FOTD -- June 04, 2009 (No Rating)
Fractal visionaries and enthusiasts:
Today's image, the fourth in the Seahorse Valley series, is a
repeat of the thing I did in yesterday's image. But in today's
image it is taken to the extreme. The Julia set of the valley
is obvious. It fills the entire frame. But there is something
quite unusual in the image.
That brilliant diagonal line across the central bay is the
Mandelbrot aspect of Seahorse Valley magnified a thousand or so
times. In today's image it looks like a featureless line, but
all the detail of the deepest parts of the valley is in there.
Tomorrow's image, which is incredibly slow and already cooking,
will show a surprising bit of this detail.
The image is a fireball fast one, though it is still always fun
to surf out to the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
and enjoy the finished product there.
FL has a way of asking questions that activate my philosophical
tendencies. On Wednesday she casually asked if science believes
in ghosts. I replied that science is not an intelligent being.
It is a rational way of gaining knowledge and determining truth.
It doesn't believe or disbelieve. Its philosophical standpoint
is materialistic and therefore it tries to explain things on a
material basis.
I explained that most scientists consider ghosts to be natural
phenomena or psychological images in the physical brain. This
assumption reduces ghosts to the material level. Science does
not consider ghosts to be surviving spirits of the dead because
it has no way of objectively studying spirits. But this does
not imply that science denies the existence of human spirits.
Perhaps spirits are fractals, things that also have no physical
existence!
Rain fell steadily most all day here at Fractal Central on
Wednesday, while the temperature fizzled out at 59F 15C. The
fractal cats took a quick glance at the outside conditions and
settled down for another two-hour nap.
My day was not too busy, but rather frustrating. The next FOTD
will be posted in 24 hours. Until then, take care, and if you
see a ghost, your brain did it.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Seahorse_Valley-04 { ; time=0:00:20.32-SF5 on P4-2000
reset=2004 type=formula formulafile=jim.frm
formulaname=ObliqueManPlus passes=t
center-mag=0/0/0.8503401 params=0/0/-0.75/0/0.0075\
/0.0075 float=y maxiter=50000 inside=0 logmap=yes
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tzztzztzzDzzEzzFzzFzzGzzG }
frm:ObliqueManPlus {;Jim Muth
z=p1+pixel, c=p2+(p3*pixel):
z=sqr(z)+c,
|z| <=100 }
END PARAMETER FILE=========================================
FOTD -- June 03, 2009 (No Rating)
Fractal visionaries and enthusiasts:
Today's image shows another surprising aspect of the four-
dimensional Seahorse Valley complex. The outer drab blue area
outlines a distorted version of the Seahorse Valley Julia set
with a C-value of -0.75, while the brilliant reddish yellow
elements inside the Julia outline are a grossly enlarged view of
the Mandelbrot aspect of the valley.
The enlargement of the Mandelbrot part of the image is due to
its hypercylindrical four-dimensional shape and the angle at
which it is sliced. In 4-D space, if the angle is right, a
hypercylindrical 4-D object may be sliced by a plane so that all
directions of the projection onto the plane are enlarged equally
up to infinity. Some careful measuring and a bit of trigonome-
try, (which I am not about to do), would reveal the angle of
today's slice.
I named the image "Seahorse Valley-03", which describes it quite
well. Since the scene has little artistic value, I gave it no
rating, though I consider it worth about a 6-1/2.
The calculation time of 15 seconds will pass in a fractal flash.
Another way to see the image is to flash out to the FOTD web
site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
and view it there with zero effort exerted.
Morning clouds and a few drops of rain gave way to plenty of
sunshine and mild afternoon temperatures in the mid 70'sF, or
around 24C. The fractal cats here at Fractal Central enjoyed
the pleasant conditions, even catching a little afternoon sun.
My day was rather busy. The next FOTD will be posted in 24
hours. Until then, take care, and regardless of whether it's
scientific or unscientific, it still might or might not be true.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Seahorse_Valley-03 { ; time=0:00:15.75-SF5 on P4-2000
reset=2004 type=formula formulafile=jim.frm
formulaname=ObliqueMand passes=t center-mag=0/0/.86
params=0/0/-0.752/0/0/0.05 float=y maxiter=16000
inside=0 logmap=yes symmetry=yaxis periodicity=10
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frm:ObliqueMand {; Jim Muth
z=sqr(p1)+pixel, c=p2+(pixel*p3):
z=sqr(z)+c
|z| <= 100 }
END PARAMETER FILE=========================================
FOTD -- June 02, 2009 (Rating 4)
Fractal visionaries and enthusiasts:
Today's image is a quickie, fast and simple enough to get the
FOTD back on its regular schedule.
The image is a view of Seahorse Valley (believe it or not)
sliced in an orientation 15 degrees from the Oblate direction
toward the Rectangular direction.
The narrow line across the center of the fractal is actually the
space between the two branches of the valley as seen from the
west side. We are in the large period-2 bud, looking east
toward the valley wall that separates us from the main bay of
the Mandelbrot set, which from this angle lies a short distance
behind the screen.
Bits and pieces of seahorse tails are scattered about the scene,
though most of them must be stretched quite a bit before they
become recognizable. But search as we may, we would never find
a Mandelbrot minibrot. They do not exist at this angle.
The name of the image is only a catalog number. The lowly
rating of a 4 is all I could give an image that is basically a
space filler.
After yesterday's marathon calculation time, today's 7-second
time is a blessed relief. And as always, the image is posted
for instant satisfaction on the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
A mix of sun and clouds, and a slightly chilly temperature of
73F 23C made Monday acceptable for the fractal cats here at
Fractal Central. They had a bit of excitement when one of the
local stray cats found and made short work of a baby robin that
had just fallen out of its nest. Luckily, FL missed the sad
event.
The next view of Seahorse Valley will be posted in 24 hours.
Until then, take care, and if I were the Big Guy up there, I
would never have designed a world where living creatures need
to kill and eat other living creatures, and then said to man,
"thou shalt not kill."
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Seahorse_Valley-02 { ; time=0:00:07.43-SF5 on P4-2000
reset=2004 type=formula formulafile=basic.frm
formulaname=SliceJulibrot4 center-mag=-0.121105/0/\
1/1/90/0 params=15/90/0/90/-0.75/0/0/0/2/0 float=y
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0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0z\
z0zz0zz0zz0zz0zz0zz0zz0zz }
frm:SliceJulibrot4 {; 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=z^(p5)+c
|z|<=9 }
END PARAMETER FILE=========================================
FOTD -- June 01, 2009 (Rating 6.5)
Fractal visionaries and enthusiasts:
Very slow image alert!! Run parameter file at your own risk!
We have not had a FOTD theme month for quite a while, so I have
decided to make Seahorse Valley the FOTD theme for the month of
June. Not only will we explore the well-known Mandelbrot and
Julia aspects of the valley, we will check the four remaining
aspects as well.
Seahorse Valley of the Mandelbrot set is actually a four-
dimensional thing, which includes not only all its Julia sets,
but the scenes in the Oblate, Parabolic, Elliptic and
Rectangular directions, as well as the oblique scenes sliced at
unimaginable four-dimensional angles. I have included a short
chart of the six mutually perpendicular planes of the Z^2+C
Julibrot:
real(C) and imag(C) = Mandelbrot aspect
real(Z) and imag(Z) = Julia aspect
imag(C) and real(Z) = Oblate aspect
real(C) and real(Z) = Parabolic aspect
real(C) and imag(Z) = Elliptic aspect
imag(C) and imag(Z) = Rectangular aspect
The names of the four additional aspects are my own invention.
The orientation of today's image is within 1/100 of one degree
of the Julia orientation. The tiny rotation is toward the
Rectangular orientation. The outer edge of the fractal is the
familiar Julia set with a C-value of -0.75,0. Cut the maxiter
to 100 to see it.
The strange-looking stuff inside the familiar Julia set is a
gross enlargement and distortion of the Mandelbrot aspect of Sea-
horse Valley. As far as I know, this is the smallest deviation
from the actual Julia orientation of Seahorse Valley that I have
yet seen.
The familiar Julia set of Seahorse Valley calculates in a few
seconds, but today's slight rotation raises the calculation time
to over three hours. The incredible increase in time is due to
the stuff on the inside of the fractal, most of which has an
iteration count in the millions, and also to the fact that the
periodicity must be turned off for the image to generate
properly.
The name "Seahorse Valley-01" is a catalog number, since I will
be doing many more Seahorse-Valley images in the month to come.
Luckily, no more images will take anywhere near today's 3 hours
to calculate. The rating of a 6-1/2 implies that I feel there
is too much mathematical interest and too little artistic worth
in the image. Also, I have posted several images very similar
to today's in the past, though the images were nowhere near as
extreme.
Those with a few hours to spare may see the image by starting
the included parameter file and coming back several hours later.
Those with more pressing things to do may see the finished image
on the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
Another perfect day prevailed here at Fractal Central on Sunday,
with sunny skies and a temperature of 77F 25C. The fractal cats
spent most of the day in the side window, watching the other
cats in the neighborhood wander by.
My day was pleasant enough. If all goes well, the next FOTD
image will be posted in about 6 hours. Until then, take care,
and when does the beginning end?
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Seahorse_Valley-01 { ; time=3:09:55.05-SF5 on P4-2000
reset=2004 type=formula formulafile=basic.frm
formulaname=SliceJulibrot4 passes=1
center-mag=0/0/0.862069 params=90/0/89.99/90/-0.75\
/0/0/0/2/0 float=y maxiter=3500000 inside=0
logmap=yes symmetry=yaxis periodicity=none
colors=000HazJczLezNgzPizRjzTkzVmzXnzZoz`qzbszduzf\
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czjczjczjczkczlhzlmzmrzmvznzznzzozzpzzpzzqzzqzzrzz\
rzzizz`zzSzzJzzBzzIzzOzzU }
frm:SliceJulibrot4 {; 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=z^(p5)+c
|z|<=9 }
END PARAMETER FILE=========================================
