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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Yesterday's image took us on a trip to four-dimensional hyperspace, where we saw East Valley as it has never been seen before. Today's image takes us to Seahorse Valley hyperspace for an equally odd view of things. To start, I must apologize. I realize that the image holds little artistic value, which explains the abysmal rating of a 3, but it does have a modicum of mathematical value, and it calculates fast as lightning, in a mere 10 seconds, which makes it a better value than yesterday's image. I named the image, "This is a Seahorse" -- a self-explanatory title. It is indeed a seahorse, or at least part of one, though I doubt that a biological seahorse could ever be sliced to give such a section. And there are also many small near-perfect seahorses scattered throughout the scene. Yes, the past two images do indicate that I am feeling a spate of writing about the fourth dimension coming on. To me, the fourth dimension is one of the most tantalizing mysteries, one that I never grow tired of pondering. But for now, the best way of ending today's discussion is to remind the FOTD readers, wherever they may be, that today's completed GIF image is available for instant viewing on the FOTD web site at: With a temperature of 95F 35C, and lots of haze and humidity, Tuesday was far too muggy for comfort here at Fractal Central. It was a good day to stay indoors and work in air-conditioned comfort, which is pretty much what I did. The fractal cats did the same, except when they started worrying me for their evening treats. Luckily, Fractal Lady served the treats, while I was lost in hyperspace. The next FOTD, probably another low-rated trip to Julibrot hyperspace, will appear here in 24 hours. Until then, take care, and why are we ourselves? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
This_is_a_Seahorse { ; time=0:00:10.28-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2a passes=1 periodicity=10
center-mag=-0.00786577872582554/+0.029190503024156\
81/340.4706/0.05931/79.6471443563626167/-55.931342\
8683244211 params=90/23/-2/36/-0.744416/-0.121192/\
-0.744416/-0.129912/0/0 float=y inside=0 logmap=24
maxiter=2500
colors=0003lw5mw9nwDowGpwKqwNrwRswUtwYuw`vwdwwgxvi\
vujutktsmrrnqqoppqnormnslnpjmmiljhkggjdfiaeh_dhXcg\
UbfRaeO`dL_cIZbGYbKXaOW`RV_VU_ZV`XUaVTbTScRRdPQeNP\
dLNZLMVKKPKHKJGLKFMKEMKFOLHQLKSKMUKOVKRXJTZJW`JYbO\
XgJ_cFYcBWc7Wc7V`7PW7IK4KK7KKAKKCKKFKKIKJKKMNKUPK_\
SKcVKdaKcgKblKbpLarS`tY_wcZzhYznWzqRaoKVlEPmGOmLNm\
PMmTMmXLm`KmeJmiJmmImqHmuEnzHlyJjyMhxOgxRexTcwVbwY\
`w_ZvbXvdWvfUuiSukRunPtpNtrMtoLrmLpkKnhKmfJkdJiaIg\
_IfYIdVHbTH`RG_OGYMFWKFUIFTCOZ7Xd1fh2di3bj3`k4Zk5X\
l5Vm6Tn7Rn7Po8Np8Lq9JqAHrAFsBDtCBtC9uD7vD6vC9nBBfA\
D_9GS8IK8KD9II9GM9EQACUABYA9aB7eB5i82nB4mE5mH6lK7l\
N8lQAkTBkWCkZDjaEjdGigHijIimJhpKhwGerLhmQkiVmhUkhU\
jhTihTggSfgSegRcgRbgRafQ_fQZfPYfPXeOVeOUeOTeNReNQd\
MPdMNdLMdLLeMMdLKcKJbKIaJG`JF_IEZICYHBXHAZGD_GG`GI\
aGLcGNdGQeGSfGVhFXiF_jFakFdmFfnFioFkpFntBvqFpoJjmN\
dkR_iVUgZOebIagEOWwMXwKYw }
frm:SliceJulibrot2a {; 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| <= real(p5+9) }
END PARAMETER FILE=========================================
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times.
