; Date: Fri, 14 Oct 2005 12:15:21 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 14-10-05 (Mandel Variation-3 [6]) ; Id: <1.5.4.16.20051014121640.38df938c@pop.mindspring.com> ; --------- ; ; 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: ; ; ; ; 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========================================= ; ;