FOTD -- May 10, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image came about in almost exactly the same way as yesterday's superb image, but in today's image the exponent has been increased to 2.9 and the number added to each iteration reduced to 1000. The result is another parent fractal that on the surface appears to be a perfectly normal Mandelbrot set, but in its depths, is entirely different. And like yesterday's image, today's image lies in the East Valley of the large minibrot on the main stem of its parent. Curiously, the minibrots in yesterday's image, which has an exponent of 2.5, are quadratic, while today's image, with its exponent of 2.9, has order 2.9 minibrots in its depths. To me, this makes no sense at all, and is a reminder that there surely is a lot to learn about the way numbers work in fractals. The comb-like detail in the image is due mostly to the coloring, though something real must lie in the fractal itself, or else these patterns would not appear. The rating of a 7.5 indicates that I am satisfied with the image. The extra half point is a reward for my coloring effort. It was not easy to bring the patterns out of the 'sand'. The name "Patterns in Sand" refers to the comb patterns, which, like patterns in physical sand, totally disappear when the light or color changes. The calculation time of 2-1/3 minutes is about all the image is worth. And even this time can be saved by viewing the completed image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Heavy clouds and unusually chilly winds made Sunday feel like anything but spring here at Fractal Central. When the tempera- ture failed to rise above 52F 11C, the fractal cats gave up on comfort and retired to their chosen resting places to sleep away the afternoon. My day was very close to average. The next FOTD will be posted in 24 hours . . . more or less. Until then, take care, and you can't know where you're going unless you know where you came from. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Patterns_in_Sand { ; time=0:02:18.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinDivBrot-2 function=recip passes=1 center-mag=-1.74884203473413/+0.00016101734317492/\ 5.143742e+009/1/-37.5/0 params=2.9/1000/0/0 float=y maxiter=1800 inside=0 logmap=260 periodicity=6 colors=000`Rf`Rg`Rh_Qj_QkZPmZPnYOpYOqXNsXNtWMuWMuV\ LvVLu_bzZeyZgxZjxYmwboyfrzkuzowztzztwzszzmzzhwzbtz\ XqzSozRmzQizQezPaxPYvOUtNSrNQpMNmLLlLIjKGfKEaQBcSC\ _TDXVDTWEQXENZHO`IOcKOhLPmNPrOPvQPzRQzTQzUQzVRzWRz\ XRzYRzZSz_Sz`SzaSAA0CA0EA0GA0IA0JA0LA0NA0PA0R90S8F\ U7KW6PY5U_4Z`4ca7db9dbCecEecHfdJfdMgeOgeRhfThfVh`a\ mVhqQoueCp4896DC7IE8MH9RJBWLC_ODdQEhSDdUCaVCZXBWYB\ TZAP`9Ma9Jc8Gd8DeYRmwhtvmovskuzguzcuz_tzVzzRzzNzzJ\ zzFztJzvMzxPztRzqTznUWkWXhXYdZZa`_Za`WcaTdbPfcMhdJ\ ieGkfDlfFmfGmfHnfJnfKofLofMofOpfPpfQqfSqfTrfUrfVr_\ XmTYiM_eF``8bX2cT7`UCYVHVWMSXRPYWMZ`J_eH`aNbYScUXe\ QafMfhIkiEpjBie9ca7YY5ST3MP1GL4KN6NP8QRATTCWUFZWHa\ YJe_LhaNkbQndSqfUthWwjYzkTydOyZmyTmxNmzHmzBzzDzzFz\ zGzzIzzJzzLzzNzzOzzQzzRzzYzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:FinDivBrot-2 { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1): z=(b)*(z*z*fn1(z^(a)+b))+c |z| < esc } END PARAMETER FILE=========================================