; Date: Thu, 14 Sep 2006 22:32:53 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 15-09-06 (A Whatsit Midget [6]) ; Id: <1.5.4.16.20060914223355.0de749da@pop.mindspring.com> ; --------- ; ; FOTD -- September 15, 2006 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Today's image shows a most curious fractal hole. But it most ; certainly is not a Mandelbrot midget. And it certainly is not a ; Julia set, though it does have some Julia characteristics. Nor ; is it an Elliptic set, a Rectangular set, a Parabolic set, or an ; Oblate set. It is actually a set in a slice oriented about half ; way between the Parabolic and Elliptic directions. ; ; As the value of the center point of today's image indicates, the ; scene is located in the vicinity of the large midget located at ; -1.75 of the Mandelbrot set. Since we are exploring 4-D space ; when we examine the Julibrot, it is impossible to describe the ; exact direction from the -1.75 midget in which today's scene ; lies. ; ; The thin straight yellow line at the edge of the solid inner ; area is actually one of the Mandelbrot valleys of the large ; -1.75 midget sliced from the side. It seems counter-intuitive ; that, from the side, a Mandelbrot valley should appear as a ; straight line, but the Mandelbrot aspect of the Julibrot is ; actually shaped like a nest of 4-D hypercylinders, which, like ; 3-D cylinders, appear straight when sliced parallel to their ; length. ; ; I named today's image "A Whatsit Midget" because I have no idea ; what else I might name it. The rating of a 6 seems about right ; for an image that is more a mathematical curiosity than an ; artistic triumph. The render time of a little over 1/2 minute ; should make the task of rendering almost enjoyable. And the job ; of rendering may be eliminated entirely by viewing the finished ; image on the FOTD web site at: ; ; ; ; Heavy clouds, fog on the hills, occasional rain, and a tempera- ; ture of only 63F 17C made conditions far less than ideal here at ; New Fractal Central on Thursday. But the fractal cats, who can ; look outside but are not permitted to go there, do not concern ; themselves with mundane things like weather. They spent the day ; searching for trouble. Luckily, they failed to find much of it. ; ; My day was near normal, and it looks as though the next week or ; so will remain uneventful. One of these days I'm going to give ; up graphic design work and start earning my living by selling ; fractals. Oh well, we can dream, can't we? The next FOTD will ; appear in 24 hours. Until then, take care, and the secrets of ; the universe may be hidden in these fractals -- if only we had ; the key to unlock the secret door. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= A_Whatsit_Midget { ; time=0:00:38.56--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-xz-yw-new passes=t center-mag=-0.16772097072767390/-1.749397401235292\ 00/514.2573/1.444/-120.75/33.166619765944354 params=0/49.68/2/0/0/0/0/0.0001 float=y maxiter=5000 inside=0 logmap=5 periodicity=10 colors=00000H00M01S02X03V04U05T06S17K28L39M4AN5BO6\ CP7DQ8ERAFSCGTEHUGIVIJWJKXLMYNOZPR_RU`TXaV_`WbaUdb\ SgbQhbPibNjbLlcKncIocGpcFqcDodBndAnd8md6kd5ic4g`3f\ Y3eV2dS2cP1bO1aO0aM0aE7aFEaJKaNN_RQYSTWQWUOZSM`QKb\ OGaME_KCYHAW38U86S78Q6AO50M40K45I6AG8FEAKCBP0ESCHV\ CKYCN`CQcCTfEUfGUfIVfLWfNXfPYgRYgTZgV_gY`m_bradvcg\ zejzgmzjozloznpzpqzrrzrrzpoznlzojzphzqdzrbzrZzrWzq\ UzpWzoYznbzmgzmfzmizmlzmozmrzmszmuzlsykoxjkwigvhcu\ g_tfWseSrdOqeKpeGoeDnfCmfAlg8kg6kg5kh3lh1lh0lg3mg5\ ng8ngAofDofFpfHqfKqeMrePreRseTtdWtdYud`udbvddvectf\ csgcrgcqhcoicnicmjclkcjkcilchmcgncencdoccpbbpbaqb_\ rbZrbYsbXtbVubUubTvbSwbQwbPxbOybNybMwcNvdOtdPseQrf\ RpfSogTngUlhVkiWjiXhjYgjZfk_dl`clabmb`mc`nd_oeZofY\ pgYphZqe_qb`r`arYasWbsTbtRbtOcuLcuJdvGfvEhwBjw9lx6\ nx4py5ry5ty6vy6xy7zy7zy8zy8zy8zy9zy9zyAzyAzyBzyBzy\ CzyCzyCzyDzyDzyEzzEzEBzDB } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } ; END PARAMETER FILE========================================= ; ;