FOTD -- May 15, 2007 (Rating 5) Fractal visionaries and enthusiasts: For today's image I resurrected the original Mandelbrot branch cut formula, MandelbrotBC1. This version actually is more versatile than the MandelbrotBC2 formula that I use quite often. Instead of having the 'floor' function hard coded, like the second version of the formula, BC1 lets the user choose any function. This ability can be quite useful, since most of the available functions make unique and quite interesting fractals. In today's image we examine the Z^(1.09)+C Mandeloid as it appears 10.6 levels up the log ladder when the 'sin' function is applied and the escape radius is raised to 1600. At this level the parent fractal resembles a distorted Mandelbrot set rotated 180 degrees. Except for the large period-2 bud, this set is without buds, but the shoreline of the main bay is edged with interesting chaos. Today's image lies in the East Valley area of its parent, which is actually on the west side of the main bay. Believe it or not, there actually is a midget far down at the center of the image. But waste no effort trying to reach it. The midget lies far beyond the breakdown point. Because the midget will never be seen, I named the image "The Lost Minibrot". Then I rated it at a 5. Some interesting debris is floating through the image, and some curious debris patterns are starting to emerge, but there is too much chaos and too little order for a higher rating. The calculation time of over 17 minutes on the P4-2000 would be over an hour on the old P200 unit. To save time, I have sent the finished image on ahead to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where it is posted for quick enjoyment. Monday began clear, with a very cold temperature of 30F -1C here at Fractal Central. And yes, if there had been any pumpkins in the field, they would have had frost on them. But by the time clouds arrived in mid morning, the strong May sun had warmed the air to 66F 19C, where the temperature stayed all afternoon. The fractal cats were exceptionally active for most of the day. My day was a bit busier than usual, resulting in a fractal that is a bit less worthy than usual. Better things will happen tomorrow however, so until the next FOTD appears in 24 hours, take care, and be careful what you iterate. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= The_Lost_Minibrot { ; time=0:17:22.32-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=sin passes=1 center-mag=-1.35514864109703900/-0.138026541520764\ 20/2.473146e+012/1/-90/3.8857806e-016 params=1.09/\ 0/19.6/1500 float=y maxiter=3600 inside=255 logmap=1740 periodicity=10 mathtolerance=0.05/1 colors=000Kedmzdmzdmydcxdjsdjvdhu_csVZqQUoLPmGLkBL\ h6Ld5La5LZ5LW5MT5MQ5MN5MK5MG5ME5NC5NA5N85N65N45N25\ L15K05J05I05G05F05E05D05C05A0590580570560540530520\ 510500500510731943A64C75E87FA8HB9JDBKECMFDOHFPIGRK\ HTLJUMKWOLYPNZRO`SPbTQcMVZG_VAcRP_AGd66i50o50m50l5\ 0k50j50i50h50g50e50d50c50b50a50`50_50Y50X61W61V71U\ 71T81S82Q92PA2OA2NB3MB3LC3KC3ID4HD4GE4FE4EF5DF5CG5\ AG59H68H67I66I65J05Q64JD3DK27Q05R15S25T35T45U55V67\ W78W89X9AYABZBDZCE_DF`EGaFHaGIbHKcILdJMdKNeLOfLQgM\ RgNShOTiPUjQWjRXkSYlTZmU_mV`nWboXcpYdpZeq_fr`hsais\ bjtckudludmnehhfcbf_WgVQgRKhMDhQ7iV0h_1id6iiBjmGjq\ MjqRkqWkq_oq`kq`hquhquaquoqulqcSqcZqcZqdZqdUqeUqeU\ qfUqfUqgUqfUqeUqdUqcUqbUqaUq`Uq_ZqZZqYZqXZqWZqWZqV\ ZqUZqTZqScqRhqQmqPrqOrqNrqMrqLrqKrqKrqJrqIrqHrqGrq\ FrqErqDrqCrqBrqArq9rq8rq8sqBqqDrqFrqHrqJrqMrqOrqQr\ qSrqcrqcrqdrqdrqdrqdrqerq } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================