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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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|<a } END PARAMETER FILE=========================================