FOTD -- March 29, 2011 (Rating *7)
Fractal visionaries and enthusiasts:
Today's image is a failure. Long ago in 1997 it failed to
measure up to the then current FOTD standards, so I filed it
away and forgot it. But now, 14 years later, I have re-visited
the old stuff and decided it is worth a second chance.
The image was created with the Mystic2 formula, a formula that
produces only empty circles of radius 1. But the blank inside
of these circles comes to life when rendered with an active
inside fill, such as the 'bof60' I used in today's scene.
The name "FOTD Failure" points out the failure of the image to
make the grade on its first attempt. The rating of a 7 with an
asterisk indicates that I now consider the old failure worth a 7.
Actually, the image is rather incredible. It appears to have no
organization or overall theme at all. A zoom into any part will
reveal detail unlike that of any other part, making it one of
the most varied images in FOTD history.
The calculation time of 49 seconds is true on the 2000mhz unit.
On the old 100mhz machine the image took almost 20 minutes to
finish.
Of course, all calculation problems may be avoided by viewing
the finished product on the currently active FOTD web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
Paul's original FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
My own FOTD web site is very near readiness. Watch for the
address to be posted in an upcoming FOTD.
The weather on Sunday and Monday here at Fractal Central was
sunny but chilly, with afternoon temperatures in the 30's F,
around +2C. The fractal cats checked the outside a few times to
be sure no unwanted stray cats were around, but spent most of
the time taking it easy.
The next FOTD will be posted whenever I get the chance --
probably on the 31st. Until then, take care, and I'm still
waiting for the final theory of (almost) everything to be
announced.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
FOTD_Failure { ; time=0:00:49.00-SF5 on P4-2000
reset=1950 type=formula formulafile=jim.frm
formulaname=Mystic2 function=cos passes=1
center-mag=-0.7639004447870409/-0.641592723009405/\
305.51/1/50/0 params=1/1/1/1/1/1 float=y maxiter=90
inside=bof60 logmap=yes periodicity=0
colors=000MgFKdCI_9GX6EU3CR2AP1AM1AK1AI1AG1AE1AD1A\
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BckBakCZkCWjDUjERiEOiFOlI }
frm:Mystic2 {; Jim Muth
a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), k=real(p3), f=imag(p3),
g=pixel, z=(pixel)^a+(b*(pixel))^c:
z=(fn1(z)+(d*(g)))^k+(f*(cos(g)))
g=sqr(g),
LastSqr <= 100 }
END PARAMETER FILE=========================================
FOTD -- March 27, 2011 (*6)
Fractal visionaries and enthusiasts:
I realize that three days have passed since the I posted the
last FOTD, but we have been quite busy on regular work and the
upcoming FOTD web site here at FC these past few days.
Today's image is a blast from the past, from around the time of
the start of the FOTD in fact, though it never quite made FOTD
status. The image is one of those indescribable things created
by the MandNewt formulas -- formula number 12 to be exact. It
is typical of the easy (by today's standards) stuff I was doing
at that time, when my machine was a 100mhz 80486.
The name "Golden Oldies" looks back with nostalgia on those days
of yore. But since the image is not a new one, I had to add an
asterisk to its rating of a 6. The calculation time of 1-1/2
minutes on the 2000mhz unit would have been closer to 1/2 hour
on the original machine.
The easiest way to view the finished image is to hop down to the
current FOTD web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
and view it, finished, there.
The old original FOTD site is available at:
<http://www.Nahee.com/FOTD/>
My own web site is nearing readiness, but not quite ready. I'll
post the address as soon as I feel it is ready.
Saturday was sunny but unusually cold here at Fractal Central.
The temperature rose from 19F -7C at daybreak to an afternoon
high of a meager 37F +3C. The fractal cats chose the sun. The
next FOTD will be posted as soon as I get a chance. Until then,
take care, and did anyone lose their mind? I saw one lurking
under the porch stairs this morning.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Golden_Oldies { ; time=0:01:32.06-SF5 on P4-2000
reset=1950 type=formula formulafile=basic.frm
formulaname=MandNewt12 float=y maxiter=430 passes=1
center-mag=3.44291/0/0.216444/1/90/0
params=3/2/5/0.5/-0.5/-1 bailout=100 inside=bof60
logmap=8 periodicity=0
colors=000jjj```kkklllmmmnnnoooqqqtttwwwzzzrrrmmmh\
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cubcwecvfbvgbvhaviavj`vk` }
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),
.0000000000000000000000000000005 <= |h| }
END PARAMETER FILE=========================================
FOTD -- March 24, 2011 (No Rating)
Fractal visionaries and enthusiasts:
Do not be alarmed when you run today's parameter file and the
screen stays blank for a couple minutes. Due to the passes=t
and the lack of detail at the edge of the frame, the image is
a slow one to get started, but things pick up once the calcula-
tion reaches the actual central crescent.
Today's FOTD is an image of the entire Mandelbrot set. Well,
the entire set is in there somewhere, but it has been so
distorted by the 'invert' feature of Fractint that it has been
reduced to a horse shoe crescent.
The center of the scene lies somewhere in the Seahorse Valley
area of the large minibrot on the main stem of the M-set, though
one would never guess it from what appears on the screen.
The name "Where in the World" refers to the difficulty of deter-
mining exactly where in the M-set today's scene is located.
Since I believe this is the first time I have used Fractint's
'invert' feature in an FOTD, I have almost no idea of what is
possible with this option, so I could give today's image no
rating.
The rather slow calculation time of 11 minutes is mostly due to
the very large maxiter of 2,500,000. This slowness may be
avoided however by viewing the finished image on the FOTD web
site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The old original FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
Wednesday began with slushy snow here at Fractal Central. By
midday the snow changed to rain, which made the slush even
slushier. To end the day with a grand finale, a thunder-shower
passed over at 6pm. The temperature held steady around 34F +1C
most of the day. The fractal cats took a few glances at the
unpleasant outside conditions, but spent most of the time close
to the heat.
In the human department, our day was busy, yet under control.
I'll try to post the next FOTD in 48 hours, but since the future
is unpredictable, there are no promises. Until whenever, take
care, and take a moment to wonder why there is a vast universe
instead of simply nothing.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Where_in_the_World { ; time=0:11:03.50-SF5 on P4-2000
reset=2004 type=mandel passes=t float=y
center-mag=-16.8104/0.928124/0.06579086/1/87.5/0
params=0/0 maxiter=2500000 inside=0 outside=real
invert=0.0001/-1.7685/0.0008 periodicity=0
colors=000VITUKUSNVRPWPSXOUYNXZLZ`KaaIcbHfcFhdEkeD\
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9gWEhdJjmO6ayCdtIgoOjjUme }
END PARAMETER FILE=========================================
FOTD -- March 22, 2011 (Rating 6)
Fractal visionaries and enthusiasts:
Today's FOTD is late. This usually means things are unusually
busy here at FC, as is true at the present time.
The name of today's image, Square root of Nothing", refers to
the power of Z that created the parent fractal. This parent
fractal resembles a Mandelbrot set with a triangular main bud
on the northwest side of the main bay and a zigzag filament
extending out from the bud, and terminating some distance to the
northwest. A cut-off nest of filament fragments lies some
distance to the east of the main fractal. Today's scene is
located in this cut-off nest of filaments.
Due to a shortage of time, I was unable to find the best color-
ing for the image, but the colors I did find are sufficient to
show the nature of the scene and allow a rating of a 6.
The calculation time of 3 minutes should cause no one undue dis-
tress. To make matters even better, the pre-calculated image
may be viewed at the FOTD 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/>
Settled and near normal conditions prevailed here at FC on
Sunday, with partly cloudy skies and a temperature of 50F 10C.
Monday brought similar temperatures, but was spoiled by morning
rain and afternoon clouds. The fractal cats took it all in
stride. The next FOTD is scheduled in about 32 hours. Who
knows if it will actually be ready in time?
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
SquareRootOfNothin { ; time=0:03:05.16-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandelbrotBC3 function=ident
center-mag=+1.294065337556993/+0.8218935124636804/\
7.008061e+008/1/70/0 params=1.4142/0/2/0 float=y
maxiter=2400 inside=0 logmap=198 periodicity=6
colors=000pcgmcckc_icWg`Se`Ob`K``KZ`KX`KV`JU_IT_HV\
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RmzGmz5mzoszsyzwvzstzorzk }
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 -- March 20, 2011 (Rating 6)
Fractal visionaries and enthusiasts:
The scale of minibrots lying very deep in the Mandelbrot set is
incredible enough, even awesome. At the scale of today's image
the entire M-set would be as large as the entire galaxy, if not
many times larger. It well might be as large as the entire
visible universe, which is about 27,000,000,000 light years in
circumference. It is large enough that the chance of today's
scene having ever appeared on any screen is effectively zero.
But with all this awesome size behind the image, why does it
rate only a 6?
The answer lies in the name of the image -- "It's All Circles".
Just as the very high order Mandeloids tend to develop a boring
similarity, these super-deep minibrots tend to grow boringly
similar. As today's image shows, they tend to consist of layer
upon layer of concentric circles, with minor changes in the
circular decorations, but with an overall similarity that is
striking at first glance but soon grows boring. (Not all mini-
brots at this depth are boring circles however. There are
exceptions, some of which I might post as future FOTD's.)
Still, the fact that today's circular image lies at a depth of
2*(10^34) makes the effort of running the parameter file
worthwhile.
The image is located in the basin of a larger minibrot in the
basin of a still larger minibrot in the basin of an even larger
minibrot on a filament extending inland from the northeast shore
line of the large minibrot on the main stem of the Mandelbrot
set.
The calculation time of 19-2/3 minutes is surprisingly fast for
such a deep scene. And even this reasonable time may be saved
by viewing the finished image on the FOTD web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original FOTD web site is still available at:
<http://www.Nahee.com/FOTD/>
Friday here at Fractal central was summer-like, with lots of sun
and a temperature of 77F 25C. The new fractal cats, who have a
much less adventurous life than the old fractal cats had, spent
Friday watching for stray cats and worrying about their next
meal. Saturday dawned cloudy, but the clouds cleared away by
midday, leading to a pleasant afternoon with a high of 50F 10C.
The next FOTD will be posted in 48 hours, more or less. Until
whenever, take care, and be with it, fractal pro.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
It's_All_Circles { ; time=0:19:42.06-SF5 on P4-2000
reset=2004 type=mandel passes=1
center-mag=-1.740745628752070677391923435253000819\
49/0.011627426705656461304987086921212283982/1.967\
708e+034/1/170/0 params=0/0 float=y maxiter=15000
bailout=25 inside=0 periodicity=6
colors=000fTdiPflLinIlqEosBqoEmlGjhIfeLcaN_ZPXVRUS\
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m9Th8Yb7aY6fS5kM4pH3uB3y6 }
END PARAMETER FILE=========================================
FOTD -- March 20, 2011 (Rating 6)
Fractal visionaries and enthusiasts:
The scale of minibrots lying very deep in the Mandelbrot set is
incredible enough, even awesome. At the scale of today's image
the entire M-set would be as large as the entire galaxy, if not
many times larger. It well might be as large as the entire
visible universe, which is about 27,000,000,000 light years in
circumference. It is large enough that the chance of today's
scene having ever appeared on any screen is effectively zero.
But with all this awesome size behind the image, why does it
rate only a 6?
The answer lies in the name of the image -- "It's All Circles".
Just as the very high order Mandeloids tend to develop a boring
similarity, these super-deep minibrots tend to grow boringly
similar. As today's image shows, they tend to consist of layer
upon layer of concentric circles, with minor changes in the
circular decorations, but with an overall similarity that is
striking at first glance but soon grows boring. (Not all mini-
brots at this depth are boring circles however. There are
exceptions, some of which I might post as future FOTD's.)
Still, the fact that today's circular image lies at a depth of
2*(10^34) makes the effort of running the parameter file
worthwhile.
The image is located in the basin of a larger minibrot in the
basin of a still larger minibrot in the basin of an even larger
minibrot on a filament extending inland from the northeast shore
line of the large minibrot on the main stem of the Mandelbrot
set.
The calculation time of 19-2/3 minutes is surprisingly fast for
such a deep scene. And even this reasonable time may be saved
by viewing the finished image on the FOTD web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original FOTD web site is still available at:
<http://www.Nahee.com/FOTD/>
Friday here at Fractal central was summer-like, with lots of sun
and a temperature of 77F 25C. The new fractal cats, who have a
much less adventurous life than the old fractal cats had, spent
Friday watching for stray cats and worrying about their next
meal. Saturday dawned cloudy, but the clouds cleared away by
midday, leading to a pleasant afternoon with a high of 50F 10C.
The next FOTD will be posted in 48 hours, more or less. Until
whenever, take care, and be with it, fractal pro.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
It's_All_Circles { ; time=0:19:42.06-SF5 on P4-2000
reset=2004 type=mandel passes=1
center-mag=-1.740745628752070677391923435253000819\
49/0.011627426705656461304987086921212283982/1.967\
708e+034/1/170/0 params=0/0 float=y maxiter=15000
bailout=25 inside=0 periodicity=6
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vtWutSttOrtKqtGptCzt8zt5zl2ze0zg3Zh5Wi8UkARlCOmFMo\
HJpKGqMErOReIcTDaRH_PLZNPXMTVKXUI`SHcRFgPDkNCoMAsK\
8wJ7zM6wP6tS5qU5nX5k_4ha4fd4cg3`j3Yl3Vo2Sr2Pt2Np1Q\
l1Sh1Vd1Xa3Z_5_Y6`W8aTAcRBdPDeNFfLGgIIiGKjELkCNlAO\
m9Th8Yb7aY6fS5kM4pH3uB3y6 }
END PARAMETER FILE=========================================
FOTD -- March 18, 2011 (Rating 6)
Fractal visionaries and enthusiasts:
Today's image takes us on a quick trip rather deep into the west
side of Scepter Valley of the Mandelbrot set, which is the
valley at -1.25 on the X-axis. In this area we find the tiny
things I call 'peanut holes'. These holes appear to be far more
plentiful than minibrots, though with an infinity of both, this
is not mathematically true.
Anyone who has ever enjoyed a bag of fresh roasted peanuts in
the shell knows that most peanuts have two 'nuts' in a shell,
but some freaky ones have only one nut in a shell, while others
have three and rarely four nuts in a single shell. The peanuts
in today's image are the 'three-in-a-shell' kind, and they
surround the minibrot, growing ever smaller and more numerous
the closer to the minibrot we look. Actually, these peanuts are
not really trapped points at all, since they fill-in when the
maxiter is raised.
When rendered in the normal manner, today's image falls kind of
flat, so to add some life, I calculated the image with the
outside set to 'real'. The result turned out to be too busy and
disorganized for a rating higher than a 6, but with a calcula-
tion time of only 1-2/3 minutes, not much effort will have been
wasted if the result proves disappointing.
The name "Chunky Peanut Butter" seemed appropriate when I
noticed the number of tiny peanut holes filling the screen. The
task of calculation may be avoided by viewing the finished image
on the FOTD 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/>
Pleasant conditions prevailed here at Fractal Central on Thurs-
day as the sun shone brilliantly and the temperature reached 61F
16C. The sun is now climbing high enough during the midday
hours that it misses the back edge of the fractal cats' window
shelf, so they spent the afternoon on the front part of their
shelf, watching for stray cats to wander by.
With the spring jobs coming in, my day was rather busy, but I
still found time to find a fractal. The next FOTD will be
posted in two days, more or less. Until then, take care, and be
wary of e-mails that want you to stand in as the heir to an
abandoned sum of 26-million U.S. dollars.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
ChunkyPeanutButter { ; time=0:01:46.73-SF5 on P4-2000
reset=2004 type=mandel passes=1 float=y
center-mag=-1.250000626757216/+0.0003126618705661/\
1.95e+011/1/11/0 params=0/0 maxiter=150000
bailout=16 inside=0 outside=real periodicity=6
colors=000U91T81S80R80P70P70S70R60P60P50N50M50K40K\
40I40L30L30K30J20I20I20C10B10C00B10B20B20130B40B40\
B50L60L60L70L80L80L90LA0LA0LC1LE1KF2KH3KK3KL4KN4KP\
5KQ5KQ6KQ6KO7KO7KO8KN8KO9KP9KOAKPAJPBJPCJPCJQDJQDJ\
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AZBAZA9ZA9Z99_98_88_78_77_67`67`56`56`46`45a35a35a\
24a24a14`02a13a14a24b25b26b36tU7tU8tU8tU9tUAtUAtUB\
tUCtUCtUDzUEzUEzUFzUFzUGz9Ht9HtAItAJtAJtD5tD5tC5tC\
4tC4tB4tB3tA3tA2tA2t92t91 }
END PARAMETER FILE=========================================
FOTD -- March 16, 2011 (Rating 5.5)
Fractal visionaries and enthusiasts:
My web site is progressing, but I had no idea how much progress
was needed. Accurate time forecasts are futile, so all I can
say is that the time is not too far off, and the wait will be
worth the impatience.
Today's image is another return to the world of 12 years ago. I
brought up the Mandnewt07 formula and set it loose to find
today's image.
I have no idea what this series of formulas was originally
intended to do, but they certainly do make some interesting
images, as today's rather disorganized image demonstrates.
With more time I might have done a better coloring job. As it
is, I could rate the finished product no higher than a 5-1/2,
which is just a tiny bit above average.
The name "Back to the Past" refers to the age of the generating
formula. The calculation time of 1-3/4 minutes means little
effort will be needed to run the parameter file.
The image may also be seen on the FOTD 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/>
My own web site will soon be coming at:
<address to be revealed>
Tuesday here at Fractal Central featured morning sun, afternoon
clouds, and light rain in the evening. The fractal cats kept
themselves busy chasing each other up and down the hallway.
My day was about average. The next FOTD, likely an improved
one, is scheduled to be posted in 48 hours. If nothing goes
wrong, it might appear on time. Until whenever, take care, and
I hear the duck has lost his job.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Back_to_the_Past { ; time=0:01:44.20-SF5 on P4-2000
reset=2004 type=formula formulafile=mandnewt.frm
formulaname=MandNewt07 passes=1 periodicity=0
center-mag=-6.78166/-12.3172/0.07303401/1/-92.5/0
params=2/3/3/1/1/-1 float=y maxiter=255 inside=atan
colors=00005W15Q35K45E65D75D95CA5CC5CD5DF5DG5EI5EJ\
5FLAFMFGOHGPJHRLISNIUPJVRJXTKYUK_VL`WLbXMcYMeZNf_O\
h_Pi`QkaRlaSnbTobUpcVpdWpdXpeYpfZpf_qg`qhaqhbqicqj\
dqjeqkfrlgrlhrmirnjrnkrolspmspnsqosrpsrqssrststttt\
uutvutvutwutxuuxuuyuuzuuzuuzuuzuuzutzttxstvrstqssp\
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PKGOLGOMHOMHNNINOINOJMPJMQKMQLLRLLSMLSMKTNKUNKUOJV\
OJWPIXPIXQIYRHZRHZSH_SG`TG`TGaUFbUFbVFcUFdTFcRFbPF\
aNF`LFZJFWHHUCJQ6LM7NL8PK9PJAPJBPKCPaWJZUIWTHSSGPR\
FLPEIODFNCBMB8KA4J91I80H7 }
frm:MandNewt07 {; Jim Muth
z=c=(pixel*p1):
a=z^3+(c-p2)*z-c
b=3*z^2+c-1
z=z-p3*a/b
0.000000000000000000000000000001 <= |a| }
END PARAMETER FILE=========================================
FOTD -- March 14, 2011 (Rating 6)
Fractal visionaries and enthusiasts:
Things have been very wet here at Fractal Central these past
few days, wet enough in fact to flood the FC basement 10cm deep.
But by Sunday the water had subsided, and things were getting
back to normal.
In the fractal department, I have returned to an old formula for
today's image -- the Mystic2 formula, which is at least 12 years
old. When the inside is set to a flat color, this formula draws
nothing but empty circles, but when an active coloring such as
the 'bof61 is applied to the inside, strange things begin happen-
ing. Today's image shows some of these strange things.
The image consists entirely of inside stuff made visible by the
'bof61' inside fill. It is very sensitive to changes in the
inside fill, the function and the p3 parameter. The p1 and p2
parameters have a far lesser effect.
The name "Shadow Dance" sounds kind of Native Americanish, but
it has little to do with the appearance of the image.
Due to the lack of organized colors, I could rate it no higher
than a 6.
The finished image soon will be available on the current FOTD
web site at:
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
The original FOTD web site may be found at:
<http://www.Nahee.com/FOTD/>
My own FOTD web site will soon be up and running, though due to
problems dealing with the flooded basement, it has made no
progress since the last report.
Sunday brought clouds and a temperature of 43F +6C to Fractal
Central. The fractal cats took it all in stride. They were
more interested in being fed. My day was spent recuperating
from the flooded basement and watching far greater disasters on
TV. The next FOTD will be posted in a couple days. Until then,
take care, and no matter how bad things seem, they are never so
bad that they could not get worse.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Shadow_Dance { ; time=0:01:31.62-SF5 on P4-2000
reset=2004 type=formula formulafile=jim.frm
formulaname=Mystic2 function=cotan passes=1
center-mag=0/0/31 params=1/-3/3/4/3/5.899 float=y
maxiter=255 inside=bof61 periodicity=6
colors=000TETTFRTHPTIMTJKTLIoMGTNETOCPQFzZ0jALHSJG\
eHFQGDOECNDBMB9LA8J87I7zH54G43E21D10C00H01C3C003DB\
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bZAcXAcVAcUD_SGWRISPLOOOKNQGLTCKV9JXAHYBFZBD_CB`D9\
aD8bE6cF4dF2eG0fG0UN0HT05Z08W0AU0DR1FP1IM2KK3MI3PF\
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E66E69E6BD5ED5HC4KC4MC4LC4JC3HC3GD2ED1CD1BD09D07D0\
6E04E02E01E00E00E00D01D22D43D74DA5DC6DF7DH8DK9DNAD\
PBDSCDUBBQB9MA7IA5F94B927 }
frm:Mystic2 {; Jim Muth
a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), k=real(p3), f=imag(p3),
g=pixel, z=(pixel)^a+(b*(pixel))^c:
z=(fn1(z)+(d*(g)))^k+(f*(cos(g)))
g=sqr(g),
LastSqr <= 100 }
END PARAMETER FILE=========================================
Here is a link to a web page with an image:
http://www.fracton.org/fmlposts/astroid_out.html
The formula for this fractal is called True_Astroid and is based on the
original Astroid_Mset by Paul Carlson. The original draws an "inside out"
astroid curve while this one draws it in true form. The orbit trap formula
is modified to use the polar form instead of the parametric form. The
changes to the formula were suggested by Gerald Dobiasovsky.
The parameter file used to make this image is below:
Astroid_Out { ; Exported from Fracton.
reset=2004 type=formula formulafile=fracton.frm
formulaname=True_Astroid passes=1 float=y
center-mag=-1.265578607178311/0.1218562499999997/2\
22.222225/1/0/0
params=0.01/0.59/8/30/0/0/0/0/0/0 maxiter=500
inside=255 outside=summ
colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40\
zz0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000\
z88 }
frm:True_Astroid {
; Based on
; Astroid_Mset copyright (c) Paul W. Carlson, 1997
; Modified for compatibility with Fractint 20.04 and
; Fracton by Mike Frazier, 2011
; Additional improvements by Gerald Dobiasovsky
;****************************************************
; Always use floating point math and outside=summ.
;
; Parameters:
; real(p1) = a factor controlling the width of the curves
; imag(p1) = radius of the astroid
; real(p2) = number of color ranges
; imag(p2) = number of colors in each color range
;
; Note that the equation variable is w, not z.
; Initialize cindex to the index of the background color
; Formula modified to avoid color index 0 which can not
; be used with outside=summ in FractInt v20.04
;****************************************************
w=0,
c=pixel,
z=0,
cindex=254,; Background color 254
bailout=0,
iter=0,
range_num=0,
i=(0,1),
r=imag(p1),
;****************************************************
; In the accompanying par file,
; we have 8 color ranges with 30 colors in each range
; for a total of 240 colors. The first range starts at
; color 1. Pixels will use color 254 when |w| > 1000.
; Other values can be used here as long as the product
; of num_ranges times colors_in_range is less than 255.
; Color 254 is reserved for the background color and
; color 255 can be used for the inside color.
;****************************************************
num_ranges=real(p2),
colors_in_range=imag(p2),
;****************************************************
; Real(p1) controls the width of the curves.
; These values will usually be in the range 0.001 to 0.1
;****************************************************
width=real(p1),
index_factor=(colors_in_range-1)/width:
;****************************************************
; The equation being iterated. Almost any equation
; that can be expressed in terms of a complex variable
; and a complex constant will work with this method.
; This example uses the standard Mandelbrot set equation.
;****************************************************
w=w*w+c,
;****************************************************
; The orbit trap curve. This example uses an "astroid"
; curve (which has absolutely nothing to do with huge
; rocks in outer space). Any two-dimensional curve can
; be used which can be expressed in parametric form in
; terms of the angle from the origin.
;****************************************************
; ang is really tan(ang) here
ang=imag(w)/real(w),
astroid=r*sqrt((ang^2+1)/(|ang|^(1/3)+1)^3),
;****************************************************
; If the orbit point is within some distance of the curve,
; set z to the index into the colormap and set the bailout
; flag.
;****************************************************
distance=abs(|w|-|astroid|),
if(distance<width&&iter>1),
cindex=index_factor*distance+range_num*colors_in_range+1,
bailout=1,
endif,
;****************************************************
; Cycle through the range numbers (0 thru num_ranges - 1)
; With two color ranges, even iterations use color
; range 0, odd iterations use color range 1.
;****************************************************
range_num=range_num+1,
if(range_num==num_ranges),
range_num=0,
endif,
;****************************************************
; Since we are using outside=summ, we have to subtract
; the number of iterations from z.
;****************************************************
iter=iter+1,
z=cindex-iter,
;****************************************************
; Finally, we test for bailout
;****************************************************
bailout==0&&|w|<1000
}
--
Mike Frazier
www.fracton.org
