FOTD -- February 23, 2005 (Rating 7) Fractal visionaries and enthusiasts: I enjoy finding well-defined fractal 'objects', such as the mathematical dead-ends for wandering points known as 'midgets' or sometimes 'atoms'. The assemblage illustrated in today's image might or might not be considered a fractal 'object', but it is an interesting collection of fractal things regardless, and it is invisibly filled with the true well-defined 'objects' known as midgets. I named the image "Seeing Triple". The name is an exaggeration of the more common phrase 'seeing double'. The name came about when I noticed that the image had left-right symmetry. Then I looked again and discovered that the opposites were reflections of reflections. They were identical. A third look revealed that the opposites are not reflections or rotations at all -- they are totally different, and no reflection or rotation can ever make them coincide. The parent fractal combines negative portions of Z^(-1.26) and Z^(-12.6). It is a variation of the parent which produced the series of FOTD images that ended about a week ago. The coloring features pastel tints inside the non-symmetrical objects, which contrasts with the intense deep blues of the surrounding environment. I am not sure the rating of 7 is totally earned, but the image does appear to be at least above the FOTD average. The render time of 7 minutes is within reason. If 7 minutes is not reasonable, the wait can be eliminated entirely by down- loading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The sun broke through in mid-afternoon Tuesday here at Fractal Central, but the temperature reached only 45F 7C, which was a bit too chilly for the paws of the fractal cats, who spent only 45 minutes outside. Their evening was improved however by a generous treat of tuna. Today is starting partly cloudy and colder. It looks rather bleak for the duo. For me the day looks normal -- at least so far. The next FOTD will appear in 24 hours. Until that magnificent moment arrives, take care, but have fun. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Seeing_Triple { ; time=0:07:11.71--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.91423665492388400/+0.003269872083774\ 09/171588.5/1.168/10.7/-2.30992197591817217e-009 params=-5/-1.26/-0.5/-12.6/0/625 float=y maxiter=5000 inside=0 logmap=129 periodicity=10 colors=000G0MG0SG0PG0TG1UG3UG4XG4XG7`GBaGCgGGgGJnH\ KpHOuJSvJKzKXzTWzXazbZzgezj`zjdzjeujdhjcojaKjaXlOJ\ lBvn0Xn0co0`q0Xq4UsBPsGMuMJwUGw`Cyg9yi7yhfyMzqBzj1\ yc0qY0l090060040030010300600900C00H00K00O01S01X03`\ 03c04g04h00h00h00h40hB0hG0cM0`S0XX0Ua0Og0Kl0Hq1Ew3\ 9z66z73zB0zCSg0Vh0Xj0`l1an4do9gqCjsGluJnwOqySszVwz\ YyzczzdzzdzzdwzdnzdgzdYzdSzdOzdOydOwdOudOsdPqdSodU\ ndVldVjdXjdXhdYhg`gh`gjadjaelccnfcodaokaqgaspauobu\ rczwdzuezzfzxgzzhzzizzjzzkzzlzzmzznzzozzpzzqzzrzzs\ zztyzuyzvwzwuzxuzywzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwz\ zwzzwzzwzzyzzyzzyzzyzzyzzyzzyzzyzzyzzyzzyzzyzzyzzy\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzusz\ qjzlczhXzcOz`HzV9zS3zM0zJ0zE0zB0z70zB0zE0zG0zJ0zK0\ zO0wS1uU4qX7oYBlaEhdGggJcjMalPYoUVsXUu`PycOzgKzjHz\ nGzw0Vw0Uw0Sw0Ow0Mw0Kw0Jw0Hw0Ew0Cw0Bw09w07S0oK06J0\ 7G09E0BB0C90E60G40H10J00K } 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=========================================