; Date: Thu, 15 Mar 2012 17:15:40 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 15-03-12 (Anti-Bifurcation [8]) ; Id: <1.5.4.16.20120315161755.2b9f4376@earthlink.net> ; --------- ; ; FOTD -- March 15, 2012 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; Sebastien recently sent me an e-mail in which he mentions the ; little white cloud on the northeast side of the large minibrot ; in the 'No Discontinuities' FOTD image of March 11, the 'pimple' ; that held the 'Outrageous Colors' image of March 12. This white ; cloud is what I call an area of anti-bifurcation. The fractals ; drawn by the "FinDivBrot-2"-type formulas are filled with such ; areas, though I have never seen them drawn by any other type of ; formula. ; ; I sometimes mention anti-bifurcation in my FOTD discussions. ; There are two kinds of this oddity that I currently am aware of. ; The more common variety occurs in the fractal patterns around ; minibrots that lie in the basins of attraction of larger ; minibrots, when the constantly doubling number of elements ; approaches infinity some distance from the minibrot, then resets ; to a much smaller power of two and resumes doubling as we ; continue diving inward toward the minibrot. This resetting can ; occur several times on the way to the minibrot. ; ; The other, much rarer, variety of anti-bifurcation is ; illustrated in today's image, where everything is backwards and ; the number of elements is cut in half as the center of repulsion ; is approached. No minibrot lies at the center. Instead, the ; center is the lowest iteration peak of a fractal mountain. The ; difference is made immediately obvious by the colors, which flow ; in the wrong direction when cycled. ; ; In today's image the outermost blue ring consists of 64 blue ; elements; the red ring holds 32 elements; the green holds 16; ; the purple holds 8; and the tiny turquoise area at the center ; holds 4. Beyond this, and beyond resolution, lies an area of 2 ; elements, and then . . . who knows. Does the series continue 1, ; 1/2, 1/4...? The answer lies well beyond the range of ; resolution, but I assume the series comes to an end at 1, with a ; minimum of around 40 iterations. ; ; The image rates an 8, about 1-1/2 points of which is due to the ; mathematical interest. ; ; The name "Anti-Bifurcation" simply describes the image. ; ; The calculation time of 45 seconds is blazingly fast, mostly due ; to the unusually small iteration count of most of the elements ; in the scene. ; ; The completely calculated image is posted on the official FOTD ; web site at: ; ; ; ; A high-definition rendering is available at: ; ; ; ; The back FOTD images are on-line at: ; ; ; ; Another gorgeous day graced Fractal Central today, with hazy ; sunshine and a temperature of 75F 23C. The fractal cats were ; warm enough without the full sun, and found comfort in the ; watered-down sun that filtered through the clouds. The fractal ; humans found satisfaction in the typical routine day, in which ; nothing went obviously wrong. This is the best typical earth- ; bound humans can ask for. The next FOTD will be posted in 24 ; hours. Until then, take care, and an activist is one who goes ; out and protests the un-affordable price the greedy big-oil ; conglomerates are charging for their products. ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= Anti-Bifurcation { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip center-mag=-1.296298258719479/+0.4418325064639432/\ 1.548763e+012/1/-77.5/0 params=5/2.5e+017/0/0 float=y maxiter=128 inside=0 outside=tdis logmap=46 periodicity=6 mathtolerance=0.05/1 colors=000mzzmzzmzzmzzUzzKzzKczKczKmzzzzzzzzzzzzzz\ zzzzzzzzcUjcUjcUlcUmcZof0Zm7ulJvdVxaTy0zz0zsyzKmbz\ JzczzKzxKgucTqcVlcW_cYYc000000000000202707C0CH0HM0\ MQ0OH0FO0JT05Y0Vc0Vd0Vg0Vh0Vl0Vo0Vs0Vv0Vy0Vz0TA0QA\ 0070`50d20p000000000000000000000000000000000000000\ 000000000000000000000000000000000000000000000Yz_Wz\ _Wz_Wz_Wz_VzYVzYVzYVzYTzYTzYTzYTzYzyzzzdzyczvazq_z\ mYzjWzdVzaTzYQzTOzOMzJJzCHz7Fz2CzFHzOMzWOxcTqjVhsY\ ay_VzcJzdAzh0zjWdzhvzuzqzzTzz0zzAzzJuzTmz_dvgYmmQc\ uHVz7JzFQzMVzTYzWczagzgjzlozoszuvzyzzzzzzzzzzzxzzs\ zzozzjyzdxz_vzWuzQszJqzCoz7ozAlzAjzCgsFdjFcaVYggVj\ sQmzJqzFuzAxz5zz2uo2oQ0j00dFJoWYyhjzvxzzzzzzzzzzzz\ zzzzzzzzzzzzzzzvzzzzzzzzzzuzzmzzhzvQvW5YuOzzczovqu\ zvxzzzzzzzzzzzzzFyzMqzThzY_xcQmhFcm2Vq2Mq2Cq22q20q\ 20qQ2ugJvxYxzjyzdzzazzYzzVzyQzxMzzVzz_zzgzzlzzszzx\ zzzzzzzzzzzzmzzT7Oz5Wz2az } 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 ;