FOTD -- February 18, 2012 (Rating 8) Fractal visionaries and enthusiasts: In most of the fractal calendars I have seen, almost every image is filled with spirals of various sizes and shapes. I have never quite understood this fascination with spirals, but there must nevertheless be something attractive about them, so in today's image I have featured a spiral. Not wanting to merely go along with the crowd, I have cast aside the countless circular spirals that fill almost every fractal and found a spiral triangle. I found the weird spiral lurking on the west edge of the extra bay in the East Valley of the parent fractal of the 'leaves' image that appeared two days ago. I found no signs of minibrots in this area, but the triangular stuff I did find, partly obscured as it is by clumps of detached elephant trunks and spotted with smaller triangles, made an image worth being declared FOTD. The triangular spiral is a bit subtle, so the image must be studied before the spiral effect becomes obvious. The rating of an 8 is based mostly on the mathematical interest. As a work of fractal art, the image rates more like a 6-1/2. The name "Triangulation" is self-explanatory. The calculation time of 5 minutes borders on unacceptable slowness. To escape the boring calculation, check the FOTD web sites. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version is at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site is at: <http://www.Nahee.com/FOTD/> The day began sunny here at Fractal Central, bringing hope of an afternoon in the sun to the hearts of the fractal cats. But clouds moved in by midday, dashing their hopes. The temperature of 50F +10C was mild enough however to blunt the disappointment. The humans, FL and I, added a bit of interest to the day by taking an antiquing expedition down to Lemoyne, PA, a city across the river from Harrisburg, where FL found a new lamp table. The next FOTD will be posted in 24 hours. Until then, take care, and every day someone finds another health hazard. It seems that to end the constant worry about health, we will need to totally eliminate all disease, aging, accidents and finally death itself. Then there will be nothing to worry about but over-population. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Triangulation { ; time=0:05:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident center-mag=-0.05117831767526577/-0.007249082889432\ 25/3.99613e+008/1/5/0 params=11/1.9/-11/2.1/0/0/0/0 float=y maxiter=1000 inside=0 periodicity=6 colors=00004E05F06H07I28J39J5AK6BK8CL9ELBGLCIMEKMF\ MNHONIQOKSOLUOOWRRYUU_XWa_Zcaaedchgfjmilrknvnpzprz\ pqznnzjjvferbamZXhVScRNZNJUJEPF9KB4F70A60560060060\ 0600600600600EwzGwzHwzIwzJuvKsrOrmRqhVpcYpZaoUEZkD\ _rC`yGYuJWrMToPRlSOiVMfYKc`H_cFXfCUiARl7Oo5Lr3Iq4M\ q5Qq6Tq7Xq8_q9cpAgpBjpCnpDqpEupFxoEtoDqoCmnBjnAfn9\ cm8_m7Xm6Tm6QhAWcD`ZGeUJjQMoSPpTSqUVrVXsW_tXbtZeu_\ gv`jwamxbpycryhmflhOpd6WoCCyIEuLGrOHoRJlTKiWMfZNc`\ P`cRYfSVhUSkVPnXMpYJs_Gv`DxZIqXNkVSeTX_S`Uhbbe_abX\ a_U`YS``VWcYRe`MhcHjfCmi7ok3qi9rgEseKtcPuaVv__wYex\ WjyUouSprQpoPplNpiMpfKpbIp_HpXFpUEpRCpOBpULqZUrdUs\ iUtnUppUfpUTaFFbF1cF4eC6dDDcEFbFMZGOXHVUIXRJcPKeML\ lIMnFNpBOr7Pt4Pv8OtCOrFOpJOnNNlQNjUNdXNb`MWfMPiMPm\ MQoMSmLUkKVhIWbGXWEYOCZHA_A8`89b8Bc8Ee7Gg7Ih7Kj6Ll\ 6Kn6Io5Fq5Cq5Cq7Do9EkAFfCGbEHZFIUHJQILMFMICMF9MC6K\ 83I50G20E40C60A708906A04C } 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=========================================