FOTD -- November 23, 2010 (Rating 8)
Fractal visionaries and enthusiasts:
I had intended November to be exclusively a month of odd slices
of the Z^2+C Julibrot, and here we are 3/4 of the way through
the month, with quite a few interesting odd-slice scenes to show
for the effort. While searching for an odd Julibrot slice today
however, I came up blank, but the workhorse MandAutoCritInZ
formula rescued me in the nick of time.
The image shows a minibrot in a valley at the southern edge of
the superb fan of the parent fractal, which was created when I
combined 11 negative parts of Z^(-1.1) with one negative part of
Z^(-11), and added (1/C).
I rated the image at an 8, including a full point for the extra
coloring effort. I named the image "Minibrot in Bloom" when I
noticed FL raking leaves out in the back-yard garden.
The calculation time of 3-1/4 minutes is well within reason for
an image that rates an 8. Viewing the image already calculated
on the FOTD web site is even more reasonable. The web site may
be accessed at:
<http://www.Nahee.com/FOTD/>
Morning clouds gave way to afternoon sun here at Fractal
Central on Monday, while the temperature reached a pleasant 57F
14C. The fractal cats occupied themselves for an hour or so
chasing the laser beam up and down the hallway. After the work-
out they were too exhausted to do much but sleep and ask for
food.
My day was rather slow. In the afternoon I spotted FL raking
leaves in the garden, but she finished before I could go out and
help. The next FOTD will be ready in 24 hours. Watch for it
then in this same spot. Until next time, take care, and I'll
tell you how if you tell me why.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Minibrot_in_Bloom { ; time=0:03:14.93-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=MandAutoCritInZ function=recip passes=1
center-mag=+1.302856921705854/-2.971635012449411/\
3.859e+009/1/150/0 params=-11/-1.1/-1/-11/0/100/0/0
float=y maxiter=2400 inside=0
logmap=290 periodicity=6
colors=000H0OD0L90J50G10D00A00800C00F31H62J83L64HC\
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mzzmzzmzzmzzmzzmzzmzzmzzmzzzz5zz7zz9zzBzzzzzzzzzzz\
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, esc=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < esc }
END PARAMETER FILE=========================================
Because of lots of busy-ness at Action Central postings to the mailing list may be a little sparse
for the next few days.
Best regards,
Roger Alexander
FOTD -- November 22, 2010 (Rating 7)
Fractal visionaries and enthusiasts:
Today's image shows a curious minibrot, (if this is the proper
name for such creatures), that lies on what remains of the main
stem of the Mandelbrot set when the Julibrot is sliced at an
angle oriented 20 degrees from the Oblate toward the Elliptic
direction.
To bring the image to reasonable proportions, I stretched it
about 4 times in the horizontal direction, which is a little
excessive, but makes the best effect.
In my opinion the image is worth a rating of a 7, not the least
of it due to the coloring, which brings blue to a new extreme.
The name "Feeling the Blues" describes the mood of the scene.
The calculation time of 23 seconds will pass in half a flash, as
also will the trip to the FOTD web site at:
<http://www.Nahee.com/FOTD/>
to see the pre-calculated finished image.
A mixture of sun and clouds and a temperature of 50F 10C kept
everyone happy here at Fractal Central on Sunday. In the
evening, Cassie, the smaller fractal cat, started growling at
something in the yard, but we could see nothing. Nicholas, the
large cat, assured her that all was well, and after a few
minutes, whatever had her concerned moved on. Meanwhile, my day
was average.
The next FOTD will be posted in 24 hours. Until then, take
care, and sometimes a person needs light to see the light.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Feeling_the_Blues { ; time=0:00:23.29-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 center-mag=-1.575725778\
/0/75.37224/3.9228 params=70/0/20/0/0/0/0/0 float=y
maxiter=3200 inside=0 logmap=29 periodicity=6
colors=00000600800A00D00F00I00K00N00Q00R00S01T02U0\
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zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:SliceJulibrot2 {; draws most 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),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
FOTD -- November 21, 2010 (Unrated)
Fractal visionaries and enthusiasts:
Today's image is not my own. It is one I found on the CD that
came with the second edition of the book "Fractal Creations".
Since the book was printed in 1993, the image is over 17 years
old.
On the CD, the image is in a directory named 'Sherry'. I have
no idea who this mysterious 'Sherry' person might be. I used
the image virtually as I found it on the disk, though I did make
it slightly smaller and add a few tints of color plus a few
brilliant highlights.
The image was calculated by the fn(z*z) formula hard-coded into
Fractint.
The name "By Sherry" indicates that I can take no credit for the
image, nor can I give it a rating. I can only stand on the peak
of the mountain that someone else carried me to the top of, and
exclaim 'what a great view'.
The calculation time is incredibly fast -- less than one second
on my 2000mhz fractal-dedicated machine, which is very faithful,
but now and then decides it does not want to start up unless its
memory cards are reseated.
The finished image is also available on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Too many clouds but otherwise benign conditions prevailed here
at Fractal Central on Saturday. The temperature topped at a
quite average 48F +9C, which was mild enough to keep the fractal
cats happy. When their happiness waned, they amused themselves
by chasing the toy laser beam up and down the hallway. They
enjoy the laser so much that they come and ask one of us for
action when they want their exercise.
As for the humans, our day was average, which is the way we like
it. The next FOTD, this time a J.M. original, will be posted in
24 hours. Until then, take care, and when we finally see the
light, what will we do with it?
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
By_Sherry { ; time=0:00:00.88-SF5 on P4-2000
reset=2004 type=fn(z*z) function=cosh
center-mag=0/0/0.28548/1.3356/90/0 float=y inside=0
maxiter=500 potential=255/500/20 decomp=256
colors=000000gggffffffeeeeeeddddddccccccbbbaaaaaaa\
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`````aaabbbbbbbbbccccccdddeeeeeefffgggggghhhiiiiii\
iiijjjjjjkkklllmmmmmmnnnoooooooooooonnnnnnmmmmmmll\
llllkkkjjjjjjjjjiiiiiihhh }
END PARAMETER FILE=========================================
FOTD -- November 20, 2010 (No Rating)
Fractal visionaries and enthusiasts:
In yesterday's image a segment of the classic Mandelbrot shape
appears in the background as the brilliant blue stuff. But the
shape is so distorted that it is almost impossible to recognize
the part of the M-set shape that is showing. In today's image
we have taken yesterday's scene, rotated, twisted, and skewed it
until we have restored the Mandelbrot shape to recognizable
familiarity.
Much to our surprise, we find we have cut a slice through the
M-set shape that covers the main period-2 bud, the northwest
part of the Main Bay and the northern period-3 bud. To find the
slice, I totally winged it by eye. It might be possible by
complicated trigonometry to determine the correct anti-distor-
tion mathematically. It works quite well with simple single
rotations, where all that is required is to enter the cosine or
the reciprocal of the cosine of the angle as the X-magnification
factor. But in yesterday's image, where four angles are
involved, the mathematical method is too complex, at least for
my Arithmetic-101 level of knowledge.
At this point, I am left wondering which version of the same
slice is more correct, yesterday's or today's. The actual
Mandelbrot part of the Julibrot is a 4-D thing, kind of a nest
of hypercylinders shaped like the M-set in the C-plane, but
extended to infinity in the Z-plane. (Don't try to visualize
the entire shape, it's impossible.) This Mandelbrot hyper-
cylinder nest becomes distorted when it is sliced at an angle,
as we did in yesterday's image.
Today's image, which corrects this natural distortion, is
actually the more distorted, and therefore the least correct
image. But at the same time, it is almost impossible to tell
our position when viewing yesterday's image, so I suppose this
makes today's image the more correct one.
All math and almost no artistic value equals no rating. The
name "Manipulated View" tells it like it is. The calculation
time of under 2 seconds is incredibly brief, and should be not
be a factor. The finished image may also be seen on the FOTD
web site at:
<http://www.Nahee.com/FOTD/>
Conditions here at Fractal Central on Friday were acceptable,
with partly cloudy skies, a temperature of 48F +9C and cats that
were fairly contented. The commercial work was about average,
while the FOTD, is more a curiosity than a work of art. The
next FOTD will be posted in 24 hours. Until then, take care,
and try to uncover the alien plot before we end up on a slave
ship to Arcturus.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Manipulated_View { ; time=0:00:01.88-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 center-mag=0.177576/\
-0.440939/0.5850274/0.3595/142.341509490465285/\
-74.8871977088931544 params=152/105/-64/49/-1/0/\
1.118/0 float=y maxiter=1800 inside=0 logmap=yes
symmetry=none periodicity=6
colors=000C36D47E58F69G7AH8BI9CKADMCEOEFQGGTIHWKIZ\
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DzzDzzEzzFzzFzzGzzGzzHzzHzzIzzIzzJzzJzzKzz4zz5zz6z\
z7zz8zz9zzAzzBzzPzzOzzNzz }
frm:SliceJulibrot2 {; draws most 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),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
FOTD -- November 19, 2010 (No Rating)
Fractal visionaries and enthusiasts:
Today's image is presented exactly as it came off the press,
with no manipulation such as rotating, stretching or skewing
applied. What appears on the screen is all there is of the
fractal. Nothing has been cropped. Such chaos is typical of
Julibrot slices at such weird 4-D angles.
The foreground features, which are colored dirty brown, are low
iteration stuff that can go in any direction at all. The
brilliant blue stuff in the background is high iteration stuff
that defines the Mandelbrot set. This blue stuff is actually a
very familiar segment of the Mandelbrot-set shape, though at the
weird angle at which it is being viewed, it is unrecognizable.
In tomorrow's FOTD however, I will post another version of
today's scene, in which I have done all the manipulation needed
to return the Mandelbrot part to its normal state. This will
include substantial stretching and skewing, as well as a
generous rotation.
Since today's image is all math with almost no artistic intent,
I could not give it a rating. The name "UnManipulated View"
describes the image.
Since the image is of such a low magnitude and maxiter, it
calculates in a fireball 6 seconds. The image should also be
available on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
Heavy clouds and blustery conditions continued here at Fractal
Central on Thursday, with a temperature of 50F 10C. The fractal
cats kept happy chasing the point of light from a toy laser
around the living room until they both began panting, and we
decided they had had enough exertion for one day.
As far as the graphic design work went, my day was slow. As for
politics, in the morning paper I saw a column by a liberal woman
columnist about how our schools are failing the young men, while
the young women are excelling. I thought it was the women who
are supposed to be suppressed beneath a glass ceiling by our
patriarchal, male-dominated society.
Regardless of who is suppressing who, the fractals are certainly
not being suppressed. In fact, the next one will be posted in
24 hours. Until then, take care, and you can't have it both
ways!
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
UnManipulated_View { ; time=0:00:06.04-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 center-mag=0.967912/\
-0.1798/0.7473842 params=152/105/-64/49/-1/0/\
1.118/0 float=y maxiter=1800 inside=0 logmap=yes
symmetry=none periodicity=6
colors=000C36D47E58F69G7AH8BI9CKADMCEOEFQGGTIHWKIZ\
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zzNzzMzzLzzKzz6zz7zz8zz8zz9zz9zzAzzAzzBzzBzzCzzCzz\
DzzDzzEzzFzzFzzGzzGzzHzzHzzIzzIzzJzzJzzKzz4zz5zz6z\
z7zz8zz9zzAzzBzzPzzOzzNzz }
frm:SliceJulibrot2 {; draws most 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),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
Today's post is another mandelbrot newton hybrid. Ready made at http://maxitersfractalfollies.blogspot.com
Mandelbrot Newton { ;fract520.gif
; blank
; calctime 0:45:28.17
; created Nov 17, 2010
; Fractint Version 2004 Patchlevel 10
reset=2004 type=formula formulafile=_m.frm
formulaname=MandelbrotInNewton
center-mag=-0.53594159502949720/+1.74212079795591200/1518260/1/-159.9999\
99995772896/-6.8065392974658856e-009 float=y maxiter=1500 inside=0
logmap=123
colors=000CGUBET9DS8BR7AQ69P57O36N24M13L02K02K13L25M36N47O69P7AQ8CR9DSAE\
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nXdmWclVbkT`iS_hRZgQXfPWeOUdNTcMSbLQaKP`IO_HMZGLYFJXEIW
}
frm:
MandelbrotInNewton(XAXIS) {; use float=yes: from CAL v4.0 by Tim Harris
z = 0, c = pixel, cminusone = c-1:
oldz = z
nm = 3 * c-2 * z * cminusone
dn = 3 * (3 * z * z + cminusone)
z = nm/dn + 2 * z/3
|(z-oldz)|>=|0.01|
;SOURCE: mnewton.frm
}
Roger Alexander
FOTD -- November 18, 2010 (Rating 6)
Fractal visionaries and enthusiasts:
Today's image is an unfamiliar slice of the Julibrot, which I
have named "Stone Arch Bridge". While searching for a name, I
noticed the row of arches across the bottom of the image, and
was reminded of the railroad bridge across the Susquehanna River
at Marysville, which is just north of Harrisburg.
The slice is centered at the western limit of the ever-smaller
string of buds lined up out the negative X-axis of the Mandel-
brot set. The orientation is at an angle rotated 31 degrees
from the Parabolic toward the Oblate, though mostly Parabolic
elements predominate.
The rating of a 6 means I am only mildly impressed by the image,
though, because of the spectacular coloring, I do consider it
worth nominal FOTD status.
The very brief calculation time of 8 seconds assures that very
little effort will have been wasted if the resulting image lays
an egg.
To avoid the possibility of ending up with an omelet, I suggest
checking to see if the image is posted on the FOTD web site at:
<http://www.Nahee.com/FOTD/>
After a heavy overnight thunder-storm, Wednesday dawned cloudy
and blustery here at Fractal Central. The conditions continued
most all day, with the clouds breaking only long enough to give
a glimpse of the setting sun. The winds made the temperature of
52F 11C seem surprisingly chilly. The fractal cats made the
most of things, checking every so often to be sure no unwanted
cats were prowling nearby.
My day was slow enough to enjoy, but not so slow as to cause
concern. The next FOTD will be posted in 24 hours. Until then,
take care, and be ever so cautious when the aliens from Sirius C
are snooping about. They're as sneaky as a cat.
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
Stone-Arch_Bridge { ; time=0:00:08.27-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 center-mag=0.572006/\
-0.350829/0.7022955/1/121/0 params=0/90/31/31/\
-1.40115519/0/0/0 float=y maxiter=950 inside=255
logmap=yes symmetry=none periodicity=6 passes=1
colors=00000A00C01E02G03I34K55M76O87RC8UF9WHAWIBYJ\
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tjmjgmaemTbmK`mB`mN`mY`mhamkammbgoblqakp`jo`in_in_\
hmZglYglYfkXejXejWdiWchVchUbgUmfTmfTmeSmdSmdPmeNme\
LmfImfGmfEmgCmg9mg7mh5mh3mh3mh3mi3mj3mk3mk3ml3mm3m\
n3mn6ml9mjCmhFmfImdLmbszz }
frm:SliceJulibrot2 {; draws most 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),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
FOTD -- November 17, 2010 (Rating !!!)
NEW FORMULA ALERT!
UNUSUAL PICTURE SHAPE ALERT!
Fractal visionaries and enthusiasts:
Today's image will begin calculating toward the center of the
screen. This is no error. Instead of a 4-3 width-height ratio,
today's image has a much wider 2-1 ratio.
Today's image rates a triple bang. This means it is of excep-
tional mathematical interest, though of only moderate artistic
value. The formula is a new one, so be sure to enter it into
one of your formula files.
The new formula takes the basic Mandelbrot expression and simply
adds a variable function to both initial Z and C. The effect of
the 'exp' (exponential) function that I applied to initial C in
today's image is to virtually place the observer inside the
plane of the image at the point assigned initial C, with the
nearby elements appearing larger and the more remote elements,
much smaller.
In today's image I stationed the observer at -1.40115518995 on
the X-axis, near the limit of the main body of the Mandelbrot
set. The things this does to the set are dramatic, thus the
rating of !!!. The question asked in the name "What Happened
Here" will be answered when the image is viewed.
In the actual M-set, the successive buds grow ever smaller as we
travel out the negative X-axis. But by stationing the observer
at the limit of the string of buds, as I have done in the image,
I have negated this size decrease and made all the buds nearly
the same size. The resulting image resembles nothing as much as
a centipede with 15+ segments.
Unfortunately, the image is a very slow one, growing ever slower
as it progresses and taking nearly an hour to finish. I have
sent the finished image on ahead to Paul at the FOTD web site.
Hopefully, he will have it posted soon.
The FOTD web site may be accessed at:
<http://www.Nahee.com/FOTD/>
To set things straight about how I feel about global warming,
IMO, the earth is getting warmer because we're still coming out
of the most recent ice age. And only a small percentage (one-
percent or so) of this warming is due to man's activity.
Little or nothing can now be done to slow the natural warming,
so instead of futilely spending vast amounts to stop the warm-
ing, we should be spending the money preparing for the minor
but inevitable sea-level rise of an inch or two in the coming
century, and at the same time developing renewable non-polluting
energy sources.
IMO, the most amusing part of the hyped-up global-warming
'crisis' is watching the hated big corporations using it as a
sales pitch, and the easily manipulated masses buying 'green'
products, thinking they are helping to save the earth when they
are actually only enriching the hated big corporations
Heavy clouds, steady rain and a temperature of 52F 11C kept man
and cats alike indoors here at Fractal Central on Tuesday.
There was enough work to keep the man's mind off the outside con-
ditions, but the fractal cats seemed fascinated by the dripping
rain and spent several hours on their window shelf, trying to
make sense of all the water.
The next FOTD will be posted in 24 hours. Until then, take
care, and I see it's the cockroaches behind the conspiracy to
end the world. That's a relief. I thought it was the aliens
from the Herculean cluster. (Actually, the roaches might do the
best job of running things.)
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
What_Happened_Here { ; time=0:45:36.12-SF5 on P4-2000
reset=2004 type=formula formulafile=slices.frm
formulaname=MandelbrotFunct function=ident/exp
center-mag=-10.0738/0/0.1943703/0.6014 params=0/0/\
-1.40115518995/0 float=y maxiter=275000 inside=0
logmap=yes symmetry=xaxis periodicity=0 passes=1
viewwindows=1/0.5/yes/0/0 mathtolerance=0.05/1
colors=000rmIqmIpmIomJomJnmJnmJmmKmmKlmKlmLkmLkmLk\
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wz7zz7zz7zz7zz7zz7zz7zz7zz8zzAzzKzzUzzczzmzztzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:MandelbrotFunct {; Jim Muth real(c),imag(c)
z=fn1(p1), c=fn2(pixel)+p2:
z=sqr(z)+c,
|z| < 16 }
END PARAMETER FILE=========================================
FOTD -- November 16, 2010 (Rating 6!)
Fractal visionaries and enthusiasts:
One should always be prepared for the unexpected, even when it
seems impossible. Today's slice through the Julibrot is a good
example.
The slice is centered on East Valley of the Mandelbrot set, and
oriented 0.1 degree from the Oblate direction, which means the
Mandelbrot stuff is stretched about 573 times its normal extent
in one direction.
In the image that I found before today's, I unstretched the
Mandelbrot parts, but in so doing, I stretched the Julia parts
about 573 times. The grossly stretched Julia stuff is visible
near two corners of today's image. When I did this stretching,
I had almost no hopes of finding any of the Mandelbrot stuff
that I had presumedly returned to its normal proportions, but
much to my surprise, I found one tiny open spot lurking in the
upper left corner.
When I closed in on the tiny spot, I found the better part of
one of the twisted minibrots that fill East valley. At first I
could not believe that any Mandelbrot features at all could
remain when the Julibrot is sliced 89.9 degrees from the Mandel-
brot orientation. But pictures do not lie, (unless they have
been manipulated on a computer), and the twisted object at the
center of today's image is most certainly the remains of an East
Valley minibrot.
The rating of a 6! means that almost all the interest lies in
the mathematical aspect of the image. The artistic worth is
minimal, though not entirely absent, and the features surround-
ing the chopped-off minibrot certainly are curious.
The name "Expect the Unexpected" relates my adventures on the
way to finding today's image.
The calculation time of 21 seconds takes almost all the work out
of running the included parameter file. The calculation work
can be eliminated entirely by viewing the finished image on the
FOTD web site at:
<http://www.Nahee.com/FOTD/>
The sun departed and the clouds moved in here at Fractal Central
on Monday, while the temperature hovered around a mild 55F 13C.
The fractal cats took it all in stride, concerned only about
their next food treat. My day was uneventful. Until next time,
take care, and beware of global warming -- it's got me worried.
How long will it be before we wake up one morning up to our
knees in the rising seas, and find polar bears extinct?
Jim Muth
jamth(a)mindspring.com
START PARAMETER FILE=======================================
ExpectTheUnexpectd { ; time=0:00:21.31-SF5 on P4-2000
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot2 center-mag=-0.023260073\
46855092/-0.00735188243689156/2294.688/0.002601/\
-179.929980454595068/89.7871683432740895
params=0/0/89.9/0/0.277/0/0/0 float=y maxiter=2400
inside=0 logmap=22 periodicity=6
colors=000A0OA0PA0QA0RA0SA2TA4UA6WA8YAA_ACaAEcAGeA\
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zzzzzzzzzzzzzzzzzzzzzzzzzznzzkzzgzzczz_zzXzzTzzPzz\
MzzLzzKzzJzzIzzHzzHzzFzzE }
frm:SliceJulibrot2 {; draws most 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),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z|<=9 }
END PARAMETER FILE=========================================
