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