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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image is a brief diversion from the world of MandelbrotMix4 into the world of exponent sub-2 fractals. In today's image, the iterated exponent of Z is 1.5874, which is the 1-1/2 root of 2. The entire formula, Z^1.5874+C is about as simple a fractal formula as possible. In the world of sub-2 powers of Z, the midgets become fewer and farther between, and much more difficult to find. But when one of these elusive midgets is found, it is always worth a closer look, for there appears to be no limit to the shape they may take. I named the image "1.5 Root of Two" for obvious reasons. I rated it a 5 for equally obvious reasons. The 16 minute render time of the parameter file may be avoided by giving Paul and Scott a chance to post the GIF image to their web sites, and then by downloading it from there. Paul's site may be found at: The fractal weather here today was a great improvement from yesterday's tornado. The partly cloudy skies and temperature of 68F 20C made the fractal cats so happy that they slept in their porch chairs most of the afternoon. Cats sleep when they are happy; people jump around and shout. I'll resume telling my thoughts about precognition in tomorrow's FOTD. All I can say at this time is that a world of difference exists between *believing* that the future can be seen and *knowing* that it can. There is no longer a need for me to discuss whether precognition exists. Because it cannot be scientifically demonstrated, some will always doubt that it exists, but precognition *does* exist, and for me the question of its existence has been fully answered. From now on I will concern myself with how it might work. It's now time to get busy and do the everyday things that need to be done. Once the things are done, I'll return with the next fractal. Until then, take care, and meditate on fractals while staring at your navel. They are very enlightening, even if the navel isn't much to look at. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
1-5_Root_of_Two { ; time=0:16:06.31--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=floor passes=1
center-mag=+0.12755286358762810/+0.806988822573071\
70/2.291871e+009 params=1.5874/0/-2.6/0 float=y
maxiter=2000 inside=0 logmap=505
colors=000000A07C07D09F0AG0CI0DJ0FL0IM0JO0LO0OO0QO\
0TO0VO0XO0XO0YO0_O0`O0`O0aO0cO0dL0cO0dQ0fT0fV1gY3g\
`6ic7jdAjgCljFlmGmoJmrLouOpxPpySrzTrzXszYsz_sz`sza\
szaszcszdszfszfsygsyisxjsxjsvlsvmsuosuosupssrssssr\
ssruspvspxsoxsoysmzsmzslzslzsjzsjzsjzsjzscyuVrxOiy\
Faz3Sz7VzAYzF_zIazMdzPfzTizXjz`mzcpzgrzjuzovzryzvz\
zyzzzzzzzzzzzzzzzzzxzzuzyryypxymvxjuxgsxdrvapv`ovY\
mvVluSjuPiuMgsLfsIdsFcrCar9`r7_r7_r9Xl9Tg9Qa9OY9LT\
AIOAFJACDA99930A61A74C97CAADCDDDGFFJFGMFIOGJQGLTIM\
XIP_JQaJSdLTgLViLXlMYoM_rO`uOaxPczPdzSazPfzOjzMoyL\
rvJvuIzrGzoFzlDziCzgFziGzjIzlLzmMzoOzpQzrSzsTzuXzv\
Yzx_zxazyczzdzzgzzizzjzzmzzozzpzzszzuzzvzzoxzipyag\
rTdjMfcFgXCiPFjIIlALm1Oo3Qp4Tr6Xs7_u9avAdxCgyDjzFm\
zGpzIszJvzLyzMzzOzzLzzOzzPzzQzzSzzTzzVzzXzz_zz`zza\
zzczzdzzfzzgzzSzzizzgzzfzzfzzdzzdzzczzczzyzzyzzyzz\
yzzxzzvzzuzzzzzyzzszzmzOg
}
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(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 20.0 PAR-FORMULA FILE==================================
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times.
