FOTD -- August 03, 2008 (Rating 6)
Fractal visionaries and enthusiasts:
What does one do on a lazy Saturday? Why search for fractals of
course. Today's fractal required very little searching, but the
day was so lazy that the FOTD was once again late.
The image is a distortion of a Julia image closely related to
yesterday's. It was distorted by double-rotating the slice
0.00015 of one degree from the Julia direction. A tiny rotation
makes a huge difference this close to the Julia orientation. To
see the pure Julia version change both the p1 and p2 parameters
to 90,90. The undistorted version is an improvement, but I kind
of enjoy imperfection in fractals.
I named the image "Isle of View". For some reason it reminds me
of a kiss. To see the connection between an island and a kiss,
walk up to an attractive young lady and whisper this name to
her. But be prepared to explain your remark or run like a deer
if her husband overhears.
I rated the image at a 6, which is a little above average,
though far from outstanding. The calculation time of 1-1/2
minutes can be avoided by visiting the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
and downloading the finished picture from there.
Saturday began with a crackling thunder-storm here at Fractal
Central, but by noon the sky cleared, leading to a pleasant
afternoon with a temperature of 81F 27C. However at 5pm the
serenity was spoiled by a surprise heavy shower that fell in
full sunlight. After that the day ended spectacularly, with
a double rainbow and clouds that had to be seen to be believed.
The fractal cats observed the goings on with disinterest.
In my department nothing much happened. The next FOTD will be
posted in about 12 hours. Until then, take care, and search,
search, search.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
Isle_of_View { ; time=0:01:32.22-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideJulibrot center-mag=0.00592736/\
0/3.122/1/-90/0 params=-89.99985/90/89.99985/90/\
-17.45247/0/0/0/5/9 float=y maxiter=1800
inside=fmod proximity=0.0175
symmetry=none periodicity=10
colors=000ovmovpowrowtqnwkfqeZk_RfUJ`OBVJ4QD3H839O\
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WblXffYj_ZmUZgWWaXTXYQR_NL`KGaI6hG8fLAePCdTDbXFa`H\
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P4uK7lN9aWCUeSMlhEpzIqzMrmQsYShdTYjUNqVCw_Avd8ui7t\
n5ss3rx2qKvISnH_gHg`GoUGwNGtKQqHZnEglCp3jP8gUDdYIa\
bMZfRWkWTo_QsaKdcEQd9BW8`N8yQ9wS9vUAuWAsYBr_BqaBpc\
ElfGihJejLbiIYiFTiCPhAKh7Gh4Bh27g96gF6gL6fR6fX6BNm\
EPjHQgJRdMSaOT_UPcZMgdIkiFonCrpCprCnsCluCjwChxCfnF\
ieHkXJmNMpEOr5Qtotfouiouk }
frm:DivideJulibrot {; draws 4-D slices of DivideBrot Julibrots
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),
aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001,
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)/(z^(-aa)+bb)+c
|z|< 1000000 }
END PARAMETER FILE=========================================
FOTD -- August 02, 2008 (Rating ?)
Fractal visionaries and enthusiasts:
NEW FORMULA ALERT!
Discard the formula that came with yesterday's FOTD, and
substitute today's formula. Yesterday's formula has a small
error, which I found soon after posting the FOTD.
While working with yesterday's formula, I noticed that I was
constantly getting two extra lobes on the elements. This is
because I had forgotten to subtract 2 from the number entered as
real(p5). This oversight explains why the elements in yester-
day's image had 7 lobes instead of 5. But today's formula,
which I am pretty sure is the final version, sets everything
right.
As an example, the value of real(p5) in today's formula is 5,
and the image is filled with five-sided elements, indicating
that all is once again well in fractal land.
Today's image is a Julia set of a small valley at the outer edge
of the third bud out the negative X-axis of its parent fractal,
which resembles a moth-eaten Mandelbrot set. I did not rate it
because I'm still not familiar with the potential of this latest
formula.
I named the image "The Mystic Star". Fractals are at least as
mysterious as anything traditional mystics have been telling us.
I wonder what a tiny rotation away from the Julia orientation
would do to today's image. Perhaps we'll find out in tomorrow's
FOTD.
The calculation time of 1-1/2 minutes may make the trip to the
FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
un-necessary. But the trip is lots of fun, so if running para-
meter files is not your glass of orange juice, don't hesitate to
dash out to the web site, where the finished image is posted for
instant viewing pleasure.
We certainly did not deserve the perfect weather that prevailed
here at Fractal Central on Friday. After all, it's supposed to
be midsummer, when we go around wiping away the perspiration or
hiding within our air-cooled cocoons. Today's blue skies, puffy
cumulus clouds, low humidity, and temperature of 86F 30C were
unexpected but fully welcomed by human and cats alike. With not
much work to do, this human worked on a fractal formula, while
the fractal cats worked on trying to get an extra treat.
The next FOTD will appear in 24 hours. Until then, take care,
and if the mysteries of mysticism are not mysterious enough,
look to modern science for some real mysteries.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
The_Mystic_Star { ; time=0:01:28.15-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideJulibrot passes=1
center-mag=0/0/3.963356/1/-90/0 params=90/90/90/90\
/-5.4262/0/0/0/5/4 float=y maxiter=1600 inside=0
logmap=11 symmetry=none periodicity=10
colors=000UGXUIXUKXUMXUOWUQWUSWUUWUWVUYVU`VUbVUdUU\
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Q`9R`9Sa8Sb8Tc8Uc8Vd7Ve7Wf7Xg7Yg6Yh6Zi6_j6_jB`hGaf\
LbeQccVdaZd`V`bRYdOUfKRgHNiDKk77tAHlCQeEZZJdnGgST`\
OdUKoNGpNHRorSelTWgUMbUDY }
frm:DivideJulibrot {; draws slices of DivideBrot Julibrots
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),
aa=real(p5)-2, bb=imag(p5)+0.00000000000000000001,
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)/(z^(-aa)+bb)+c
|z|< 1000000 }
END PARAMETER FILE=========================================
FOTD -- August 01, 2008 (Rating ?)
Fractal visionaries and enthusiasts:
NEW FORMULA ALERT!
Today's FOTD uses a new formula, which I wrote today. The
formula combines the DivideBrot routine with the Julibrot
routine to draw different slices of the curious DivideBrot
Mandeloids.
The new formula is number 6 of the SliceJulibrot series. I
wrote the formula to make it easier to work with both the Julia
and Mandelbrot aspects. I have not yet investigated the odd
slices, though they probably hold some interesting scenes.
Today's image has no parent fractal. It is the parent fractal.
The image is a Julia set of what remains of the Seahorse Valley
of the ruined large minibrot on the main stem of the correspond-
ing Mandelbrot set. To see the ruined minibrot in the Mandel-
brot aspect, simply change both the p1 and p2 parameters from
90,90 to 0,0.
At first glance, the image appears to have X-axis symmetry, but
a closer examination will reveal that it has no symmetry at all.
The imag(p3) parameter is extremely critical, with the slightest
change totally altering the image. I have not yet tried
different values of the remaining parameters, but I see much
potential for excitement.
The formula combines Z^2 and Z^5. From the way the image is
filled with 7-sided elements however, one would never guess it.
The calculation time of a very brief 25 seconds will cause no
one any pain.
Since I have no idea of the potential of the new formula, I
could give today's image no rating. The name "New Boy on the
Block" refers not only to the new formula, but also to the new
tomcat that lurked around FC for acouple minutes this afternoon.
The most convenient way to see the image is to visit the FOTD
web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
but before you will be able to work with the image, you will
need the new formula entered into one of your Fractint formula
files.
Thursday proved to be a thoroughly delightful day here at
Fractal Central, with blue skies, puffy cumulus clouds, lower
humidity, and a temperature of 86F 30C. The fractal cats
enjoyed the conditions, but became alarmed when they spotted an
unwelcome beat-up tomcat prowling in the yard next door. Just
as Nicholas reached full bristle however, the intruder moved on,
returning peace to the cat community.
My day was about average. The next FOTD will be posted in 24
hours, plus or minus a few. Until then, take care, and fractals
are not only good for the soul, they might be what the soul is
made of.
Jim Muth
jamth(a)mindspring.com
jimmuth(a)aol.com
START PARAMETER FILE=======================================
New_Boy_on_Block { ; time=0:00:25.12-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot6 center-mag=0.0187793/\
4.44089e-016/0.9861933 params=90/90/90/90/-14.1496\
5667/0.0052/0/0/5/8 float=y maxiter=1200 inside=255
logmap=3 symmetry=none periodicity=10
colors=000_MjeSekXajZcj_eiagibiicjfagd_ebYc`WaZU_X\
TYVRWTPTRNRPLPNKNKILIGJ133GEHECECACA9A878656434212\
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lIMlHMlGMlFMkHOjJQjLRiMTiOUhQWhRXgTZfV`fXaeYce_dda\
fdbgaYiZTkWPmTKoQFqNBsUHn }
frm:SliceJulibrot6 {; draws slices of DivideBrot
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),
aa=real(p5), bb=imag(p5)+0.00000000000000000001,
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)/(z^(-aa)+bb)+c
|z|< 1000000 }
END PARAMETER FILE=========================================
