FOTD -- July 23, 2008 (Rating 6) Fractal visionaries and enthusiasts: For today's image we return to the formula that has supplied more FOTD fractals than any other -- the MandAutoCritInZ formula. We check the fractal that results when 1.5 negative parts of Z^(-5.5) are combined with 1.3 negative parts of Z^(-1.3) and (1/C) is added. The parent fractal reminds me of a large ant complete with head, thorax and abdomen, crawling southward across the screen. Today's image is located in the east branch of the valley where the thorax meets the abdomen. When I named the image, I was pondering one of the unanswerable theological questions that I once pestered my religion teachers with -- why does an all-good, all-knowing and all-powerful god permit bad things to happen to good people. This explains the name I gave the image --"Theological Puzzle". I really should curb my theological pondering. It constantly gets me into trouble. God, whatever truth lies behind that idea, must lack at least one, and possibly all of these attri- butes. Perhaps God is not all-good. After all, goodness is a human concept, and why should God's idea of ultimate good be the same as ours? Or perhaps God is not all-knowing. Could even a god know absolutely everything, which by definition must include what every sub-atomic particle in the universe has ever done, is now doing, and ever will do -- things that by their nature are unknowable? Or perhaps God is not all-powerful. Could even an all-powerful god do something that is impossible, such as making 2 plus 2 equal 7? Of course, theology is not the only discipline with unanswerable questions. Check one of the popularized science books about cos- mology or quantum theory, or grab one of those currently trendy books about new-age mysticism. As I often say, 'we don't know what we don't know'. And to make matters worse, I don't even have the option of avoid- ing the theological question by trying to convince myself that God does not exist and then claiming to be an Atheist. Now that I have indulged myself in this theological diversion, it's time to get back to the fractal business at hand. I rated today's image at a 6, which is all I think it is worth. The cal- culation time of under 3 minutes will not be much of a problem. The finished image is also posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A light midday shower did not spoil the otherwise near-perfect midsummer weather on Tuesday here at Fractal Central. The high temperature of 86F 30C and lower humidity were great for everything but snowmen. The fractal cats imagined themselves tigers as they watched a chipmunk in the back yard grass. My day was average, which means nothing happened. The next FOTD will be posted in 24 hours. Until then, take care, and ponder the hard questions. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Theological_Puzzle { ; time=0:02:53.84-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.934500853218/+1.854567358803/14309/\ 1/-120/0 params=-1.5/-5.5/-5/-1.3/0/0/0/0 float=y maxiter=1800 inside=0 logmap=120 periodicity=10 colors=000lcmkamj_miYmfWmcUm`SnYOoVKpRGpOCqL7vL8qL\ 8mL8hL9dL9_R1bL9WGGPBNJGQKLTKQVLuYLZ`MzbMheNzgNud2\ vcBwbKwaTx`ax_jwKow4tu9utDurHuqLvoPvnTvr_svhpoinhk\ lanjVphLvkOrfRnaTjXWfSZbN`ZIcVDhS4eR8bRB`RFYRIVRLT\ RPQRSEXWORVXMUmHTwEWzB_m8bi5egFVfOLeXAde0ad8ZdGWcN\ TcVLVkQca_hdVkTQnImq7KmAIiDGeGEbIKWPPPWa5nUJaMWPFh\ DGeCHbCI_CJYCKVBLSBMPBMNBzzAFv9mrFQoLVlR_iWeezjbzo\ _ztXzoJzk6ziFzhOzgRzgTzfVzfXzj_zfZzcYz`XzYXzUWzRVz\ OUzHRzLUzOWzRZzU`zXcY_eTbgPXdORbNUa5M`M5j`FfbPcdZ_\ fiVigXgeYfcZda_c_`aYa`Xb_YaYYaWZ`UZ_S__Q_ZO`YM`YKa\ XIaXHjFubNsVUrOapGho9on7Rh52bBA`HIZNPXTXWZdUdkUjsZ\ pzclwhitmfrrcov`lzYjzVgzSdzPbzM_zJ_yGawDcuAesDgq7i\ o8km8mk8oi8qg8se9uc9wg9xl9yq9zuKzuUzuaztczudzuezvf\ zvgzvhzwjzwkzxlzxmzxnzyozypzypzupzqpznpzjpzgpzcvz`\ rzYozVkzThzQdzNazL`zO`zR_zU_zX`za_z_ZzZZzYYzXXzVXz\ UWzTezEWzSMzdDzqMzmVzjtzh } frm:MandAutoCritInZ {; 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)+(p4)), 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=========================================