############################################################## Jim, I enjoyed your 'hexic' fractal (below): [FOTD 01-06-05 (Hexa-Something [5])] but while zooming out until I could see the entire fractal I did not immediately see anything that had obvious three, four or five-fold symmetry along the way (though I'm afraid I was zooming out pretty rapidly):
Even more unexpected are the much smaller and near-perfect quadratic, cubic and quintic midgets scattered invisibly through the scene.
How does one view 'invisible' midgets? - Were you able to apply a certain rendering method to render them visible? - Or does 'invisible' in this context just mean that they are too small to be seen at the scale of the Hexa-Something fractal? Also, are you using the phrase 'quintic midget' to refer to: - a midget that has five lobes, - one that has five-fold symmetry around it (the way Hexa-Something has six-fold symmetry) or - one generated by an equation with a variable raised to the fifth power? - Hal Lane ######################### # hallane@earthlink.net <mailto:hallane@earthlink.net> # #########################
-----Original Message----- From: Jim Muth [mailto:jamth@mindspring.com] Sent: Wednesday, June 01, 2005 10:07 AM To: fractint@mailman.xmission.com Cc: philofractal@lists.fractalus.com Subject: [philofractal] FOTD 01-06-05 (Hexa-Something [5])
FOTD -- June 01, 2005 (Rating 5)
Fractal visionaries and enthusiasts:
We start June with an enigma of the fractal variety.
The thing at the center of today's image is a puzzle. It shows all signs of being a hexic object, if that's the proper name for equations of the 6th degree. But the parent fractal was created by a combination of Z^3 and Z^5. Its formula contains not a hint of Z^6. I guess that's how fractals are -- always doing the unexpected.
Even more unexpected are the much smaller and near-perfect quadratic, cubic and quintic midgets scattered invisibly through the scene. I will check further into this situation later today. When the suspected unexpected is found to exist, can the unsuspected unexpected be far behind.
All this talk of mysterious things does not make a great fractal however. Despite its mystery, today's image rates only an average 5. I named the image "Hexa-Something" because, despite the numerical confusion, there is something 6-ish about it.
The render time of 2-3/4 minutes is true on the 10-year-old computer with the balky fan, which I have dedicated to fractals. On a more modern unit, the image will render in less than a minute. But regardless of the speed of your computer, if you can get onto the internet, you can download the completed image from the FOTD web site at:
<http://home.att.net/~Paul.N.Lee/FotD/FotD.html>
With a high temperature of 77F 25C and full sun, Tuesday turned out to be one of the all time best days for the fractal cat duo. They went out before noon and stayed out until after 8pm. As far as I know, nothing disturbed their peaceful day in the holly thicket. Today is starting with a few more clouds and a bit cooler. After yesterday, the cats can't complain.
For me it's work before play. The next FOTD fractal will appear in 24 hours. Until then, take care, and do we place too little or too much faith in the scientific method?
Jim Muth jamth@mindspring.com jimmuth@aol.com
START PARAMETER FILE=======================================
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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 PARAMETER FILE========================================= ############################################################## -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.323 / Virus Database: 267.6.7 - Release Date: 6/10/05