; Date: Sat, 26 Jul 2008 19:19:26 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 27-07-08 (The Limbo Factor [6]) ; ; Id: <1.5.4.16.20080726191956.2b574a7e@pop.mindspring.com> ; --------- ; ; FOTD -- July 27, 2008 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; In today's image I tried to go down to an exponential level only ; half as far from unity as yesterday's exponent of 1.0125. But I ; could find nothing of interest in the fractals with an exponent ; of 1.00625, so I tried an exponent of 1.009375, which is 3/4 as ; far from unity as yesterday's 'forest floor' image. ; ; The searching down there was difficult, minibrots were nowhere ; to be found, but I finally found an interesting patch of chaos ; in the Z^(1.009375)+C Mandeloid fractal right at ground level of ; the complex hyper-ladder. Today's image shows a small sample of ; that interesting chaos. ; ; To me, the most amazing thing with the image is that the graph ; of its generating expression is virtually a straight line. But ; even such a tiny departure from straightness can do unexpectedly ; intricate things when iterated a sufficient number of times. ; ; In today's image we have areas of near total chaos, areas that ; are totally featureless, as well as areas of fractal patterns ; that repeat at ever smaller scales. There are also several dis- ; tinct fractal themes in the image. Despite the ridiculous expo- ; nent, today's fractal image is as fractal as any fractal could ; be. ; ; I named today's image "The Limbo Factor". After all, the point ; of the Limbo is to go as low as possible. Then I rated it at a ; 6. My inability to find a minibrot in the parent fractal cost ; the image at least one whole rating point. ; ; The calculation time of under 4 minutes on a computer running at ; 2000mhz is reasonably brief. And the trip to the FOTD web site ; at: ; ; ; ; to view the finished image there can be equally brief, if not ; briefer. ; ; The next FOTD will be posted in 24 hours. Until then, take ; care, and view the world through fractal-colored glasses. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= The_Limbo_Factor { ; time=0:04:54.34-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-10.29306825/+0.0410706/163.76/1/142.5/0 params=1.009375/0/0/3500 float=y maxiter=16000 inside=0 logmap=456 periodicity=10 colors=000KBULBUM9UN9UO8UP8UQ8TR6SS6TT4RU4RU4RU2PU\ 2NU1NU1MU1MU0KU0IU0IU0HU0FU0FU0DU0BU0DU0DU0FU1FU4F\ U6HU9HUBIVDIVHIXIKXMKXNMYRMYSMYUN_XN_YP_aPabPafRbg\ RbiSblSdmSdpUdrUfuVfvVbvSdxUfxVgxXgyXiyYjy_jy_lzam\ zbozdozdpzfrzgrzgpslojomarmSulIxj8zg0zi0zj0zj2zl4z\ l8ymBxoFvoHupKspNrrRpsSosVmuYluajvbixfgxifyldymbzp\ azs_zvYzxXzzVzzUzzSzzRzzPzzNzzMzzKzzMzzNzzPzzRzzSz\ zUyzVxzXvzYuz_sz_rzapyboxdmvflugjsiirjgplfomdmmblo\ ajp_irYgsXfuVdvUbxSayR_zKVzNXzPYzS_zVYzU_zS_zRazPa\ zNazMbzKbzIbzHdzFdzDdzBfz9fx8fv6gs4gp2ip1ip0ip0jp0\ jp0jp0lp0lp0lp0mp0mp0mp0lr0lr0jr0js0is0is1gs4gu6fu\ 8fuBdvDdvFbvHbvKaxMaxN_xR_ySYyUYyVXyYXz_VzaVzdUzbV\ zbVzbVxbVubVrbVpbVmaXjaXgaXdaXbaX_aXXaXU_YR_YP_YM_\ YI_YF_YBgV1bX6_Y9XYDU_HR_KNaNKaRHbUDbX9d_6db2ff0gg\ 0fi0fi0fi1fj1fj1dj1dj2dl2dl0Kl0Km0Mo0Km0Kl0Il0Ij0I\ i0Hi1Hg1Ff2Ff2Fd4Dd4Db6Ba } 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|