FOTD -- January 12, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's excursion into the HyperMandelbrot set takes us to the East Valley area, where we check the condition of the large minibrot on the shoulder of the period-32 elephant on the southern side of East Valley. What we find is "A MiniBrot in a Spot". Minibrots are supposed to be empty on the inside -- this emptiness is what defines a minibrot. But the minibrot in today's image is filled with superfluous, concentric rings of curious stuff that makes me wonder whether it is still proper to call it a minibrot at all. I suspect that this extra stuff is not truly real. It easily might be an artifact of the math routine, when such tiny values as 10^(-100) are entered into it. But wherever the stuff comes from, it is one of the most curious things I have stumbled upon in all my 20-some years of fractal exploration. In tomorrow's image I will see what unexpected surprise goodies I can find on the inside of today's minibrot. The rating of a 6 is not as high as I would have preferred, but the fast calculation time of just over 2 minutes means that little effort will be required to run the attached parameter file. And for those with calculation problems, the finished image is available on the currently active FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site, maintained by Paul Lee for almost 14 years, may be accessed at: <http://www.Nahee.com/FOTD/> but it is probably not up to date. Heavy clouds hung over Fractal Central all day Tuesday, and to make matters worse, snow began at 3pm. The temperature rose from 16F -9C at daybreak to an afternoon high of 28F -2C. The fractal cats checked the outside a couple times to keep track of the snow, then settled on their shelf by the heat. My day was about normal, which means everything stayed well under control. The next FOTD will be posted in 24 hours. Until then, take care, and it seems as though the more I learn, the less I know. Jim Muth jamth@mindspring.com START PARAMETER FILE======================================= A_Brot_in_a_Spot { ; time=0:02:06.93-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=HyperMandelbrot2 passes=1 float=y center-mag=+0.2596401989/-0.0015216554/33755.27/1\ /-162.5/0 params=0/0/0/0/-4.4/0/1e-100/0 maxiter=3000 inside=0 logmap=84 periodicity=0 colors=000MUWMTWNSVNSUNRUOQTOPTOPSPORPNRPMQPMQNPRM\ RRLTSJVSIXTHZTGaUEcUDeVCgVAiW9kW8nX7pX5rY4tY3vZ2xZ\ 4vX6tW8rUAqTCoSEmQGkPIjOKhMMfLOdKQcISaHU_GWYEYXD_V\ CaTAcR9eQ8eO9eM9eL9eJAeIAeGAeFAeDBeCBeABe9BfACfADf\ BEfBEfCFfCGfDHfDHfEIfEJfFKfFKfGLfGMfHMfHNfIOfIPfJP\ fJQfKRfKSfLSfLTfMUfMUgNVhOVhPWiQWiRWjSXjSXkTXkUYlV\ YlWZmXZmYZnY_nZ_o__o``pa`pbaqcaqcardbrebsfbsgcthct\ hcpgdmfeifffegceh_diXdjUckQclNbmKbnHZhFVcDRZBOU9KO\ 7GJ5CE3994BA5DA6EA6GA7HA8JA9LB9MBAOBBPBCRBCSBDUCEW\ CFXCFZCG_CHaCIcDIdDJfDKgDLiDLjDNkFPkHRkJSkLUkNWkPX\ kQZkS`kUbkWckYek_gkahkbil`il_ilZimYjmXjmWjnVjnUknT\ koSkoRkoQlpOlpNlpMlqLmqKmqJmrImsHntGpwFrzEtzDvzCxz\ DzyEzxKzwPzvUzuZztczshzrmzqrzpvzozznzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzumzymzzmzzmzzmzKOfPWyVUj`PUmOHzVz\ czzzz0tlJUzCz`khPzcDzcDzg2zQZzXcz0hzTmzXmz`mzHmzNm\ zTmzZmzFmzPmzZmzgmzlmzpmz } frm:HyperMandelbrot2 {; periodicity must be turned off a=(p1),b=(p2): q=sqr(a)-sqr(b)+pixel, b=(p3+2)*a*b+p4, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================