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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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 20.0 PAR-FORMULA 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 20.0 PAR-FORMULA FILE==================================