FOTD -- May 13, 2005 (Rating 5) Fractal visionaries and enthusiasts: Today is Friday the 13th, an event that happens once or twice every year. It is supposed to be a bad luck day, though I doubt that is any unluckier than any other day of the year. Nothing unusually bad has ever happened to me on a Friday the 13th, so I consider the bad luck thing to be an unfounded superstition, most likely originating long ago, when the decree that ordered the elimination of the Knights Templar was passed on a Friday the 13th. My view would seem to be confirmed by today's image, which is notably un-notable. Today's image is a scene in a fractal that is almost a Mandelbrot set. What keeps it from being a Mandelbrot set is the exponent of Z in the iterated formula, which is 2.00001. This is a very tiny difference, but to make a big deal of a minor event I examined the fractal 100,000 levels up the complex log hyperspiral, at a level where it has rotated approximately 70 degrees. At this level the negative real axis cuts through what is normally the S.S.W. shoreline of the M-set. At this lofty level, the parent fractal still resembles a classic Mandelbrot set, and the inner detail is basically unchanged. The one difference is along the negative real axis, where a tiny discontinuity exists. This break is so small that it does not become visible until the magnitude reaches 500000, but the break still does strange things to the inner detail of the area. The name "Near a Mandelbrot" refers to the exponent of Z, which makes the parent fractal nearly but not quite a perfect Mandelbrot set. The rating of 5 means that I am not unusually impressed by the image. The render time of almost 17 minutes is slow, making a download of the completed image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> a wise choice. The clouds cleared unexpectedly on Thursday afternoon, giving the fractal cats an unexpected great afternoon in the holly thicket. For 15-year-old cats, a great afternoon means a peaceful uneventful afternoon, and peaceful it was. When they returned indoors in the evening, a small tuna treat closed their day with a whimper. Today is starting with sun and clouds. It remains to be seen which will prevail. For me the work is rather light, which will give extra time for fractals. The next FOTD will appear in 24 hours. Until then, take care, and if life serves you an apple, make it a napple. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Near_a_Mandelbrot { ; time=0:16:54.64--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.70976131907690630/+0.000002313855428\ 97/3.870999e+007/1/42.5000007756963427/-1.18881678\ 390359014e-007 params=2.00001/0/100000/0 float=y maxiter=4000 inside=0 logmap=395 periodicity=10 colors=000aPTaOUbOVcOWcNXdNYdMZeM_eL`fLafLagK_gKZg\ KYgKXgJWgJVgJUgJTgJSgIRgIQgIPgIOgINgHMgHLgHKgHJgHI\ gGHgGGgGFgGEgGDgFCgFBgFAgF9eC9gF8hH8iK8kM7lO7mR7oT\ 7pW6qY6s_6tb6ud5wg5xi5zj3yk5yk7yl8ylAylBymDxmExmGx\ nHxnJxnKxoMwoNwpPwpQwpSwqTwqVvqWvrYvrZvr`vsavscvsd\ tqcrobpmbnkaliajg`hf`fd_db_b`Z`ZYZXYXVXVUXTSWRQWPO\ VNMVLKUHIZKJUMKPOLLRLGTMCVN7XN3DWh`YWw_JvYOvWTvVXv\ TauSeuQjuPnuNsuMwtNusOtsPsrQqrRpqSoqTnpUlpVkoWjoXh\ nYgnZfm_em`clabkbakc_jdZjeYifXigVhhUhiTgjRgkQflPfm\ OenMeoLdpKisFdpJ_mNWjRRgVNdZIabEZf9bj4fo5gn5fn5dm5\ em6el6dl6ak6fk7cj7Sj7Si7Si8Rh8Rh8Rg8tg9zf9zf9Qe4Od\ 7Pe9QeBQfDRfGRfISgKTgMThPUhRUhTViVViXWi_XjaXjcYkeY\ khZkjZll_ln`mq`msamuanwbnybnx`oxZoxXpxVpxTpxRqxPqx\ NrxLryLsxKrxJrxJrxIrwHqwHqwGqwGqwFqvEpvEpvDpvCpuCo\ uBouBouAou9ot9nt8nt7nt7ns6ms6ms5ms4ms4mr3lr2lr2lr1\ ls0mt0mu0mv0mw0mx0my0mz0m } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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=========================================