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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Quite a while back, I received an e-mail from a forgotten someone who asked me why I so often end my FOTD discussions with such silly questions. Maybe it is because I am such a silly person. After all, why would any sensible person devote as much time and energy as I do to such a fruitless endeavor? But as for the questions, they are not supposed to be answered. They are merely philosophical thoughts in the guise of questions. Today's closing question for example asks about Julia sets on the head of a pin. It cannot possibly be answered because fractals are abstractions with no definite size. Anyone who tried to answer it would soon find themselves thinking about the true size of a fractal and would realize that a fractal is not the same kind of thing as a speck of dust or a planet. Today's image is a fractal. This much is certain. Yesterday's image was a Julia set of the south branch of Seahorse Valley of the Z^(2.01)+C Mandeloid as it appears 17 turns up the logarithmic spiral. Today's image is a Julia set of the north branch of the same valley. But don't assume it is a repeat. The corresponding Mandeloid has no X-axis symmetry, and this makes today's image quite different. Yesterday's image consisted mostly of 'inside' stuff made active by the 'zmag' inside fill. Today's image shows a Julia set that consists totally of 'outside' stuff, quite a bit different from both yesterday's image and what would be expected in a conventional Julia set of Seahorse Valley of the familiar M-set. I named the image "A Julia Set for All-2". It is the second and maybe not the last in the series of similar Julia sets. The rating of a 5 indicates that I consider the image to be of average quality. The render time of 1-plus minutes assures that not too much time will be wasted if the image proves to be unsatisfactory. The finished product is available on the FOTD web site at: The partly cloudy skies and 52F 11C temperatures here at Fractal Central on Friday did not keep the cats from enjoying their usual time in the yard. The lack of wind made it easy for them to hear approaching danger. Today is starting cold, but it is sunny and the wind is calm. When it warms up this afternoon, the cats will have a good time. My day looks peaceful also. Until the next FOTD appears in 24 hours, take care, and how many Julia sets could fit on the head of a pin? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
AJuliaSetForAll-2 { ; time=0:01:16.95--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=JuliaBC passes=1
center-mag=0/0/0.9861933/1/-17.5/3.88578058619e-016
params=2.01/0/17/0/-0.7496/0.2947/0/0 float=y
maxiter=1000 inside=255 periodicity=10
colors=000A0PA0PA0PA0PA0PA0PA0PA0PA0O90N90N80O80O7\
0P70P60Q60Q50R50R80QB0QE0QH0PK0PM0PPLQWNVbP_hQdoSi\
uTnsTkrThqTepTboT_nTXmTUkTRjTOiTLhTIgTFfTCeTAWY_Mb\
ywQduScsTcqUboVbmWalXajYahZ`f_`d`_cb_acZ`dZ_eZZfYZ\
gY_hX`iXajWbkWckWdiUefTdcRc`QaYP_WNYTMUQLQOJOMINMH\
MOHMRHOVHTZHYbHcfHhjHnnHsrHxvHusIsqJpnKnlKkjLigMge\
NdcNb`O_ZPYWQVUQTSRRPSONTMLTJIUHGVFEVEGXEIYEKZDM`D\
OaDPbCRcCTeCVfBXgBYhB_jAakAclAen9go9hp9jq8ls8nt8pu\
8qvCrqGsmJshNtdRt`UuWYuSavOdvJhwFkwBltDlqFlnGlkIli\
JlfLlcMl`OlZPmWRmTTmQUmNWmLXmIZmF_mCamAbfDa`GaVI`O\
L`IO_CQ_DRYDSXETVEUUEVSFWRFXPGYOGZMG_LH`JHaIIbGIcF\
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gJYdF_aCaZ8cW4eT1gR8iSEjTLlTRmUYoVcpVdoUemSflRgjQh\
iOigNjfMfgLcgK`gJYgIVhHShGOhGLhFIiEFiDCiC9iB6iB8jD\
9jFAjHBjJCjLDjNFjPGjRHjTIkUJkWKkYMk_NkaOkcPkeQkgRk\
iSkjlJeoHdqFcsDbuCbpHcQLR }
frm:JuliaBC { ; Formula by Andrew Coppin
e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)),
r=real(p2)-q, C=p3, Z=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < p4+100 }
END PARAMETER FILE=========================================
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times.
