ground here at Fractal Central.
After being fortified with hot coffee, the fractal he-man
cleared the snow from the sidewalk, while the fractal cats
watched from the window. The high temperature of 37F +3C took
care of the patches the he-man missed.
The next FOTD will be posted in 24 hours, but this is no
guarantee. So until whenever, take care, and claiming that
there is no answer to the question of the meaning of life does
not make the need for an answer any less urgent.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
TheMysterious_East { ; time=0:06:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=ident float=y
center-mag=-24.05351569280277/-43.55790391067416/\
1.961119e+010/1/-110/0 params=1/1.2/-1/1.3/0/15000\
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zgzzfzzezzbzz`zzZzzXzzVzz }
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=========================================
...that the weed has overgrown.
The image has a crazy crosswise
symmetry, which means the right
half, not shown, is upside down.
;
No-, I will save my superlatives -
judge yourself. No zooms either -
the spots are undefinite again.
BUT - create your own ones
and mail them - please.
Thanks
;
https://www.dropbox.com/sh/6s7m1a0mt2r6pjv/BiNGOewaIn
;
Cheers,
Albrecht
FOTD -- February 13, 2014 (Rating A-7,M-7)
Fractal visionaries and enthusiasts:
Today's image exists in the parent fractal that results when
10.5 parts of Z^(-1.1) are combined with 1.2 parts of Z^(-5.5)
and (1/C) is added on each iteration. This parent is a hugely
oversized circular island with three large bays spaced evenly
along its perimeter. The surrounding ocean is infinite. The
image is located in a valley enclosing a small but curious
double bud on the eastern shore line of the island.
The name "X Marks the Minibrot" refers to the chunky X-shaped
element almost filling the frame.
The art rating of a 7 is average for a FOTD fractal. I see a
certain 'forced' effect in the deep violet background, which
appears just a little too artificial to give the image an above
average rating.
The math rating of a 7 is average for images created with the
overworked MandAutoCritInZ formula. This formula has probably
been the most prolific of the FOTD formulas.
The calculation time of 4-1/4 minutes is slower than I would
prefer. I leave it to the individual fractal fan to set up and
run the parameter file, and then decide if the result was worth
the effort. All risk of wasting time may be eliminated however
by checking the web sites.
The image has been calculated and posted for instant viewing 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 day began with a temperature of 16F -9C and light snow here
at Fractal Central. The snow turned heavy by 10am and continued
until mid-afternoon, when it slacked off to a light misty snow.
The temperature heached a high of exactly freezing, which would
have been fair enough if there had been no snow. The fractal
cats were fascinated by the snow, and spent much time in the
windows, wondering why everything had turned white. The humans
spent the day working and setting up for snow clearing.
The next FOTD will be posted in the near future, most likely
tomorrow. Until whenever, take care, and the more one thinks
about the meaning of life, the less one knows.
Jim Muth
jimmuth(a)earthlink.net
START PARAMETER FILE=======================================
X_MarksTheMinibrot { ; time=0:04:15.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=+3.233638461699/-1.500873564601/2418817\
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ziMifGwpBip6zzAkk5zq9mWDwlHoGKoZJhHIhHHaHGZHFWIESI\
DPICMIBJIBKJDLKFMKHNLJOLLPMNQMPQNRRNTSOVTOXUPZVP`W\
QbWQdSUaOY_KaXGeVCiTP9aSB`UC_XDZZEY`FXcGXeHWgIVjJU\
lKTRH7SF6SD5zJ4S93pG2S61kGAb7JgCSl8_cBVVDQXaZZyf_u\
d`rcanbbk`ch_ddZdaXeYWfVVgSThOSiLRiIQnLXkMaiNfgNkd\
Op8icAdTC`JJWGQSEWOBbJ9hF6oB4u72kH8bQDTZIKzmBrcImV\
OcYVY_`RbgLea8gmOhdNibZjpnknoflpajqXhqzfrNrszcsDqq\
zdoLemPolSfjWfh_gfcgefdaabYX_VSYRNVNITKDQG8OD4OW3O\
n2UjA_fIebPkZXpVckSafP`aMZYJYTGzODzJAzF7z7Vz0qzCcz\
Ocz_czEczGczIczKczMczOczQczRmzUmzXmz_mzamzdmzgmzim\
zczzYzzTzzNzzIzzCzz7zzFzz }
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=========================================
HI,
;
before I started I knew that it would be a difficult task.:
To have the outside and the inside of a mandel
completely and clearly separated and in
different colors: Two different worlds!
This involves hardcoding of the borders,
- the contour of the mandel - which is more
or less a matter of try and error.
;
But as you can see I succeeded and it has
become a beautiful image!
;
https://www.dropbox.com/sh/8mew4zq3u8904u7/XW4A5snwYP
;
Cheers,
Albrecht
