; Date: Sat, 05 Dec 2009 23:49:01 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 06-12-09 (As Low As One Can Reach [5]) ; Id: <1.5.4.16.20091205234903.2a073782@pop.mindspring.com> ; --------- ; ; FOTD -- December 06, 2009 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; Today's hasty image is an example of what happens when the ; bottom falls out of the exponent of Z. Today's exponent is ; 1.075, which is pretty close to being linear. But as the image ; shows, when the iterations pile up, close to linear is quite far ; from being totally linear. ; ; The parent fractal of today's image was created by the formula ; Z^(1.075)+C as it appears 18 levels up the logarithmic ladder ; when no function is applied. This fractal is little more than ; an oversized parabolic shaped hole with areas of chaos at its ; southwestern extremity. Today's image is located at the edge of ; this chaos. ; ; As for the image itself, there is little that can be said about ; it and the rings of debris that surround the tiny minibrot at ; the center. Due to its lack of a defined theme, it rates only a ; 5. The name "As Low As One Can Reach" refers to the unusually ; low exponent of Z. ; ; The calculation time of just over 3 minutes is a bit more than ; the image is worth, though it still might be worth a try just to ; see what a minibrot of such a low order might look like. ; ; A better way to see the scene is to visit the FOTD web site at: ; ; ; ; and view the finished image there without the chore of calcula- ; ting the parameter file. ; ; Snow fell all day here at Fractal Central on Saturday, which ; gave the fractal cats a chill, but the falling flakes held just ; enough interest to keep them in the window that serves as their ; TV. The freezing temperature kept the humans on the street well ; wrapped however. By day's end about 2-inches, 5cm of snow had ; piled up. ; ; My day was troublesome. FL was moody because the weather was ; too bad for us to go on the antiquing trip she had planned. I ; was moody because the furnace cut out a couple times, and it ; looks like a service call might be needed. But whatever might ; happen, the next FOTD will be posted in 24 hours. Until then, ; take care, and search for the cosmic hypersphere. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= AsLowAsOneCanReach { ; time=0:03:04.42-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-14.9460780195969/-2.324758143896453/\ 2e+010/1/-162.5/0 params=1.075/0/18/1500 float=y maxiter=3600 inside=0 logmap=253 periodicity=10 colors=000hVuiUukTulcUmcVmaTmZRmWOmTMmRKmOHmLFlICd\ EDXAFO5HS6JX8LaANfCPkERpGTuIVzKXuJYoH_iF`cDbZCcTAe\ N8fH6htf9ncDh_HaXLWTQPQUJMYCIbIIdOHgUGj`FmfFplEsrD\ vyCylKuZSqM_m8ghEgeKfaReZXdVbcRibOoaKv`GteGqkFopFl\ vEPjN1ZW2VW3RW4NV5JV6FU4_h1uwGsiVpWjmHjnJjoLjpNjrQ\ jsSjtUjuWiwZip_ii`iaahVchOdhGeh9fg1hc7i_DjWJkSQmOW\ nKaoGgpCnrx8lt7fo6`j5Ve4P`2JaLNccScaQbZNJmBNnIRoPW\ pV_qacrhgrnaipW`qQTsKKtECuj8LiAOiCQhEShGUgIWgKYgM_\ fOafQceSeeUgdWidYkd_ma_iZ_eW_aU_YR_UO_RL_NJ_JG_FD_\ BB_8HYCMXFRVIWUM`SPeRSjQVkPTlORmNPnMNoQLpUJqXHr_Gs\ aEtcCufAvh8wm6xr4yv3EzWGzXHzYJzZKz_zzzNzzzzzQzzRzz\ zzzUzzzzzXzzZzzzzz`zzzzz6zzAzzzzzzzzzzzzzzzzzzzuzz\ tzzsozrwzqzzphzsZzuXzpVzlUzhSzdRz`PzXUzTczNmzZrzZz\ zZzzZIzq3zpBzfIzuPzuWzuVzuUzuTzuSzuRzuQzuPzuOzuPzu\ QzuRzuOzuMzuKzuLzuMzuNzuPzuQzuRzuSzuTzuVzuWzuXzuYz\ u_zu`zuazubzuczuezufzugzu } 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|