; Date: Thu, 19 Dec 2013 18:25:22 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 19-12-13 (Grounded in Zexpe [A-7,M-6]) ; Id: <1.5.4.16.20131219182533.2a3f0272@earthlink.net> ; --------- ; ; FOTD -- December 19, 2013 (Rating A-7,M-6) ; ; Fractal visionaries and enthusiasts: ; ; Today's image takes us to the fractal that many years ago was ; named the Zexpe fractal by Lee Skinner, who did extensive work ; on it. The Zexpe is the fractal that results when the ; expression Z^(epsilon)+C is iterated in the Mandelbrot mode. ; The usual Julia variations also exist, but we are not concerned ; with these in today's image. ; ; The Zexpe fractal is just one of an infinity of fractals that ; can be created by the manzpower formula of Fractint when the ; value of the exponent is varied. But the manzpower calculation ; involves complex logarithms, which are multi-valued and when ; calculated by the MandelbrotBC3 formula, can create an infinity ; of fractals for every possible fractional value of Z. So there ; are actually an infinity of Zexpe fractals to be explored. ; ; Today's image lies in the Zexpe Mandeloid fractal that comes ; about when the expression Z^(e)+C is iterated by the ; MandelbrotBC3 formula at ground level of the hyperladder with no ; function applied. This parent resembles a quadratic M-set ; rotated 90 degrees, with an ersatz main bud on the north side ; and an ersatz East Valley on the south side. There is some kind ; of pathological growth on the southwestern side of the main bay, ; but this does not enter into today's image, which lies in the ; East Valley of the parent. ; ; The name "Grounded in Zexpe" implies that the image lies in one ; of the Zexpe fractals and was calculated at ground level of the ; hyperladder. The art rating of a 7 and math rating of a 6 ; indicates that the artistic worth is about average and there is ; little new stuff to be found in the math aspect of the image. ; Luckily, the calculation time of 1-3/4 minutes is fast enough to ; keep fidgetiness and impatience at bay. The web sites can ; eliminate the fidgetiness. ; ; Enjoy the finished image at: ; ; ; ; Where the image may be seen without the chore of calculating it. ; And be sure to check the variations at: ; ; ; ; ; ; ; ; The sunshine was dimmed by haze today here at Fractal Central, ; but the temperature of 41F +5C was the warmest in two weeks. ; New fractal cat Jazzy celebrated the thaw by starting a tussle ; with Nico, but when Nico forgot his strength and got a bit too ; rough, Jazzy called it quits and ducked under the bed. The ; fractal humans simply had another normal day. ; ; The next FOTD will be posted in the appropriate time, whenever ; that might be. Until then, take care, and before we condemn the ; evil big greedy corporations who care only about their profits ; and don't concern themselves with poverty, let's check to see ; who is giving them the money that makes them so profitable. ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= Grounded_in_Zexpe { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=+0.0911597350623097/-0.3661580031587182\ /1.7e+011 params=2.71828182845905/0/0/0 logmap=249 maxiter=5000 inside=0 periodicity=6 mathtolerance=0.05/1 colors=0000KH0KH0KH0KH0KH0KH0KH0KH0JG0JG0JG0IF0IF0\ IF0HE0HE0HE0GE0GD0GD0FD0FC0FC0EC0EC0EB0DB0DB0DB0CA\ 0CA0CA0B90B90B90A90A80A809809709709708708708607607\ 60750650650650540540540430430430330320320220210210\ 11011010000000zp0zo0zn0zm0zl0yl5xkAxjFviKuhOthNrgN\ qfMpeModMndLmcLkbKjaKi`Kg`Jg_JfZIeYIdYHcXHbWHbVGaU\ G`UF_TFZSFYREXQEWQDVPDUOCTNCSMCRMBQLBPKAOJANIALG9J\ E9GC8EA8B97887577065053041030020010000000000000wzz\ rzzmzzjzzgzzdvzarz_mzYhzWfzUdzTbzSazR`zQZzQZzPXzPW\ zOVzOUzNTmMSzMSzLSzLSzKSvKTrJSmJRhIQcIQZHRUHRPGROG\ TNFXNE`MEcLKZKUUJcSJcRIcQHUPGUOFUMFUKEQIDMGCKEBICB\ GBAEA9C98A87877666555444333223112111000zzczzczzczz\ czzUzzKzzAzz0gU7jT6mS6pR6sQ6vP5zO5zN5zM5zL4zK4zI4z\ H4zG3zF3zE3zD3zC2zB2zA2z92z81z71z61z51z40z30z20z10\ zZDzYCzXCzXCzWCzWCzVBzVBzUBzUBzTBzTAzSAzSAzRAzRAzQ\ 9zP9zP9zO9zO9zN8zN8zM8zM8 } 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|