; Date: Thu, 16 Aug 2012 15:31:21 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 16-08-12 (The Ultimate Zexpe [8]) ; Id: <1.5.4.16.20120816153450.0d87bb50@earthlink.net> ; --------- ; ; FOTD -- August 16, 2012 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; The name of today's image, "The Ultimate Zexpe", is more a wish ; than a fact. It took two days to find a Zexpe fractal that ; qualified for the status of ultimate, and even after finding it, ; I'm not so sure how ultimate it is. If ultimate is taken to ; mean 'the best', its supremacy is quite doubtful, but if ; ultimate is taken to mean 'final', then today's image certainly ; is the last, at least in the present series. Tomorrow's FOTD ; will feature the first in a similar series of 'Zexpi' (exponent ; PI) fractals. (You ain't seen nothing yet.) ; ; Today's parent double-Zexpe came about when I calculated ; Z^(epsilon) at a level of epsilon steps up the hyperladder with ; no function applied. I omitted the function for the sake of ; simplicity. This parent has both main buds on the same side ; (the northeast side) of the single main bay. The scene lies ; in a minor valley on the west side of the main bay. (I often ; choose to explore valleys because they emphasize the mathemati- ; cal characteristics of the particular area in which they lie.) ; ; The first impression of today's image is its brilliance, which ; earns it the rating of an 8. The calculation time of 3 minutes ; is slower than I would have preferred, but still well within ; reason. The web sites take the effort from viewing the image. ; ; The finished image is posted at: ; ; ; ; A high-definition rendering is posted at" ; ; ; ; The back images and discussions are online at: ; ; ; ; A near perfect summer day was fully appreciated here at Fractal ; Central today. The temperature of 81F 27C, low humidity and ; Photoshop blue skies decorated with puffy white clouds were just ; what the fractal cats ordered. They spent a good bit of time ; gazing out the window, wishing they could get outside to ; explore that big forbidden room. ; ; The humans had too many other things to do to appreciate the ; weather. (By the time humans have enough free time to enjoy good ; weather, it's too late in life to enjoy very much of anything ; [except fractals]). The next FOTD will be posted in a proper ; amount of time. Until whenever, take care, and make that big ; decision today. ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= The_Ultimate_Zexpe { ; time=0:03:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident float=y center-mag=-0.332850274478/+0.147018580443/5e+007\ /1/-172.5/0 params=2.718281828459/0/2.718281828459\ /0 maxiter=6400 inside=0 logmap=272 periodicity=6 colors=000BooCjmCfkDaiEXgETeFOcGJaFE`GF_HFZIFZJFYK\ FYLFXMGXNGWOGWPGVQGURGUSGTTHTUHSVHSWHRXFRVFQV77_HL\ dRhiWzjayjbykcxkdxlewlfwmgvmhvniunjuoktoktlhqieogb\ ld_jbXh_UeXRcVO`SLZQJXRIUSHRTGOTGLUFIVEFVECWD9XC6X\ C4YF5ZH5_K5`M6aP6bR6cT6dW7eY7f`7gb8he8ig8ji8ijAhjC\ gkEfkGelIdlKcmMbmOamQ`nS_nUZoWYoYXp_WpaVpbXo`YnZZm\ Y_lW`kUajTbiRchQdgOefMfeLgdJj`DhcIfeNdgSbiX`laZnfX\ pkVrpTtuRprPmoOjlMgiLdgJadHZaGWZETWDQUCRSCRQCSPCSN\ CSLCTKCTIBUGBUFBUDBVBBVABW8BW6CX2BW5BW7ATAAPC9NE9K\ H8NJ8QM7TO7WQ6WT6WV5WX5W_4Wa4Wg3Wm3Wz2Wz2Wz2Wz5Xz7\ _z9azCczEegGgfJidLkcNmaPm`SmZUmYWmXZmV`mUbmSdmRgmP\ imOkmMnmLpmJrkInkHhmOimQimRimSimTilUikVjjWjiXjhYjg\ _jf`jeakdbkcckbdkbekbfjchkbgkbgkaglagm`gn`go_gp`gq\ agrbgscftdfuefvffwgfxhfyifzjfzkfzlizmfznczo`zpYzqV\ zrTzsQztNzuKzvHzwFzxCzy9zz6zz3zzVzzXzzZzz`zzazzczz\ ezzgzzizzjzzlzznzzpzztzzq } 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|