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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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|<a } END PARAMETER FILE=========================================