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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today is starting on an up note: there were less than 100 spam e-mails in my emailbox when I checked a while ago. But at the same time, there is a down note. I have not yet received that apology from the administrator, if one exists, of the fracprogrammers list that I am waiting for before I re-subscribe. No matter, there is no noticeable decrease in the number of letters I am receiving from the list. More ominously, I am starting to receive returned mail from the Fractint list that I never sent out. Since I have no sneaky viruses or worms in my system that could send out e-mail without my knowledge, and I never use the programs that get infected by these critters, we'll see where this 'returned mail' leads. Now on to the fractal for today. Today's image is named "Strawberry Fields" not because I like the music of the Beatles, which I rather do, but because the phrase simply came into my head while I studied the image in search of a name. I guess the pinkish terraces inspired the name. The parent fractal is a distorted Mandeloid with no East Valley, lying in the proper orientation, with X-axis symmetry. Unlike the classic M-set however, the parts of this Mandeloid are not connected, and it is surrounded by a cloud of tiny isolated midgets, every one of which, with the exception of its mirror image, is different. The formula subtracts Z^2 from lesser portions of Z^4, Z^6, and Z^8. This combination produces a fractal with three critical points, one of which is located at Z=0,0. The remaining two critical points, around Z=+-0.77, produce nearly but not exactly identical Mandeloids, which might hold some interesting scenes and might be worth investigation. The largest satellite midget of today's parent fractal is located on the negative X-axis. Curiously, this midget is rotated 180 degrees, so that its East Valley is on its west side. Today's scene is found near a larger midget in the interior of the north branch of the Seahorse Valley of the very large satellite midget. My standard rendering method, where the outside=iter, produces a fair enough image, but the outside=tdis option that I used does a little better. When rating the image, I felt a bit more satisfied with it than usual, and gave it a rating of a 6. The parameter file's render time of 14-1/2 minutes is slow. Downloading the completed image from one of the FOTD web sites is fast. Those sites are: Sunny skies, gentle breezes, low humidity, and a temperature of 79F 26C made the cats very happy again on Thursday. They spent the entire afternoon in the yard, romping and resting. In fact, they have been getting so much quality time in the yard this past week that they actually seem to be growing bored with it. Perhaps the rain that is forecast for later this afternoon and over the week-end will give them reason to appreciate days such as yesterday. As for me -- I must finish a pile of work before I can appreciate anything, so until next time, take care, and when life serves up a lemon, make lemonade and then blow your top. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Strawberry_Fields { ; time=0:14:35.73--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix3a function=ident passes=1
center-mag=-1.22979885859737000/+0.002659402810015\
19/2.341307e+010/1/-125/0.00485842217789580338
params=-1/2/0.5/4/0.25/6/0.125/8/0/0 float=y
maxiter=1500 inside=0 outside=tdis periodicity=10
colors=000Cgg8fk4fnAblF_jLXhQUfWQe`NcfKakH_pEZ_AUJ\
6P33LLEQaPVbOXbNZcN`cMbdMddLfeLheKjfJlfJngIpgIrhHt\
hHviGxiGzjJyjMxjPwjSvjVujYtj`tkcskfrkiqklpkookrnku\
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`VR_WV_X__Xceubdr`cpZbnYalW`jV_hTZfRYcQXaOW_NVYLUW\
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rBEdAMSAUFA`zbpvYgsT_oORlJJUG9CD0DI5DN9DSDDWID`MDe\
QDiUKoOQtIWyDQxHLxKGxNIyLJyKKzILzHMzGTwG_tGeqGlnGs\
kGyhGBMgGQaLUWQYQUaLHb7T`HdZRpY_oTaoOcoJenEgn9in4k\
dCnWJpNQsEXu5cwD`nLZfSWY_UQgRHnP9`bNNo_OUkO8vH6XB4\
7ABE9HL8OS7UZ6`e5fkLh_Hhc }
frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }
END 20.0 PAR-FORMULA FILE==================================
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