; Date: Sun, 15 Apr 2007 23:26:03 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 16-04-07 (Alphabet Fractals [8]) ; ; Id: <1.5.4.16.20070415232958.2ba7b6b0@pop.mindspring.com> ; --------- ; ; FOTD -- April 16, 2007 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; In today's image we have a glimpse of what happens when a ; Mandeloid with an exponent of 1.99 is calculated 10 levels up ; the logarithmic ladder. This exponent is so close to 2 that ; any midgets in it will be almost perfectly quadratic, yet it is ; far enough removed from 2 that the fractal it creates rotates ; and changes as we move up and down the log ladder. ; ; In today's case, the parent fractal is a near Mandelbrot set ; that has rotated about 7 degrees CCW. Most of the details of ; the M-set are still undisturbed, but the rotation has totally ; changed the northern branch of Seahorse Valley, where today's ; scene is located. Instead of coming to a sharp point, the ; valley has changed into a blunt, rounded stub filled with ; rampant discontinuities. ; ; I have named today's image "Alphabet Fractals" after the ; prominent letter'X' that dominates the frame. I rated it at an ; 8 because it is unusual enough to draw attention, and I rather ; like the contrast between the purple foreground and the ; brilliant green letter 'X'. And yes, there is a midget at the ; center of the 'X', a rather attractive midget at that. ; ; The calculation time of 3-1/3 minutes is close to average for a ; FOTD fractal, though I have no idea what the exact FOTD average ; might be. But the calculation time becomes irrelevant when the ; finished image is viewed on the FOTD web site at: ; ; ; ; Heavy clouds, intermittent rain and an unusually chilly ; temperature of 43F 6C made Sunday a totally indoor day here at ; Fractal Central. The fractal cats took the weather in stride, ; since they are indoor cats every day. In my department, things ; continue to relax, but such pleasantly slow periods rarely last ; for any length of time. The next FOTD will appear almost by ; magic in 24 hours. Until then, take care, and think fractal ; thoughts. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Alphabet_Fractals { ; time=0:03:18.98--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.74318801921539530/+0.003050140052798\ 84/6.698834e+009/1/41.0069304495305431/0.003473070\ 27143493874 params=1.99/0/10/0 float=y maxiter=800 inside=0 outside=tdis periodicity=10 colors=000_kTZjUXiVWhWVgXTfYSeZRd_Qc_P`YOZXNXWMVVM\ SULQTKOSJMQIKPIHOHFNGDMFBLF9KIDJKHJNKJPOJRSJUVJWZJ\ ZaJ`eJbiJelJgpJisJfoLdlNbiO_fQYcRW`TTYVRVWPSYMPZKM\ `IJaKHcMGdOEeQDfRCgTAiV9jX7kZ6lZ5lY6jW7gU8dT9bRA_P\ BYOBVMCTKDQJEOHFLFGJEGHLcJSwKZwLmwMzzNzzQzzTzzVzzY\ wm_whbwcdr_gmXihUlcRnZOqULsPIvKGxFIrAJl6Li8NfAPcCR\ `ETYGVWIXTKZQM`NObKQdISfFUhCWj9Yl6_m4Zk5Xi5Wg6Ue7S\ c8Ra8P_9OYAMWBKUBJSCHQDGODHPIIPMIQQJQVKQZKRbLRfMRk\ MSoNSsNSwzdluajp_hlYggWecUd_SgXRiTPkQOmNNoJLqGKsCI\ u9Hw6Gy8FuAFrCFoEFkGFhIFeKFaMFZOFWQFSSFPUFMWFIYFF_\ FCaGEbGFcGGdGHfHJgHKhHLiHMkIOlIPmIQnIRpHSqHSrHTsHT\ tHUuHUiJVZKWOLXDMYCN`BObAOd9Pf8Ph7Qj6Rm5Ro4Sq3Ss2T\ u1Tw5Rt9PqDNnHLkLJhPHeTFbXD_`BXd9Uh7Rk6OmBRnFTpKVq\ OXsTZtX`vabwedxifyWiyIly5ow7ku9hsAeqCaoDZmFWkGSiIP\ hJMeLNbMO_NPXOQUPRSRSPSTMTUJUVGVWEWXGXXHYXIZXKZXL_\ XM`XO`XPaXepOdoPcnQamR`lS } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100, p=real(p2)+PI q=2*PI*floor(p/(2*PI)), r=real(p2)-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|