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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is something entirely different. It is a slice, cut in a different direction, of the same abstract four-dimensional figure that gives us the well-known Mandelbrot set and the infinite variety of Julia sets. But it resembles neither the Mandelbrot set nor a Julia set. The orientation of the slice is very near but not exactly the Oblate direction. It has in fact been rotated 0.008 degree of arc toward the Julia direction. When one is exploring the Julibrot, a tiny rotation can sometimes make a big difference. If the 0.008 value of real(p1) is changed as much as one degree, the entire image will collapse into a mere horizontal line. The location of the center of the slice is near the tip of the negative stem of the M-set, but removed 1.3 units from the tip, along the real(z) axis. The image, which has been stretched horizontally by a factor of almost 1300, features both a hyperbola and a point of contact. Since I have many hyperbolae in my fractal collection, I named the image "Point of Contact". For some reason, the idea of today's image seems to exceed the quality of the image itself, and I could give it a rating of only a 4. But there can be no disappointment, for the render time is so fast that the image will be finished before disappointment can set in. Rendering may be dispensed with entirely by downloading the already-rendered image from the FOTD web site at: With a temperature that never rose above freezing and brisk winds from the north, Thursday was an indoor day for the fractal cats, who took their pleasure watching birds from the comfort of their window shelf. The usual treat of tuna kept them happy. Today is starting sunny and quite cold, but the wind has died and it is due to turn warmer this afternoon. The fractal cats should be more tolerant of these conditions. It looks like an average day coming up for me, which means do what needs to be done, then move on to fractal land. The next glorious fractal will appear in 24 hours. Until then, take care, and don't get scammed. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Point_of_Contact { ; time=0:00:20.76--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=multirot-XY-ZW-new function=ident/flip
center-mag=-1.29966327214381100/+0.000037418181458\
39/11605/1281.9 params=0.008/90/2/0/0/0/-2/0
passes=1 float=y maxiter=95 inside=0 outside=tdis
logmap=28 periodicity=10
colors=000D00E00F00G00H00I00J00K00L00M00N00O00P00Q\
40R20S10T4FU6FV8HWAIXCJYEKZGK_IK`LIaNHcPGdRKfTPfWU\
hZZhccghhfmmerrdwwczzhzzmzzmzzrzwwzrzzmzzhzzczzczz\
czzczzczzczzczzczzczzczzczzczzczzczzc000000000000J\
aXLcVNdTPeQRfOThMViJXjHZkFXlHVmITnJRoKPoLNpMMqOKrP\
IrQGsREtSCuTBuUFnZIgbM`gPUkTNpWGtVJrUMqTOpTRoSTnRW\
mQZlQ`kPcjOeiNhhNkgMmfLpeLrdKtjKvoJxtJyyLzuNzrOzoQ\
zkSzhTzeVzbXzZYzW_zTazQbzMdzJfzGgzD2Bj5Ei7Gh9IgCLg\
ENfGPeJSeLUdNWcQZcS`bUbaWda__YbVUeRQhMNkIJnDFq9Cp8\
Bp8Ao89o78o77n76n75n64m63m62m62aGgeKiiNjlQkpTmtWnw\
Zou_ns_nr`np`nn`nmankanjanhbnfbnecnccnacn`dnZdnYdn\
Zcm_bl`ak`aja`ib_hcZgcZfdYeeXdeXcbYa`Z_YZZW_XT_WR`\
UOaSMaRJbPHbOOWMUPK`JJfCHl6Gl9IlCKlFMlIOlLPlORlRTl\
UVlXXlZYfaQacJWeCRg5QcMQ_aQWqPVmOViNUeMUaLTYKTTJSP\
ISLHRHGRDFQ9EQ5DQ1FR3N9UN8XO7`O7cO6gO5jO5mP7lQ8lRA\
kSBkTDjUEjUGjVHiWJiXKhYMh }
frm:multirot-XY-ZW-new {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4:
z=z^(p2)+c,
|z| <= 36 }
END PARAMETER FILE=========================================
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times.
