; Date: Mon, 05 Nov 2007 21:39:25 -0500 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 06-11-07 (Caught in an Orbit [7.5]) ; ; Id: <1.5.4.16.20071105214049.2ad7f676@pop.mindspring.com> ; --------- ; ; FOTD -- November 06, 2007 (Rating 7.5) ; ; Fractal visionaries and enthusiasts: ; ; ALERT -- TODAY'S FORMULA IS A NEW ONE! SAVE IT! ; ; Monday evening I reached the point where I could no longer ; endure the flawed MandelbrotBC2 formula, with its ground level ; at +3.14159... so I added PI to the fifth line of the BC2 ; formula and named the tweaked version MandelbrotBC3. Today's ; image was created with the BC2 formula and converted to the BC3 ; formula, which explains the odd value for real(p2). (The value ; was 89 in the BC2 version; the value in the BC3 version is 89 ; minus PI.) In addition, I generalized the function. ; ; Today's fractal was created by the expression Z^(1.09)+C, which ; is so close to being linear that one could hardly expect it to ; produce an interesting fractal. But we are dealing here with ; fractals, and fractals, even those of such a low order, do not ; always behave in a predictable manner, especially when they are ; calculated 85.8584... levels up the logarithmic ladder. ; ; At this height, the parent fractal of today's image resembles a ; torpedo. Not surprisingly, the minibrot in today's image also ; resembles a torpedo, or perhaps a rocket ship that has landed on ; a lost planet circling the red-dwarf star Wolf-359. ; ; I named today's image "Caught in an Orbit" for a reason I have ; long since forgotten. The rating of a 7-1/2 includes the extra ; work I put into the coloring and also minor task of writing the ; new formula. ; ; The calculation time of 2-1/2 minutes is slightly slow, but the ; image is worth it, and relief from iteration pains is available ; on the FOTD web site at: ; ; ; ; where the pre-rendered image is posted for instant viewing. ; ; Monday turned out better than expected here at Fractal Central. ; The skies were sunny, the wind was light, and the temperature ; reached 57F 14C. The fractal cats checked the pigeon situation, ; then spent most of the afternoon on their shelf in the sun. ; Rain moved in after dark, but by then it had already been a fine ; day. ; ; My day was close to average, the way every day should be. The ; next FOTD will appear in 24 hours. Until then, take care, and ; how many visionaries does it take to see an actual fractal? ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Caught_In_An_Orbit { ; time=0:02:35.44-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 center-mag=-1.8897526870\ 35/+16.753530446161/2324853/1/-170/0 params=1.09/0\ /85.858407346/3500 float=y function=floor maxiter=36000 inside=255 logmap=135 periodicity=10 colors=000YSCVRAXR9WRAWRAVRBVQBVQBUPCUPCTODTNDTNDS\ MESNESNERNFRMFQLGQLGQKGPKHPJHPJHNIGLHFKGFIFEGDEFBD\ D9CB9CA8B87B66A5693591580683B96G99L9CO9FSAHSAK_ANb\ AQfBTjBWnBYqBhzCZnCZmCZlC_kC_jC_iC_hD_gD`fD`eD`dD`\ cDabDaaDa`Ea_EaZEbYEbXEbWEbVEbUE`TG_SHZRIYRJXQKVPL\ UOMTONSNORMPPLQOLRNKSMJTLIUJIVIHWHGXGFYFFZHH_IJ`JK\ aKMbLNcNPeOQgPSiQTkRVmTWoUYqVZsW`uXawZcx_dy`fzagzb\ izcjzahy`fxZdwYbtX`qVZnUXkTVhRTeQRbPP_NNXMLULJPJHK\ IFFHDBFB9E96D84H79L7DP7IT7MX7Q`6Ve6Zk6cq6gw6kt8jq9\ inBhlCglDfkFejGdiHdiJchKbgLafN`eO_eQZdRZcSYbUXbVWa\ WV`YU_ZT__TY`UXaUWbVVcVTdVSeWRfWQgWOgXNhXMiXLjYJkY\ IlYHmZGnZFnZHk`JiaLgbNecPbdR`eSZfUZgW_hY`i_ajabkcc\ lddmfenhfojgplhqnirojsmkpllnkmkzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzmmz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|