May 31, 2012: Fractal in the Sea | May 30 | June 1 | 2011 | FOTD Home |
Fractal visionaries and enthusiasts:
Today's
image rates
a 9.75, which is one of the highest FOTD ratings of all time.
At
least 2.75 points are a bonus for the coloring effort.
Without
the colors the image would have rated no more than an everyday
7.
I granted myself the unusually large bonus for the very convincing
effect of a fractal object floating on the surface of a serene
lake. (Actually, the program created the basic
palette. I
merely tweaked it.)
Yes, I know there are formulas that apply this lake effect to fractals,
but today's image achieves the watery effect using nothing more than
the natural numbers. The scene is appropriate -- Seahorse
Valley
area of the Z^2+C Julibrot. In today's image the valley is
viewed
from an angle about halfway between the Oblate and Rectangular
directions.
The reason for the name "Fractal in the Sea" will become apparent as
soon as the <enter> key is struck and the image, which is
a very
fast one, begins building on the screen.
FOTD old-timers with sharp memories may remember a virtually identical
image from several years ago. That image was created with a
different formula however, and suffers from too much periodicity
checking. Today's version retains the old colors but shows
the
total image with nothing left out.
Though the image finishes in a mere one minute, it is still necessary
to contend with the nuisance of setting up and running the parameter
file. All such nuisances may be escaped however by visiting
the
FOTD web sites.
Drier air and crystal blue Kodachrome skies dotted with puffy cumulus
clouds made today a prize winner here at Fractal Central.
Since
Kodachrome film is now a thing of the past, it might be better to
describe the sky as digital blue, but somehow it just doesn't sound the
same. One thing that never changes however is the way
temperature
feels, whether it's measured in Fahrenheit or Celsius, and the high of
79F 26C fell right in the middle of the comfort range.
The fractal cats were far too interested in their new cube complex to
concern themselves with the outside weather. They enjoyed
exploring the cube maze so much that they raised their tails in eager
anticipation and dragged the very light cubes out of
alignment.
Perhaps we humans need to add some weight on the bottoms of the cubes
to anchor them in place. But we don't want to make the cube
bottoms too lumpy for the cats to curl up and sleep in.
The next FOTD, much drier than today's watery image, will be posted
before long. Until then, take care, and I hear that the end
of
the world scheduled for this coming December 21 has been
cancelled. I was looking forward to it with abated breath.
Jim Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
Fractal_in_the_Sea { ; time=0:01:00.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 center-mag=-0.0518924/0\
/2.548364/0.9081/90/0 params=40/90/0/90/-0.75/0/0/\
0/2/0 float=y maxiter=100000 inside=255
logmap=yes periodicity=0
colors=000Q0hR2iS5jT8kUPnVSmWTnXVoYXpZZq_`r`bsadtb\
fuchvejwfkwglxfkzekwdjvciubhtagrafq`ep_doZcnYbmXak\
X`jW_iVZhUZgUYgTXfSWdRVcRUbQTaPS`OR_NQYMPXMPWLOVKN\
UJMSILRHKQGJPGIOFHNEGLDFKCEJBDIBCHABG9AE89D78C67B5\
6A55944733622511400300600810A30A509709908B07D07F06\
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3102002002002001001001001000000000z0Qn0mm0ml0mk0mj\
0mi0mg0Mf0Le0Kd0Kc0Jb0Ja0I_0IZ0HY0GX0GW0FV0FT0ES0E\
R0DQ0DP0CO0BN0BL0AK0AJ09I09H08G07E07D06C06B05A0590\
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LOEKNDJLCHKCGIBFHAEF9CE8BC7AB68A678567455334222111\
0ENuDMsDLrL4dL4dL3eL3eaKa }
frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=z^(real(p5))+c
|z|< esc }
END PARAMETER FILE=========================================