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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: The Z^1.5+C Mandeloid always has been one of my favorites. (The Mandelbrot set holds top spot.) The Z^1.5+C is the most changeable of the Mandeloids with an exponent of Z between 1 and 2. Today we examine this fractal as it appears at ground level of the complex-logarithmic ladder. In my opinion, at this level the Z^1.5+C Mandeloid resembles a midget racing car. At other levels it appears totally different. Today's scene is located in the driver's shoulder, on the northeast side of the fractal. When rendered in the normal manner, with the inside set to 0 and the outside set to 'iter', today's image is rather lifeless. To add a bit of excitement, I rendered it with the outside set to 'fmod', which produces the star-like effect. The curves and cusps that fill the image remind me of the pattern that is seen around street lights when one looks through a rain droplet on a window at night. This pattern inspired the name "Window Droplets". The rating of a 6 seems appropriate for today's image. Far better images will be needed before we can reach the ratings of 8 or 9. With a render time of just under 16 minutes, today's image is a bit slow. But relief for impatience is available on the FOTD web site at: The near perfect weather went unappreciated here at New Fractal Central on Sunday. The new fractal cats were more concerned with chasing each other up and down the long hallway and exploring the nooks and crannies of the basement. From what I hear from Old Fractal Central, the ex-fractal cats are spending their days sleeping, hanging out in the holly patch, and receiving treats of tuna as they always did when their home was known as Fractal Central. My day was slightly busy -- just the way I like it. The next FOTD will appear in 24 hours. Until then, take care, and watch for the strange and unexplained events. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Window_Droplets { ; time=0:15:52.47--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC2 passes=1
center-mag=+0.66433854815324980/+0.662251585236201\
20/178817.2/1/12.5/-1.06402237715075287e-009
params=1.5/0/0/0 float=y maxiter=16000 inside=0
outside=fmod periodicity=10
colors=000797989B7BD6DF5FI4HL9FPEDUIBZNAaR8dW6g`5j\
d3mi1om0glA`lKTlTMlbIriFlkCgl9an6Xo3Rq0Kr1Mr1Or2Qr\
2Rr2Tr3Vr3Wr4Yr4_r4`r5br5dr6fr6gr6ir7kr7lr8nr8pr9s\
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Mj7Ki7Ii7Gh7EhADgCDgEDfGDfJDfLDeNDePDeSCdUCdWCdYCc\
`CcbCcdCbfCbiAchCbgEbfGaeIadKacM`bO`aQ`aS_`U__W_ZY\
ZY_ZXaZWcYVeYVgYP`TNaSMaSKaSJaSIaRGaRFaREbRCbRBbQA\
bQ8bQ7bQ5aP6bQ6cQ6dQ6eQ6eQ6fR6gR6hR6hR6iR6jS6kS6kS\
6lS6mS6nT6nT6oT6pT6qT6qT9oSCnRFmQIlPLjOOiNQhMTgLWe\
KZdJacIdbHo`8faGZaORbWJbcBck0et3cs5bs7`r9_rBZqDXqF\
WpHVpJTpLSoNQoPPnROnTMmVLmWHoXKmYMlZOk_Rj`ThaVgbYf\
c_ecadddbefafh`gk_hmYioXjrWktVmxTkvUjuVitWgsXfqYep\
Zdo_bn`ala`kbZjcYidXgeWffUegTdhSbkQajP`kO_lNZlMXmM\
WhMVeLUaKT_JSXIRVHQSGOQFNNEMLDLICKGCJDCIBCH8DH5CG6\
CG6CF6CF7CE7BE7BD8BD8BC8BC9BB9AB9AA9AAAA9AA9AA8B98\
B97B97C96C96C96C2D14B35A5 }
frm:MandelbrotBC2 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*floor(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END PARAMETER FILE=========================================
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times.
