FOTD -- August 01, 2013 (Rating A-7,M-7) Fractal visionaries and enthusiasts: In today's image we *subtract* 0.0000000000000001 part of Z^(-2) from 100 parts of Z^2. This combination creates a tiny Mandelbrot set 1/100 of the normal size, which, when blown up, appears on the surface to be perfectly normal, but does strange things in its deepest depths. And at a magnitude of over 10^15, you can't go much deeper, at least with DOS Fractint. Today's scene lies in the East Valley area of the large minibrot on the west branch of the filament extending from the period-3 bud on the north side of the main bay of the tiny parent M-set. Traces of East Valley stuff abound in the scene, but the overall donut-like pattern is quite unexpected. The four brilliant red areas are fine examples of what I call 'peaks of anti-bifurcation', where the iteration count grows smaller as the center is approached, while the number of elements is cut in half instead of doubling. I named the image "Planetary Nebula" when I was reminded of the gaseous shells puffed off by dying stars. The art and math ratings are both a 7, indicating near average interest. The calculation time of 2-3/4 minutes can be avoided by checking one (or all) of the FOTD web sites. FOTD images are available on the following web sites. <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Lots of clouds and occasional periods of rain prevailed here at Fractal Central today. The fractal cat enjoyed the near perfect temperature of 79F 26C. The humans, not being quite as fractal as the cat, spent the day doing what needed to be done. The next FOTD will be posted soon. Until we find out now much time 'soon' implies, take care, and since all the world's problems are caused by someone else, no one needs to do anything about the problems. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Planetary_Nebula { ; time=0:02:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident passes=1 center-mag=-0.00153754810877916/+0.010303790076819\ 72/1.344536e+015/1/-70/0 params=100/2/-1e-016/-2/0\ /0/0/0 float=y maxiter=1500 inside=0 logmap=190 periodicity=6 mathtolerance=0.05/1 colors=000z0Lx0Lm0Mc0MU1OK230000000000000000010120\ 2303404505606707808919A2AB3BC4CD6DE8EGAFICGKCILBKM\ BNLAQK9UJ9ZI8cH8hGDjHIlINnISoJXpJaqKksXku`mwdrzhzz\ lzzptzdovTmrImmHmhGhcFcZEZUDUPDQKIMKNILSFOWCU`F_eH\ ejJknGlqElsClvAlx8lzDktIjoNiiShdXgZafUfeOjdJdbL_`M\ U_NPYOJWQEVR8TS3STAYRGcPMhOQjUTl_WmdZoj_qnapobopdn\ qemqflrhksijttemlnxjitieqh`ngXkkRihShfThdThbUh`UhZ\ VhtbhXVhANhBSgBXgBagBfgBkgBpgBug5uhIlYVdOfXENdJ4kO\ l5EKoVRePYWJdMDjC7nRHreRdZVSTZEMb1GeoeneiiWmdNp_Vn\ UblPjjKrhFpkJVZWoEgdQaVaWAqSGoRLmQQlPVjO_iOddXh`dl\ XlrNvqQupTtoWsoZsnarmdqlbsmgqmkojkymonosdtyPqwVou`\ ltfjrlgprdwxeowehwfawfVwgOwgHwgAwhGqiLkjQekV`l`Vme\ PnjJrnHnoEkoCho9dp7ap4Wu1Zp2ak3df4fa5iX6lS7oN8xT0t\ O5qJ9mFEjAIg6Me9SdCXbFbaIgkQm`LlRGkGBj67jLHdPGh_Q_\ i_RqpAshJuaRwU_yNgfrRpZczGojLdWQVHVLN`OTeQZjSUYaPM\ kLAuPWjVueTq`SmXQjSPfO1zA } 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=========================================