; Date: Sun, 15 Jan 2012 23:38:58 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 15-01-12 (Reverse Fractal [7.5]) ; Id: <1.5.4.16.20120115234019.2a27587e@earthlink.net> ; --------- ; ; FOTD -- January 15, 2012 (Rating 7.5) ; ; Fractal visionaries and enthusiasts: ; ; I try to keep the FOTD on its regular daily schedule, but ; perfection seems to always elude me. This time I became more ; concerned in formula writing than actually finding fractals, ; which occupied me most all day Saturday, resulting in another ; day with no FOTD. (Hey, the world didn't end.) Only one ; worthwhile new formula emerged however, and even that one is ; more a reworking of an older formula than an all-new one. ; ; NEW FORMULA ALERT! ; ; Yes, you read it right. Today I am rolling out the MultiExp ; formula, which draws fractals with minibrots that can be morphed ; between quadratic and any other higher order. And as long as ; the 'other' order is a whole number, the minibrots will have ; none of those annoying discontinuities that spoil fractals such ; as those created by an expression such as Z^(2.5)+C. ; ; Unlike most of my formulas, with up to 10 variables, the ; MultiExp formula has only 2 parameters. The real part sets the ; 'other' order; the imag part controls the degree of morphing. ; When the imag part is set to zero, the fractal is a perfect ; Mandeloid of the 'other' order. When it is increased, the ; fractal it draws gradually morphs into the Mandelbrot set. When ; it is set to a negative value, the fractal morphs into a ; Mandelbrot set rotated 180 degrees. A nuisance I have not yet ; worked out is that the entire fractal quickly increases in size ; as the imag parameter is increased. (I corrected this ; deficiency, which appeared earlier in a similar formula, when I ; wrote the AllNewDivideBrot formula a couple years ago, but in ; doing so, I robbed the earlier formula of much of its potential.) ; ; At first glance, the parent fractal of today's image is an ; oversized Mandelbrot set much too large to fit on the screen. ; An out zoom is needed to bring it onto the screen. Today's ; image lies in some order-7 debris still filling the inside of ; the large minibrot on the main stem. ; ; I named it "Reverse Fractal" because the elements appear to be ; pointing in toward the central minibrot rather than radiating ; outward from it. The rating of a 7-1/2 might have been higher ; if I had given the coloring a bit more time. ; ; Perhaps the best feature of the image is its very fast ; calculation time of 45 seconds, which will leave little time for ; disappointment to build if the image lays an egg. ; ; To avoid all chance of being stuck with an omelet, check the ; finished image on the FOTD web site at: ; ; ; ; and the high-definition version of the image at: ; ; ; ; And remember the original FOTD web site at: ; ; ; ; Today here at Fractal Central began with a snow shower and a ; temperature of 10F -12C. The rest of the day brought lots of ; sun, but the temperature topped out at only a very chilly 25F ; -4C, which kept the fractal cats lurking around the radiators. ; FL escaped the worst of the cold by spending the day with a ; friend back in Baltimore, where the temperature reached 36F +2C. ; ; The next FOTD will be posted in 24 hours. Until then, take care ; and maybe the universe was created by a great fractal. (One of ; these days I'll reveal my beliefs about religion, but today is ; not the day.) ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= Reverse_Fractal { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MultiExp function=recip passes=1 center-mag=-17.657530419327/+0.063742372081/6e+007\ /1/20/0 params=7/10 float=y maxiter=1500 inside=0 logmap=50 periodicity=6 colors=000f0Gf0Fe0Ee0Dd0Cd0Bc0Ac09b08b07b06Z05V04R\ 03N02K12G22C31841650561872B83D94GA5JB6MC7OD8RD9UDA\ XDBZDCaDDdDEgGJjJPmOZqTitWssarseqriprmoqqnqunrvasw\ PuxUwymxzzzwzztzzqzznzznzUmfUljPecK_XJZVIYTHXSGWQF\ VPEUNETLDSKCRIBQHAPF9OD8NC8MA7L96K75J54I43H23H14I2\ 4J34K44L54L54M64N74O84O84P94QA4RB4SC4SC4TD4UE4VF4V\ F4WG4XH4YI4YI9WKEULISNNRORPQWNR`MTdKUiIWmHXkIWjIWh\ IWgIWeIWdJVbJVaJV_JVZJVXJVWKUUKUTKURKUQKUOKUNLTLLT\ KLTILTHLT3NQGLTTKWeIZsEbrHarK`rN_rPZqSYqVXqXXq_Wpb\ VpdUpgTpjSplSlhzidzf`zbXz_TzXQzZRz_Rz`SzaSzbTzcTzd\ UzeUzfVzhVziWzjWzkXzlXzmYznYzoZzpZzmYzjczgczdczacz\ ZczWczTczQczNczKczHczMczQczVczZczcczgczdczacz_czXc\ zVczSdzQczNczMczLczLmzLrzCczLwzQczVczZczcczgczlczr\ czpcznczmczkczjczhczgczeczdczbczaczPczDczEczEczFcz\ FczGczGczHczHczIczIczJczJczKczKczHczKczMczPczRczUc\ zYczWczVczTczSczQczgczgcz } frm:MultiExp { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), b=imag(p1)+0.00000000000000000001: z=z*z*fn1(z^(a)+b)+c |z| < 100000000 } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;