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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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|<a } END PARAMETER FILE=========================================