FOTD -- August 11, 2014 (Rating A-7,M-8) Fractal visionaries and enthusiasts: Start with the number 5, extract the square root, add 1 and divide the sum by 2. The result is 1.618034... the Golden Ratio. This number is also the exponent of Z in today's image, which is why I named it "Golden Perfection". To add to the interest, I calculated Z^(1.618034)+C one level up the complex logarithmic hyperspiral. At this not-so-lofty level, the parent fractal resembles a twisted Mandelbrot set rotated so that East Valley faces southwest and the large main-stem bud faces northwest. Today's scene lies on what should be the northern shore line of East Valley. The art rates a 7, since I really could have done a little more with the colors. The math rates an 8. This minibrot is one of the most symmetrical I have yet found in the fractal exponent range between one and two. The calculation time is 3-1/3 minutes, a time that could breed impatience. But this time may be saved by checking the FOTD web sites. Be sure to visit the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Morning and early afternoon were perfect today here at Fractal Central, with sunny skies, puffy clouds and a temperature of 82F 28C. But later in the afternoon, heavier clouds moved in, with rain expected tomorrow. The fractal cats, who expect nothing more than play and food, were unconcerned with the coming rain. The humans, who will be working inside tomorrow, had equally little concern. The next FOTD will be posted in the appropriate time, whenever this might be. Until then, take care, and if religion is doing its job, why is the number one question of life, 'what happens to us after we die?' Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Golden_Perfection { ; time=0:03:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=BranchCutGen passes=1 periodicity=6 center-mag=-0.1804690692893928/-0.1268348854197519\ /7.09888e+011/1/-152.5/0 params=1.618034/1 inside=0 maxiter=3600 float=y logmap=428 mathtolerance=.05/1 colors=0008ZI9_G9`ECZFEXGGVHITIKRJMQJMUNMXRM_UMbYM\ eaMhdOfcPecQdbRbbTaaU`aVZ`WY`YX_ZV__UZ`TZbRYcQYdPX\ eOX_QWUSVPUVJWUEXULQPSJLZDHe6Dl09p4Fs7LvARh8KV7EH6\ 8452861C71G81J81N91RA1VB1YB1aC1eD1hD1gF6fGBfHFeIKe\ JOfHPhEPjCQkAQOMK0YE2WC4VB6UA8S8AR7CQ6EP5GN3IM2KL1\ MK0LKRKKpsCVnCCgAFa8IV6LP5OI3RC1U60W93UB5SD7RGAPIC\ NKEMNHKPJJRLHUOFWQEYSC`VAbX9dZ7f`6db8bcA`eBZfDXhEV\ iGTkHRlJPmLNoMLpOJrPHsRFuSDvUBwVEnWGeXJXYLOZNFZRGY\ VGXZGWbGVfGUjGTnGSrGRsJStMStOSuRTuUTvWTvZUwaUwcUxf\ VxiVykVynWzqWzsWjlgVfsUhdS_ePRfNIgL9hJAcIB_GCWFDRD\ ENCFJBGFJCDR9BZ69e37h8GkCPnGYqLftPovTxkWv`ZtQarmmW\ zzDvu0qt4ms8irBeqF`pJXoMTnQPnTekrcgzfhzikzlnzbkz`x\ z_zzZzzYzzYwzYtzYpzYmzYizYfzYczcnzcrzcrzcmzcmzchzc\ hzchzMmzKmzJmzcmzcmzcmzcmzcmzcuzcuzcuzmuzmzzmzzmzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:BranchCutGen { ; Jim Muth Z=C=Pixel: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<100 } END PARAMETER FILE=========================================