; Date: Thu, 22 Apr 2004 10:27:12 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 22-04-04 (Rabbit Ears [6]) ; Id: <1.5.4.16.20040422103037.38df9f8a@pop.mindspring.com> ; --------- ; ; FOTD -- April 22, 2004 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; To create the parent fractal of today's image, I took Z^(-1.6) ; and added 0.26 part of Z^(-6.1) to it before adding (1/C). The ; MandelbrotMix4 formula mixed these ingredients thoroughly. ; ; The 1200 iterations produced a fractal that retains many of the ; characteristics of the Z^(-1.6) and Z^(-6.1) Mandeloids, yet at ; the same time is something entirely new, with many features of ; the Z^2+C Mandelbrot set, such as bays, buds, valleys and ; midgets. Today's scene lies in one of the many valleys of this ; parent. ; ; The escape radius of the classic Z^2+C Mandelbrot set may be ; increased to as large a number as can be entered as a parameter, ; and the result will be nothing more than an outward shifting of ; the iteration bands. But when the escape radius of a fractal ; such as today's parent is increased, the image quickly falls ; apart. By the time the escape radius reaches one-googol, ; nothing is left but empty space. All the points have become ; trapped. I call this process 'evaporation'. ; ; Things are not lost however. All the points might be trapped, ; but they are still active, and the results of this activity can ; be made visible by rendering the image with the inside option ; set to something like 'bof61', which I believe colors the points ; according to which iteration takes them closest to the origin. ; ; All this stuff is relevant because the escape radius of today's ; image is indeed one-googol, and all the points have therefore ; been trapped. The original scene has evaporated. What we see ; on the screen are the things that the trapped points are doing ; in their confinement, made visible by the dynamic 'bof61' inside ; fill. ; ; What I see while staring at the image is a forest of rabbit ; ears. Maybe this means the residents of Fractal Land have ; over-the-air TV, but more likely it's just a coincidence. ; Whatever the reason, I named the image "Rabbit Ears", then ; rated it at a 6, which gives an overall value of a 66. ; ; Don't waste time investigating the detail inside the rabbit ; ears. This detail consists of moire patterns -- artificial ; patterns caused by limited screen resolution, which vanish ; faster than one can go after them. ; ; The only thing faster than a vanishing moire pattern is the ; download of today's pre-rendered GIF image from: ; ; ; ; On Wednesday the temperature reached 73F 23C here at Fractal ; Central, while the sun shone frequently and the wind blew gently ; from the east. The cats enjoy such conditions, and made no ; exceptions on Wednesday, when they spent half of the morning and ; the entire afternoon lounging in the yard. Today is similar. ; The cats are already on their window shelves, gazing at the sun ; and planning a lazy afternoon. ; ; For me, it will be another in a seemingly endless string of days ; with work before play. The next fractal will hatch when the ; work is finished. Until next time, take care, and be back in 24 ; hours for the next fractal. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ Rabbit_Ears { ; time=0:09:08.16--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.20067893060894/+0.02108591826425907/\ 685450.6/1/-20/-1.18714037711242781e-007 params=1/-1.6/0.26/-6.1/0/1e+100 float=y maxiter=1200 inside=bof61 periodicity=10 colors=000ISTRYfXcrg_fpXUzTHzR2xXBnaKcgSTlZHpfIfnI\ XuINzIBz4zK8zXBrhEltHfzKevNenOefRcYTcPUcGWZOXWWYSa\ YOhZIo_EuaAza5zbDvcKkePZfWNf_8G8TOAUWBUaBWhDWnDWiI\ ZfObbTfYYiUbmRgockqpnrzqt0404PHBgZHxnTtlcpkmlhwhgz\ efxbep_chZb_XaSW_HGS70Ibz0hzBmzRhmYeZeaIlY0qXSgXnX\ z8zHiBSXW_IlhDmo8nv4oz0pz0pz0qz0rz0tx0tu0ur0vo2wm2\ wkEnhPegZXifSllNmqHoxBqz5rz0zzzzxwzpvzhuzZtzRrzHqz\ 7pz4mr2ii0f_0bX0aT0aP0_N0_I0ZE0ZL0OM0N52T58P5GL5LG\ 5SB5X7DZAKaBRcDWfGahHgkIigKo_frOzbRpNShYIahAUr0Ov7\ LzDIzIGzODzTAzPGzLLzHPzDUz8Zz4bz0gx0kkGlYXmKlnIhkI\ egHaeHYaGUZGRWGNTT_bcmlispmvrqwttxvzzzzzzzzzzzwzzu\ wzqvxotvlrtiqrgrveuxbvz_wzYxzUxxSxvOxtLxqIzoEzmBzk\ 8zh4zf0ze0wb0va0u_0rZ0qY0pX0nW0mU0lT0iS0hR0gP0fO0e\ N2eN8cLDcLIcKObKSbIXbI_aHeaHi_Gm_Gq_EvZEzZDzZDzHAx\ 08o4EmAKlGPkLUiSZgXcfahefmckpbokXteSxZNzTHzNBuULk_\ U_fbOmkBrr0xzzg7ze52E0BLE } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } ; END PARAMETER FILE================================== ; ;