; Date: Tue, 22 May 2007 21:25:20 -0400 ; ; To: fractint@mailman.xmission.com ; cc: philofractal@lists.fractalus.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 23-05-07 (Something New [8]) ; ; Id: <1.5.4.16.20070522212952.2bf7af80@pop.mindspring.com> ; --------- ; ; FOTD -- May 23, 2007 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; The four-dimensional HyperMandelbrot set is virtually ignored. ; And why not? Very little totally new stuff is to be found in ; it. But is it actually as devoid of new stuff as would first ; appear? Today's image answers that question with a resounding ; NO! ; ; Today's under-used formula draws the 4-D HyperMandelbrot set, ; and does some strange things with it. I do not fully understand ; all the things this formula does, but one thing is certain. It ; plays some very interesting tricks with the familiar elements of ; the classic Mandelbrot set. ; ; The familiar M-set has been quite well explored, at least down ; to the level where the slow arbitrary-precision math kicks in, ; and most of the features to be found in its upper depths have ; been well investigated. It would be curious indeed if something ; truly new were to be uncovered in this range. ; ; Well, today's image uncovers something totally new. As far as I ; know, nothing like it has ever been found in the familiar two- ; dimensional M-set. Today we are investigating the four-dimen- ; sional Hyper-M-set however, so it is no wonder new things are ; popping up. ; ; I named today's image "Something New" because that's what it is. ; I rated it at an exceptional 8 because it truly is something ; new. The calculation time of 55 seconds is on the P4-2000. On ; the P200 it would take about 3 minutes to finish. ; ; But why not forget inconveniences like calculating parameter ; files? View the finished image on the FOTD web site at: ; ; ; ; With full sun and a temperature of 75F 24C, Tuesday was not ; quite perfect here at Fractal Central; the sky was slightly ; hazy. But despite the lack of a pure blue sky, the day came so ; close to having perfect weather that only a professional weather ; observer would notice the deficiency. ; ; The fractal cats most certainly never noticed the gray haze. ; They were far too busy watching four squirrels that were running ; around in the yard all afternoon. ; ; My day was average. Only the above-average fractal saved it ; from being a dull day. The next FOTD will appear in 24 hours. ; Until then, take care, and reasoning about fractals could be ; unreasonable. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Something_New { ; time=0:00:55.15-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=1 center-mag=-0.11351018609400590/+0.857731703162649\ 10/13846.92/1/-12.5/1.19338289250592311e-011 params=0.33/0.33/1/0/0/5e-015 float=y maxiter=980 inside=0 logmap=40 periodicity=0 colors=000GFp7Jp9LqANrBOrCQsDRsETtFUtGWuHYvIZvJ`wK\ awLcxMdxNfyPhzOjzOkzNlzNmzNnzMmzMkzMizLgyLexLcwK`v\ KYuKVsJSsJQrJOrIMqIKqGGrIJqKLqLNpNPpORpQUoRWoTYoV_\ nWanYdmZfm`hmajlclleqodnlcljbjgahe`eb`c`_aYZ_WYXUX\ VRXTPWRMVOKUMHTKFRGBTIDUJEVKFWLGYMHZNJ_OK`PLbQMcRN\ dSOeTQgURhVSiWTjXUkYVjZWiZXi_Yh_Zg`_g``faaeabebcdb\ dcceccfbdgadh`fgadhabia`jY_iUZiRZhNYhKYgGXgCWf9Wf5\ Ve2Ve2Xc2Yb2Za2_`2a_2bZ2cY2dX2fW2gV2hU2iT2kS2lR2mQ\ 2nP7mRClTHkVMjXQiYVh__gadfcgcchedhgdiheijeilejmfjo\ fjqfkrgktgkugksekrckqako_knYkmWklUkjTkiRkhPkgNkeLk\ dJkcHkbFk`Ek_CkZAkY8kW6kV4kU2nS0kT1hU1eU1bV1_W1XW2\ UX2RY2PY2MZ2J_2G_3D`3Aa37a34b32b3IT9XKEZMG_NH`OJbP\ KcQLdRNfSOgUQhVRjWSkXUlYVnZWo_YpaZrb`scatebwgdyiez\ kgzjfzifzhezgeyfexedwcdvbcuact`cr_brZbrYbrWarVarU`\ rT`rS`rQ_rP_rO_qP`pP`oP`nP`mQakQaiQagQaeRbcRbaRb_R\ bQTcZRbgPapOajX`dd_ZmZTuY } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } ; END PARAMETER FILE========================================= ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint