FOTD -- December 02, 2009 (Rating 7) Fractal visionaries and enthusiasts: Sometimes the irrational number 'epsilon' does strange things. When applied to the world of fractals it is not quite so strange, but as today's image shows, it still creates some interesting images. Today's image lies in the parent fractal that is created when the formula Z^(2.718...)+C is iterated at ground level and no function is applied. This fractal resembles a Mandelbrot set with its main stem pointing north and an extra cove attached to the southwest shore of its main bay. Today's scene is located in the East Valley of the main bay of this parent. The name "Epsilon Experiment" was almost automatic. The rating of a 7 might be a bit generous. The calculation time of under 3 minutes will bring no grief, but viewing the finished on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will bring even less grief. Tuesday dawned cloudy here at Fractal Central. The clouds hung overhead all day, depressing the moods of the fractal cats, while the chilly temperature of 45F 7C helped not a bit. The cats displayed their displeasure quite vocally, and did not quiet down until an extra serving of tuna appeared. Except for the routine stuff, my day was uneventful. The next FOTD will be posted in 24 or so hours. Until then, take care, and why is the "Monty Hall problem", which is not a puzzle at all, so difficult to explain. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Epsilon_Experiment { ; time=0:02:51.43-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.09115973506230973/-0.366158003158718\ 20/1.700819e+011 params=2.71828182845905/0/0/0 float=y maxiter=5000 inside=0 periodicity=10 mathtolerance=0.05/1 colors=000cKHbKGbJGaJGaJG`IF_IF_IFZHEYHEYHEXGEWGDW\ GDVFDUFCUFCTECSECSEBRDBQDBQDBPCAOCAOCANB9MB9MB9LA9\ KA8KA8J98I97000I97H87G87G86F76E76E75D65C65C65B54A5\ 4A54943843843733632632522421421311211210100000zpSz\ oRznRzmQzlQylPxkPxjPviOuhOthNrgNqfMpeModMndLmcLkbK\ jaKi`Kg`Jg_JfZIeYIdYHcXHbWHbVGaUG`UF_TFZSFYREXQEXQ\ DWPDVOCUNCTMCSMBRLBRKAQJAPIAOI9NH9MG8MF8LF7KE7JD7I\ C6HB6GB5GA5F95E84D74C73B63A52A42932831721110000Vez\ UdzTczTczSbzSazRazR`zQZzQZzPXzPWzOVvOUrNTmMShMScLS\ ZLSVKSUKTUJSTJRSIQRIOQHNQHLPGJOGJNFINEHMEHLDGKDFJC\ FJCEIBEHBDGACFACF9BE9AD8AC89B78B68A679578567457456\ 3453342332231121110004b93`83_83Z83Y83X73W73V73U73T\ 62S62R62Q62P52O52N52M52L42K41I41H41G31F31E31D31C21\ B21A2092081071061051040030020010oZDnYCmXClXClWCjWC\ iVBhVBgUBeUBdTBcTAbSA`SA`RA_RAZQ9YP9YP9XO9WO9WN8VN\ 8UM8TM8TL8SK8VKAXKA_KAaKF } 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=========================================