; Date: Tue, 08 Jun 2010 22:15:38 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 09-06-10 (Beyond the Horizon [7]) ; Id: <1.5.4.16.20100608221657.2a77301a@pop.mindspring.com> ; --------- ; ; FOTD -- June 09, 2010 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; Today's formula, the FinDivBrot-2, certainly creates some ; interesting and unexpected parent fractals -- and it's only 4 ; lines long. (I have always avoided those overblown formulas ; with 40 or 50 lines, most of which are devoted to coloring ; tricks. I much prefer the coloring tricks to come from the ; fractal math, not the fractal artist.) ; ; Today's formula, along with the type=Mandel, MandAutoCritInZ, ; MandelbrotBC3, and SliceJulibrot4 formulas (formulae) are the ; ones I turn to almost automatically when I boot the Fractint ; program. They rarely disappoint me. ; ; In today's FOTD, the FinDivBrot-2 formula produced a parent ; fractal that resembles a Mandelbrot set pretty closely until its ; main stem is examined. Instead of one main stem, this parent ; has two main stems, both of them infinitely divided into ever- ; smaller curled stems. Today's image is located in the East ; Valley area of the minibrot on the northern main stem. ; ; I named the image "Beyond the Horizon" because I did go a bit ; beyond the limit of perfect definition to find the scene. The ; rating of a 7 means the image is kind of good, but nothing to ; get excited about. ; ; The calculation time of just under 4 minutes may be avoided by ; viewing the finished image on the FOTD web site at: ; ; ; ; Another picture perfect day prevailed here at Fractal Central ; on Tuesday, an exact repeat of Monday. The fractal cats, now ; convinced that the unwanted intruder cat has moved on, spent ; most of the day sleeping. My day was busier than Monday, but ; still left lots of time for fractal diversions. The next FOTD ; will be posted in 24 hours. Until then, take care, and pass ; the time pleasantly. ; ; P.S. If a Klein bottle is given an extra twist, the result is ; a surface known as a 'projective plane', which needs a full five ; dimensions to be seen in its full unsquashed, non-intersecting ; glory. But don't ask me to describe the shape of this surface. ; Describing the Klein bottle is hard enough. And unless I'm ; mistaken, a projective plane may also be created by widening ; a Mobius strip until the single edge closes on itself to form a ; single-sided edgeless surface. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Beyond_the_Horizon { ; time=0:03:54.18-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip logmap=506 center-mag=-1.418212964957334/+0.03225319123708284\ /1.626e+013/1/167.5/-0 params=-0.05/-10/0/0 float=y maxiter=1500 inside=0 mathtolerance=0.05/1 colors=000L1UK1SK1QJ1OJ1MI1KH1IH1GG1EG1CF1AE19E18D\ 07D06C05B04B03A02001A00900800800700700600500500400\ 40030020020010010000000000000000000000000000000000\ 0000000000000000000000000000000000000000000000IwzF\ zxCzw9yv6xu3wsGuqEsnDojCjfBfbAbZ9YV8UR6QN5LJ4HF3DB\ 207hhZzzhrrZmoPhkFci5Zf0Ud0Sa0Q_0OY0NV0LT0JQ0HO0GL\ 0EJ0CH0AE08C0790570340120BqVAmT9jR9gP8dN7aL7YK6VI5\ SG5PE4MC3JA3F92C7195163031Ave8o`7hW6bS5WN4QI3JE2D9\ 1640SO0OL0LI0IG0FD0CA098065zczw`zsZzoXzkUvhSrdQm`N\ hXLcZJhSGbMETOBWF9FB7A74z32zB5V94z73K52F31A105aZuY\ VoUSiQOcMLYJHTFENBAH77B335PvWOtVNrUNqTMoSLnRLlRKkQ\ JiPJhOIfNHeMHcMGbLG`KF_JEYIEXIDVHCUGCSFBREAPDAOD9M\ C8LB8JA7I97c96c85c75c64c53c43c42U31U21c10U0zUszUpz\ UnzUkzUizUfzUzVUzTUzRUzPUzNUzLUzJUzHUzFUzDUzBUz9Uz\ 7Uz5Uz3Uz1UzUUzTUzSUzRUzRUzzzEzzEzzEzzDzz1zz1zz0zz\ 0zz0zz0zz0zz0zz0zz0zz0zz0 } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;