FOTD -- December 20, 2004 (Rating 5) Fractal visionaries and enthusiasts: For today's fractal we break out the MandelbrotBC2 formula, which takes advantage of the multi-valued nature of the complex 'log' function, and gets an infinity of fractals from formulas that would seem limited to only one. The additional fractals are especially interesting when the exponent of Z is set to a value between 1 and 2. Today's image uses a value of 1.1 -- a value in the lower part of that range, where the images explode in size as we travel up the logarithmic spiral and the changes are the greatest. The parent fractal is an oversized thing resembling a dead bird lying on its back, with its pointed bill facing upward. Today's scene is located in the valley that forms the lower edge of the bird's bill. Not wanting to make allusions to a dead bird in the name of the image, I decided to name it "Fractal Flight". The question of whether fractals can fly is moot. Fractals are abstractions, and abstractions can do anything we wish them to, though usually they do nothing. In today's image I saw a flight of fractal somethings taking off into a blue sky and vanishing beyond the upper left corner of the frame. Perhaps they have been frightened by approaching danger. (It is hard to imagine how a fractal could come to harm however.) The 'objects' (if that's what they are) share a curious similar- ity. In some ways they are alike; in other ways, each has a character of its own. Even the larger groups of objects share this partial similarity. The image is a true fractal. In it, the same pattern is repeated again and again at the deeper levels. Of course, the deeper we explore, the slower the calcu- lation becomes. With nothing really exceptional to raise its rating, the scene could be rated no higher than an average 5. Its render time of almost 23 minutes gives it an overall worth of only 22. It is still an interesting image to see however, and well worth the small effort of downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Heavy clouds, a chilly temperature of 36F 2C, and a cold rain kept the duo indoors for the entire day on Sunday. Their moods were surprisingly good considering their confinement. As night fell, the rain changed to snow, which soon froze solid, making for tricky walking and worse driving. When the duo saw the bad conditions, they actually seemed glad to be indoors, where a generous serving of tuna was available to assure their content- ment. This morning is starting sunny, but with a temperature of only +7F -14C and a wind of 20mph 30kph, I doubt that the duo will want to go outside. The work is still heavy in my department, but I hope to squeeze in a fractal or two before the day ends. The best of what I find will appear as tomorrow's FOTD. Until then, take care, and keep your cool when the snow falls. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Fractal_Flight { ; time=0:22:55.83--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=+0.77134655541610010/+0.189518755374709\ 60/3732.587/1/-12.5/-1.07880579469643578e-011 params=1.1/0/23.8/0 float=y maxiter=3000 inside=255 logmap=304 periodicity=10 colors=000HHUJIULJTNKSPLRSMRVOQXPPZQO`RNbSNdTMfULh\ VKjWKlXJoYIrZHs_Fr_Hp_Jn_Kl_Mi_Og_Pd_Rb_SZ_UX_WV_X\ T_ZQ_`O_aM_cK_dL`eL`eM`eM`fN`fN`fN`gOagOagPahPahPa\ hQahQaiRaiRbiRbjSbjSbjTbkTbkUbkUblUclVclVclWcmWcmW\ cmXcnXcnYdnYdoYdoZdoZdp_dp_dp_dp_dp`ep`fp`gq`gqahq\ aiqajrajrakrblrbmsbmsbnsboscpscptcqtcrtdstdsudtudu\ udvuevvewvexveyveyvfurfqofmmfmmgmmgmmgmmgmmhmmhmmh\ mmhmmhmmgmmfmmfmmemmemmdmmdmmcmmbmmbmmammamm`mm`mm\ _mmZmmZmmYmmYmmXmmXomWqmWrmXqmYqmZqmZqm_qm`pm`pmap\ mbpmbpmcomdomeomeomfomgnmgnmhnminminmjmmkmmlmmlmmm\ mmnlmnlmolmplmplmokmnkmnkmmkmmkmlkmlkmkkmkkojkpikq\ ikrhkshktgjugjvfjzfjxejydjzdjzcjzckzblzbmzanzaoz`p\ z`qz_rzZszZtzNuzNuzNuzOuzOuzOuzOuzPuzPuzPuzQuzQuzQ\ uzRuzRuzRuzSwzRvzRuzRtzRszRszQrzQqzQpzQpzQozPnzPmz\ PmzPmzPmzOmzOmzQmzOmzLmzJmzHmzFmzDmzAmz8mz6mz4mz2m\ z0mz3mz5mz7mz9mzBmzDmzFmz } 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=========================================