FOTD -- December 29, 2011 (Rating ?) Fractal visionaries and enthusiasts: The rating of today's FOTD image is a question mark. I'm not sure how to rate it. I think this is the first FOTD image to actually make the breakdown of definition its main feature. The magnitude of 4*(10^9) is not all that great, but something like a quantum uncertainty principle must exist in Julia sets, which prohibits any trick that might reveal detail beyond the standard Mandelbrot magnitude limit of 10^12. Actually, such attempts merely shift the decimal point rather than add the imaginary extra precision of extra decimal places to the math. Curiously, when today's image is calculated by the standard math routine used by the type=julzpower formula, the breakdown is notably more severe. Today's image is actually part of one of the Julia sets of yesterday's image. This parent Julia set is filled with variations of today's scene, some of which are worth FOTD status in themselves, and might appear in a future FOTD. The name "Total Breakdown" exaggerates the situation quite a bit. A total breakdown would be either a flat color covering the screen or a screen full of featureless fractal sand. The calculation time of 1-3/4 minutes is reasonably brief for an image whose rating is a mystery. Those who do not enjoy mysteries yet do enjoy fractals may view the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-definition version posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> will reveal even more of the breakdown of precision, though I doubt that any new stuff will be revealed. Perfect resolution may be achieved only by calculating the image with the type=julzpower formula, which does support arbitrary precision math. But doing this will increase the calculation time from seconds to days. The original, now classic, web site may be accessed at: <http://www.Nahee.com/FOTD/> The day began with a brilliant sunrise and a temperature of 21F -6C here at Fractal Central. But clouds moved in during the morning, and hung around for the rest of the day. The high temperature of only freezing was near normal, but compared to the well above-average weather we have had so far this season, felt quite cold. Luckily the wind was light. The fractal cats spent the day seeking warmth, finally finding it on the shelf over the radiator in the hallway. The humans passed the day wondering when everything will fall apart. With the government paralyzed and unable to switch from hand-out-the-benefits mode to cut-the-benefits-and-raise-the- taxes mode, the day of collapse can't be too far off. The next FOTD will be posted in 24 hours, unless the collapse comes before then. Until next time, take care, and be ready to bite the bullet. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Total_Breakdown { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=slices.frm formulaname=JuliaN center-mag=-0.0089014397\ 2939820/+0.01721564886246437/4.252493e+009/1/-10/0 params=2.0001/0/0/0/-1.940345965619678/7.483135796\ 9939e-008 float=y maxiter=5000 inside=0 periodicity=6 mathtolerance=0.05/1 colors=000zOEzLCzKJcUIc3Hz3zW3FZ3Fa3Ed3Dh3Ck3Bn3Aq\ 39t38w37z37v26s26p25o23m25j25g24c14`14Y13V13S13P12\ M12Im2Fm1Lm19z1zz030zcm2_m1Wm1SG1OD1KA1I91mUzE70C6\ 0A508406304202109VI8RG7OE6KC5HA4D83A6264132F_mDWgB\ SaAOX8KR6GM5CG38B145T0RQ0NN0KK0HH0DE0AC09B07906705\ 503302101jzY`lTLePI_MGUJDOGAJC8E9596243EzzCpmBkcAf\ R9aO8XL7TI5OF4JC3E9296143BlM9cI7WE5OB3G7183K2rE1oD\ 1cC1eB1ZA1WA1U91R81P71M60U50M50I40F30D207105002zvz\ UUc31z20k20k20c20X20V20T10R10O10M10K10I10F00D00B00\ 9006004002IYKGWMFVNETODSPBRQAPR9OS8NTGVYObaViebqii\ xmciYYVITG2XUA_fIbsQ9Jl8Sh8`d8h`8qX8yT9iNAVHBGBZcT\ eZTlTSsOSuUPvZNwcKxhIymFzrDniHbaLRTPFLT4DWp70q60r5\ 0s40t40u30v20w20x10y00zKHzKEzKBzU8zK5z7Hz6Gz6FzUEz\ 5Dz5Cz5Cz4Bz4Az4cz38z38zc7z26zc5z2mz14z13z1mz01z00\ zAzz80z7zz7Zz6Xz6Wz6Uz5Sz5RzKPz4Nz4Mz4Kz3IzKGzUFz2\ Dz2Bz2Az18z16z15z03z01zRG } frm:JuliaN {; Jim Muth b=p1, z=p2+pixel, c=p3: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================