FOTD -- October 14, 2005 (Rating 6) Fractal visionaries and enthusiasts: Today's old long-unused formula is named "Test0622". It is so simple that it barely deserves being called a formula. It draws only the Mandelbrot set with a changeable parameter and function added to initial C. But as today's image shows, in the world of fractals, little initial changes can produce great final results. Despite its unlikely appearance, the segmented worm-like shape filling today's cropped image is the Mandelbrot set. The shape and proportions have been changed, but topologically the set is unchanged. Nothing has been added or taken away. It is the exponential function and parameter which have been applied to C that are responsible for the craziness. I'm not certain how, but when this function is applied to C, the effect is to enlarge the designated point to infinity, resulting in an image something like what one might see if he were actually in the world of the Mandelbrot set, standing at the point and looking at the scenery surrounding him. In today's image the point is in a remote valley on the northern shoreline of the main bay of the M-set. The main bay itself is the open area farthest to the right, where East Valley and the main negative stem are vaguely visible. The wide-screen effect does not mean something is wrong with your monitor. I have changed the proportions of the image to avoid repeating parts of the distorted M-set. A single outzoom will reveal that today's image is part of an infinite repeating series of identical images. In order for the image to render properly in the vicinity of the central point itself, the periodicity must be turned off. I have done this in the parameter file. The maxiter of 45000 would seem to be far beyond what is necessary for an image of the entire Mandelbrot set, but carefully check the left edge of the image. The maxiter there is barely adequate. Though most of the value of today's image is mathematical, it has enough artistic worth to rate a 6. The name "Mandel Variation-3" is a simple description. The render time of 9 minutes is reasonably fast, but the image may be seen much faster by downloading it from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A most unpleasant chilly drizzly day here at Fractal Central on Thursday made the Fractal Central cats most unhappy. Extra tuna in the evening made them less unhappy. Today is starting the same as yesterday, but without the drizzle. I expect little happiness to come the cats' way. My work is reasonably caught up, so I am neutral. The next FOTD will appear in 24 hours. Until then, take care, and look for the fractal lining. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Mandel_Variation-3 { ; time=0:09:15.85--SF5 on a P200 reset=2004 type=formula formulafile=jim.frm formulaname=Test0622 function=exp center-mag=-6.53\ 755/1.20746/0.2636167/0.6249/14.1598813307994735/\ -1.23373533611470521e-014 params=0/0/-0.2217009427\ 4/0.79843333763 float=y maxiter=45000 inside=0 logmap=yes periodicity=0 viewwindows=1/0.5/yes/0/0 colors=000IYTIZVJ_WK`YL`_Ma`NbbOccPdePefQfhRgjShkT\ imUjnVkpSkrUkqVjqWiqXhqYgqZeq_cqaaqb_qcZqdXqeWqfUq\ gTqhRqjPqkOqlMqmLqnJqoIqpGqrEqsDqtBquAqv8qw7qx5qz2\ sy3ry4qy5py6oy7ny8ny8my9lyAkxBjxCjxDixEhxEgxFfxGex\ HexIdxJcwJbwKawLawM`wN_wOZwPYwPYwQXwRWvSVvTUvUTvUT\ vVSvWRvXQvYPvZPv_Ou_Nu`MuaLubLucKudJudIueHufGugGth\ FtiEtjDtjCtkCtlBtmAtn9to8to8sn9rm9qm9pl9ol9nk9mj9l\ jAliAkiAjhAigAhgAgfAffBeeBeeBddBccBbcBabB`bC_aCZ`C\ Z`CY_CX_CWZCVZCUYDTXDSXDRWDRWDQVDPUDOUENTEMTELSEKR\ EKREJQEIQFHPFGPFFOFENFDNFDMFCMGBLGAKG9KG8JG7JG6IG3\ HH5IG6IG7IG8JGAJGBJFCJFDKFFKFGKFHKFILEKLELLEMLENME\ OMEQMDRMDSNDTNDVNDWNDXOCYOC_OC`OCaPCbPCdPBePBfQBgQ\ BhQBjQBkRAlRAmRAoRApSAqSArS9tT9uU9vV9wW9xX9yYAzZAz\ _Az`BzaBzbBzcCzdCzeCzfCzgDzhDziDzjEzkEzlEzmEzmFzmF\ zmFzmGzmGzmGzmGzmHzmHzmHzmIzmIzmIzmIzmJzmJzmJzmKzm\ KzmKzmKzmLzmLzmLzmMzmMzmM } frm:Test0622 { ; Jim Muth z=p1, c=fn1(pixel)+p2: z=sqr(z)+c |z| <16 } END PARAMETER FILE=========================================