; Date: Fri, 23 Mar 2007 21:29:43 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 24-03-07 (FOTD for Mar 24, 2007 [No Rating) ; ; Id: <1.5.4.16.20070323203318.38b75f66@pop.mindspring.com> ; --------- ; ; FOTD -- March 24, 2007 (No Rating) ; ; Fractal visionaries and enthusiasts: ; ; I keep trying to find things in the Mandeloids with an exponent ; of Z between 1 and 2. I have never had much success, but I just ; can't seem to give up. Today's un-named and unrated image lies ; in the Z^(sqrt(2))+C Mandeloid as it appears 54 levels up the ; logarithmic ladder. ; ; At this level, the parent Mandeloid resembles a bent mushroom, ; with its cap on the northeast side and its bent stem jutting out ; toward the southwest. Today's image is located in a filament ; extending from a small distorted bud sitting on the top of the ; mushroom's cap. ; ; The image was created with the MandelbrotBC2 formula, the second ; most useful formula in my collection. This formula takes advan- ; tage of the multi-valued nature of the complex log function. It ; calculates a virtually limitless number of the fractals that the ; infinity of possible log values can create. ; ; In my experience, I found that the most interesting fractals ; result when the exponent of Z is set to a value between one and ; two. The value of today's exponent happens to be the square ; root of two. I often use significant numbers such as square and ; cube roots as exponents. It doesn't make much of a difference ; in the finished product, but it adds a bit of fun. ; ; The value given real(p2) determines the level of the logarithmic ; ladder at which the formula will be calculated. I have found ; that with this parameter, one guess is as good as another. The ; exception is a value of PI, which calculates the ground level of ; the formula. ; ; Today's image may have no name or rating, but it makes up for ; this lack by its speed. The included parameter file calculates ; in only 2 minutes, about the same time required to visit the ; FOTD web site at: ; ; ; ; and view the finished image there. ; ; Heavy clouds and light rain kept a damper on outdoor things here ; at Fractal Central on Friday. The temperature of 54F 12C was ; within reason, but few people ventured outside to enjoy it. The ; fractal cats spent most of the day washing each other's faces. ; Indoor cats usually do not concern themselves with weather. ; ; My day was rather busy. Unless something unexpected comes up ; however, the rush should be ended by next week. The next FOTD ; will be posted at this same spot in 24 hours. Until then, take ; care, and be vigilant. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= FOTD_for_Mar_24_07 { ; time=0:02:04.96--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 center-mag=+0.4068061806\ 1157590/+0.56106825018401520/60085.32/1/117.5/-2.2\ 9250507466360887e-011 params=1.4142/0/54/0 float=y maxiter=2500 inside=0 periodicity=10 colors=000oS_oTYpUWpVUmTVjRVhPWeNWcLWbP_bTbbXeb`hb\ ckYbfTaaO`YJ_TEZP9YK5YGFXHOXHYXIfXIpXJyXJzRQzLXwKQ\ tJJqIDmH6jG0gF0eG0cH6aIC_JIYKPWLVUM`TMfHJa6HY8QeAY\ mGWWMUEST0WW4_ZBcaHgcOkfUoi`skfmf_gaTaXNWSGROAYL8d\ I7kF6rC5yA4wF6vK8tOAsTCrXEcg6Qr0Cz0Jx0Qt5P`OOHfPJe\ PLdQMdQOcRPcRRbRSbU_PWfB4ziCv`JrTQnLXiCce2ja0_e9Qc\ 8TZ7XW6_O6XHLUA_S4cP8`NCZLFWJJTHNUFQQFQKFQUFQKFQJF\ QQFQXFQcFQjFQgbIe_IcYHa000000000000000000000000000\ 000000000000000000000000000000J_HPcFVgD`kBQn9Rr7Up\ BXnFpzIbkMpzPhgTkfWpzQpzKRtEmz8mz3XfFnKQYSPI_OPVOz\ QO`MOaQMzTKbXIz_GzbEdfCziAzl8zg7nc7TjC7pHzoLLnPRmT\ YlXdk`jjdqihwilmh_dgNWgA`e4ec0jb0ga0d`0a_0Z_1WZ3TY\ 5QX7NX9SbFXhLanQftWjz`fuWbqSZmOWjKwzEwz8wz2wz0wy1w\ z6wuBwzGwzKwgJwzJqPIsFIt6IuBKuGLuLMuQNuVOu_PucQdgZ\ Pkg9opKbhUR`xuVzvQzxMzyIrzNhoSZjXPeaF`f5WjCjjJxjqF\ BhGG_HLSIQJJVBK_mPfnQcnRa } 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|