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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: According to certain traditions, man's present civilization, which began around 8,000 years ago, is not the first. These traditions tell of an earlier, now lost civilization, known as Atlantis, and of an even earlier civilization, known as Lemuria. There are also a few tales of a third lost civilization -- the earliest of all -- Hybornea. At this time, I'll not state my opinion about the existence of these civilizations. (At least not until my next outburst of Philosophy.) But even if the legends have absolutely no basis in fact, their mere existence and persistence in the face of absolutely no physical evidence is fascinating. Also fascinating, and equally unlikely, is today's fractal image, which I have named "Hybornean Minibrot", after the third and least likely of the lost civilizations. I gave it this name because the chance of today's particular fractal scene ever becoming a FOTD was virtually zero, yet here it is. The formula that was iterated to create the image is 0.5(Z^(-0.75))+0.05(Z^(-7.5))+(1/C), a rather unwieldy expression that nevertheless creates an interesting fractal consisting of the usual Mandeloid, facing east, with the usual extra bays, buds, valleys and filaments. Today's scene lies near a node of a chaotic area extending from the southeast shoreline of the main bud. The rating of an above-average 7 is well earned. With a render time of slightly under 8 minutes, the parameter file is the slow way to see the image. A faster way is to download the image from: The fractal weather today at Fractal Central was totally uneventful, with some sun, some clouds, moderate humidity and a temperature of 84F (29C). The cats, who enjoy uneventful weather, had a very uneventful and happy day. My day will be happy when I finish the work that lies before me. It will be happier when I find the fractal that will appear as tomorrow's FOTD, but the happiest day of all will be when my philosophical muse once again appears. Until tomorrow, take care, be skeptical of credulity, but remain credulous and curious. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Hybornean_Minibrot { ; time=0:07:46.15--SF5 on a P200
reset=2001 type=formula formulafile=allinone.frm
formulaname=MandelbrotMix4 function=recip passes=1
center-mag=+3.570095649530768/+0.14560619319789/5.\
826806e+010/1/-72.606/0.091 params=0.5/-0.75/0.05/\
-7.5/0/800 float=y maxiter=1450 inside=0 logmap=155
colors=0000ER0DP0CN0AK09I08G07D06A0580360230210521\
723926C28E2AH2DJ2GL2IO2KQ2NT2PV2RU2TT2PP7NOCJKHHKK\
E2IC8HAEG8JE7PD5VC3`AAe9Ak8Kq7Kv6Uw8Ux9cyAczCmzEmz\
GwzHwzIhzJhzPUwVUs`Zqfcmlhjrmfxrdzucyvcuxcqyalzagz\
adz__yYWwVTvTOsQKrOHpLCoJ8lH5kG1pEAuDKyDTrHWlJZfL`\
`OdVQfOThIVkCYo6_q0as0dv0gu2ju6luAouEquIsuNvuQxuUz\
uVxsWvrWsqYqpYooZlm_jl_gk`ej`cha`ga_g_aeZcdYdcWf`V\
g_ThZRjYQlVPmUOoTLpRKrPJsOIuNHvLJsPKqTLoVOmZPk`Qhd\
TggUejVcmWap`fmeklhojmshrxfvzeuzgszhrzjqzlqzmpzooz\
pmzrlzslzukzvjzxhzygzzgzzaxuWsoRogLhaHdVA_P6VJ8UI9\
TIATHDRHEQGGQGIPEJPEKODNNDONCPLCRKATKAWNKZQNbTQeWT\
gZWjaZlbaoYZqROsKIvECx76y11zG9zTIzeQycRvaRq`Rm_Tj`\
TeaTacTZdUUeUQfUNgVIhVEjVAkVClVCmVCoVCpVDqVDrVDsVD\
uVDvVEwVExVEyVEzVEzVHzaJzgLzmOzuQzzTzzLzyEzsHzmIzh\
JzcKzZNzTOzOPzUQzZRzcYzhazpYzjUzdQz_NzUJzPGzJCzEAz\
DAzDAzD9zD9zD9zD8zD8zD8zD
}
frm:MandelbrotMix4 {; Jim Muth
a=real(p1), b=imag(p1), d=real(p2), f=imag(p2),
g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j,
k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel):
z=k*((a*(z^b))+(d*(z^f)))+c,
|z| < l
}
END 20.0 PAR-FORMULA FILE==================================
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times.
