; Date: Thu, 03 Jun 2010 00:32:50 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 03-06-10 (Square-Root-of-Three Minibrot [8.5]) ; Id: <1.5.4.16.20100603003405.2b57e1a8@pop.mindspring.com> ; --------- ; ; FOTD -- June 03, 2010 (Rating 8.5) ; ; Fractal visionaries and enthusiasts: ; ; The parent fractal of today's image was created by iterating the ; expression Z^(sqrt(3))+C with the MandelbrotBC3 formula at a ; level of 12 turns up the complex logarithmic hyperspiral with ; the 'round' function applied. This parent consists of a large ; circular main bay, with strangely enough, two large period-2 ; buds, one on the northwest shore line, the other on the north- ; east shore, with the whole thing resembling the head of Mickey ; Mouse. Today's scene is located on the western edge of the ; northwest period-2 bud. ; ; The MandelbrotBC3 formula takes advantage of the multi-valued ; nature of the complex logarithm. Unlike the expression Z^2+C, ; which, regardless of the value given real(p2), always draws the ; Mandelbrot set, an expression such as Z^(sqrt(3))+C has no ; single fractal associated with it. It has instead an infinity ; of different fractals, every one of which is the result of itera- ; ting the expression Z^(sqrt(3))+C. Asking which fractal is the ; correct one is meaningless. ; ; Today's image is named "Square-Root-of-Three Minibrot". The ; reason for the name is obvious. The rating of an 8-1/2 might be ; a bit liberal, but I did do some extra work on the coloring, and ; I feel I deserve the reward. ; ; The calculation time of 1-3/4 minutes is well within the comfort ; range for fractal generation. The comfort may be increased yet ; further by surfing out to the FOTD web site at: ; ; ; ; and viewing the image there, already calculated. ; ; Lots of sun and lower humidity made Wednesday a rather pleasant ; day here at Fractal Central. The fractal cats were up and about ; most of the day, getting into various kinds of mischief -- a ; good sign that they approved of the drier conditions, if not the ; higher temperature of 88F 31C. ; ; My day was acceptable, if not great. The next FOTD will be ; posted in 24 hours. Until then, take care, and if you're a ; serf, be faithful to your lord and master. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= SqrtThree_Minibrot { ; time=0:01:45.08-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=round passes=1 center-mag=-0.9914563737440867/+0.4862853210787398\ /1.758179e+011/1/-67.5/0 params=1.732051/0/12/0 float=y maxiter=3000 inside=0 logmap=162 periodicity=6 mathtolerance=0.05/1 colors=0004Kp5Kn6Kl6Kj7Kh8Kf8Kd9Jb9I`9HZ9GX9FV9ET9\ DRzzzzzzzzzzzzzzzzzzzzzzhzzUfzGpzwVzs_mpcDh_JaWPVS\ wUOtLLjCKb7KW2KOFJ000KKIPRHUYGYdG`lLkrOsuQzzS9cU7G\ R5MZ3K`2Jb8NeDQgJTjOWlT_oZbqcethhvagoWgiQfcKfYEeS8\ eM2eG6dRAc`EbkHbuQWqZPngIjrBgz5doBYeHRXMKNSDEX7GZz\ HmzImzMWZPQYSKXVEWY8V_EY`K`aPbiSdpVfwYhlVnbStTQyUS\ uUUqUVmVXiVYeV_aV`ZYXW`UTbQReNOgJMjGJlDHkBzzczzczz\ czzazzUzmUknqgkjjicmgXpeRrgWqh_qicqjgqllpmppntpoxp\ senwOmz6lqJehWZ_hSStLSpKSlJSiISeHSaGSZFSVESSESJRSA\ cS2oMVsNPqNKpNEoN9nI7iE5d94`52W11S72XC2aH2eN2jS2nX\ 2sa2wb7zcBzdFzeJzgNziRukVmmZcrSUvLKzEBz77zC8zG9zLA\ zPAzTBzZCzcDzhDzmHzrLzvPzzTzzSzzRSzQQzPPzONzNLzMKz\ LIzKHzKKzJKzIzzIzzHzzGzzGzzFzzEzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzz8zd8ze8zf8zg9zh9zi9zj\ 9zk9zlAzmAznAzoAzpAzqGzqLzqRzqWzqazqfzqkzqgzrdzr`z\ rYzsVzsRzsOzsLztHztazYjzi } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-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|