; Date: Thu, 08 Nov 2007 07:43:02 -0500 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 08-11-07 (A Riot of Colors [7.5]) ; ; Id: <1.5.4.16.20071108074427.0cf76ad6@pop.mindspring.com> ; --------- ; ; FOTD -- November 08, 2007 (Rating 7.5) ; ; Fractal visionaries and enthusiasts: ; ; The name of today's image, "A Riot of Colors", says it all. It ; is perhaps the most colorful FOTD image of all time, helped in ; no small degree by myself. The parent fractal is the Z^(1.75)+C ; Mandeloid as it appears 11 levels up the complex logarithmic ; ladder, which could perhaps be more accurately described as a ; hyper-helix. As a matter of interest, the formula for calculat- ; ing the complex natural logarithm is: ; ; (1/2)ln(x^2+y^2)+i(atan(y/x)+2kPI) ; ; The logarithmic ladder, or hyper-helix, exists because k can be ; given any value from minus to plus infinity. ; ; Today we are at step +11 of the infinite ladder, where the ; parent appears as a single large oval bay with, strangely ; enough, two large period-2 buds, one on its east side, the other ; more irregular one on its northwest side. A large area of chaos ; extends north from the irregular bud, and today's scene lies ; just east of a larger minibrot lying near the northern tip of ; this area of chaos. ; ; The image is far too gaudy to earn a superior rating, but it is ; well worth a 7 plus the 1/2 point I gave myself for the little ; extra work I did on the color palette. ; ; The calculation time of 3-1/4 minutes is perhaps a bit slow for ; the total image, but the colors alone will assure that those who ; take the time to run the included parameter file will not be ; totally disappointed. ; ; Iteration frustration may also be avoided by visiting the FOTD ; web site at: ; ; ; ; and viewing the finished image there. ; ; Typical late autumn conditions prevailed here at Fractal Central ; on Wednesday. Brisk northwest winds blew, the sunlight alterna- ; ted with dark scudding clouds, and the temperature reached only ; 43F 6C. Snug indoors, the fractal cats spent the day by the ; heat, warm as toast, while I kept warm fighting with a job that ; just would not do what the customer wanted. The next FOTD will ; be posted in 24 hours give or take a few. Until then, take much ; care, and be at ease with this mysterious world. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= A_Riot_of_Colors { ; time=0:03:18.17-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=floor passes=1 center-mag=-0.30648810766/+1.86666607889/6240791/\ 1/77.5/-9.14082472e-009 params=1.75/0/11/0 float=y maxiter=32000 inside=0 logmap=160 periodicity=10 colors=000zNQmON`QJNQIBSE0SD0U90U80L40E2680G20D009\ 0080340420600900B00D30J90QG0WO4bWBibGnkNvrUzzZzvUz\ rQvnNnkJigGbdDX`9QX6LU3GQ09N04J00G00D00900600B00G0\ 0L00Q00W00`00e00k00p00v00z00n2DbDOQNbEZn3kz0vzz0mz\ 0gz2dz6`z9WzDSzIOzLJzOGzUDzX8zb4ze2zi0zn0zr0zv0vv0\ rv0nv0kv0gv0bv0Zv0Wv0Sv0Ov0Up0Xk0`g0db0zX0kU0nO0rJ\ 0zG0tI0rJ0pJ0nL0zL0mN0kN0iO0gO0eQ0eQ0bO2`O4ZO8XNBW\ NEUNISLLQLOOLUNJXLJ`JzdIggGZkEZnDLfIBYN4ZN0QS0NY0P\ b0QzxNztJzpGzmDzi9zd6zZ3zU0tO0nL0iO0eS0`W3WZ6Sb9Nd\ DJdGGeIDeL9eN4gQ2gS0iW0iX0i`0kb0ke0mg0mk0mm0pg0rb0\ vX0xS0zN0zI0zD0z86z3Ez0Nz0Wz0dz0mz8vzGzzQzz`zzizzt\ zzzzzvzznzzgzz`zzUzzNzzOzzdzzvzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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|