; Date: Wed, 21 Sep 2011 22:12:03 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 21-09-11 (Crack in the World [7]) ; Id: <1.5.4.16.20110921221201.13b771f8@pop.earthlink.net> ; --------- ; ; FOTD -- September 21, 2011 (Rating 7) ; ; Fractal visionaries and enthusiasts: ; ; Today's image is named "Crack in the World", meaning the world ; of fractals. The name points out that the scene is located very ; near the negative X-axis of its parent fractal, where everything ; is broken apart. This parent was created when I calculated the ; expression Z^(2.01)+C at a level 11 turns up the logarithmic ; hyper-spiral with the 'floor' function applied. (Actually, I ; think the 'floor' function gives the most accurate values of the ; multi-valued complex logarithm, but it would take a better ; mathematician than me to figure it all out.) ; ; The parent fractal is a distorted Mandelbrot set rotated about ; 15 degrees clockwise, so that the southern branch of Seahorse ; Valley intersects the negative X-axis. Today's scene is located ; near this point of intersection. ; ; With its inward-jutting low-iteration elements, the image ; appears as though it is very near the bailout cut-off point. ; Actually, it is very near the X-axis, which serves as a cut-off ; point in the image. ; ; The rating of a 7 is perfectly average. ; ; The calculation time of 5 minutes is a bit slower than I would ; have preferred, but still brief enough to make the calculation ; no more than a minor annoyance. ; ; All the calculation problems may be avoided by viewing and ; hopefully enjoying the finished image on the official FOTD web ; site at: ; ; ; ; And check the high-definition version at: ; ; ; ; The classic FOTD site may be accessed at: ; ; ; ; Heavy clouds kept an all-day damper on things here at Fractal ; Central today. The temperature of 73F 23C was pleasant enough, ; at least for the fractal cats, who approved of the lack of rain ; as they enjoyed the outdoors from indoors. ; ; My day was uneventful, which makes dull reading but a pleasant ; experience. FL had a more active day with black-spot infested ; roses. The next FOTD will be posted in 24 hours. Until then, ; take care, and be ever alert for charlatans. ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= Crack_in_the_World { ; time=0:05:02.53-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=floor center-mag=-0.8068576369195436/+0.0000047645303079\ /2.951255e+008/1/-67.5/0 params=2.01/0/11/0 float=y maxiter=7200 inside=0 periodicity=6 colors=000424CCzlwzzzzGK8R0OK0ID0C606vtgjhZZYQNMHB\ B899AG02EjjFbiFViGNhHFgH8gNBjTDmYFoRGmLHlFIj9Ji3AA\ DPdMTaWXZd`VndSwhPmbOdXOVRNMLNCFM3AM5KO7UP8ccAmmBw\ SBHuj5gm6ao6Xr6Rt6Mv6Hg4C745T38E14HXFERCBMA8G75B52\ 52bGpJ8QWokRgdM`YITRDMK9ED476B49836524212mzT1zO1VJ\ 1NE0F9074h6zX4jM3VB1FXTXOLOGEG878VzHKeBAL5alFS_BJO\ 79C3gBP`9LV7HP6EI4AC37689ACFBAAJ9XFEQBHK7BD356nzPf\ qL_hHT_ELRAEI7793nZOaQIPHCC86UgZKTNAEBzPjeGVL8FDif\ 6NL68G348Z5BU49P37K26F24A135016gQ4XJ3MD1B6rkST6gL4\ XE3M71BtQChK9YF7MA4B52Wb0RX0MR0IM0DG09B0450nzAYe6H\ L3Dxq8c_4KIpi`ZUOHFCoq2fh1Y_1QR1HI0890nyGgqEaiCVaA\ PV8JN6CF4672vS4lN3bI2TE2J91940sRE`I9I94K39H27F26C1\ 5A14713502201KI1JwlCcW6KGcekZ_eUV_PQUEFIFFIAAC556o\ EzQ7VNyUJnPFdKBVF7KA3A50sJ0lG0eE0Zm0S90L70E4072efX\ XYQPPJGHD886`07R05I03901IrEFhBC_99R76I4392c3sX2iQ2\ `K1SD1I609OEQKBLG9HC7D848 } 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|