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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's formula, DivideBrot4, is another new one -- the final version of the DivideBrot series. The only change from DivideBrot3 of the series is in the real(p1) parameter, where the number 2 is subtracted from the entered value before iteration begins. This change permits the order of the minibrots to be directly defined by the value entered as real(p1). The real(p2) parameter defines the escape radius. The imag(p2) parameter is not used. The imag(p1) parameter controls the prominence of the higher-order elements in the resulting fractal. A smaller value of imag(p1) results in a greater prominence of the higher-order elements. A larger value gives more prominence to the underlying order-2 Mandelbrot set, while at the same time enlarging the size of the fractal, which makes the real(p2) parameter necessary to expand the bailout radius so that the entire fractal fits within it. Today's image is named "No Fault Lines". I gave it this name because the central minibrot is of the order 3.5 and such fractional-order minibrots are always surrounded by discontinuities, which spoil the surrounding patterns of the minibrots. Today's minibrot however is a horse of a different color. Its surrounding pattern consists of seven elements, and these elements are intact. Seven, of course, equals two times 3.5, the order of the minibrot. The name refers to the lack of discontinuities. The image is located on the west side of the northern branch of the Seahorse Valley of the oversized Mandelbrot set that is its parent fractal. The Seahorse Valley characteristics are very prominent throughout the image. The order-3.5 characteristics are obvious only in the shape of the minibrot. I rated the image at a 7. It consists of too much mathematics and not enough artistic value for a higher value. Rendering the scene with the outside set to 'tdis' helped a little, but not enough to grant the image a rating of 8. With its calculation time of 1-3/4 minutes, the job of running the included parameter file should offend no one. But in this modern day and age, some computers have forgotten the old ways and don't know what to do with DOS programs such as Fractint. Those with such new-fangled instruments may still see the image however by going to the FOTD web site at: Warm temperatures, high humidity and showers prevailed here at Fractal Central on Friday. The fractal cats dislike a temperature of 86F 30C, so they were not too happy with the conditions. But cats are cats, and before long the feline duo had found a cooler place in which to sleep. My day was kept busy by a customer of the worst kind -- one who needs his job at once, but doesn't know what he wants, and as a result, keeps calling in changes. In the end, common sense won out. I refused to answer the phone after the fifth call. The last I heard, he was satisfied. The next FOTD fractal will be posted in 24 hours. Until then, take care, and look up. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
No_Fault_Lines { ; time=0:01:44.21-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=DivideBrot4 passes=1 float=y logmap=110
center-mag=-7.662916327120194/+1.181354355289796/3\
.256997e+007/1/-98.25/0 maxiter=5000 periodicity=10
params=3.5/10/1000/0 inside=0 outside=tdis
colors=000JP3UgDP0DK99FH65zX7mN9`DhsH_kDRcAIW6NwsH\
rbFjUDcLBWCW8Nor4ah3OZ331vtV3My`IlPE`EnHocJbULRKNF\
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BXcCAlT4LYWNbwPPfECR4rEPWKE47X6CP7GI9LAOQJHPBveti`\
fYXUMTG4iC6c97Z79U52LPKFtFKU`wQUnKNeEGX8SYENVBJT8E\
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CTHDf6BY4eWPYUJQSEIQ8DMICNEBOAAP6oa7aX5OT4QaEIV8JT\
`GRPDQEh3LXBFLI9MaJGVBBp4Ai3Ab3AW3S4p9TLASGARCAQ7t\
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XpTLbG7sCcfBWa9PY7HT5p5naCZOJJdbQPWEK6yHBjFGWCLHQM\
4IO3H42FA3DF3BK3O3HJBCEI7Z4JMhz8csDYmCVfBRG6EX8KIt\
LDhI9PL6XCTPHKHLBBMvANhAOVAPHKeFBadAXSATFERCCQ7AI5\
Ac4Ac4Ac34cR6mJ8mBOmr4m36m3zz3zzuzzgzzUzzGzzRzzFzz\
jzzWzzHzzezzWzzMzzCzz2zz3 }
frm:DivideBrot4 { ; Jim Muth
z=0, c=pixel, a=real(p1)-2,
b=imag(p1), d=real(p2)+100:
z=sqr(z)/(z^(-a)+b)+c
|z| < d }
END PARAMETER FILE=========================================
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times.
