; Date: Wed, 23 Jul 2008 22:36:28 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 24-07-08 (Ratcheting Onward [6]) ; ; Id: <1.5.4.16.20080723223655.21571320@pop.mindspring.com> ; --------- ; ; FOTD -- July 24, 2008 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; I have made a decision to stay more on topic. Starting today I ; will no longer post a copy of the FOTD to the philofractal list. ; Except for the FOTD, the philofractal list has been dead for ; years. ; ; The topic of the Fractint list is fractals, not my ideas about ; God, science, or the paranormal. There are quite a few forums ; where these things are eagerly and properly discussed. And I'm ; not too sure of the importance of the daily weather report from ; central Pennsylvania, which can always be found on the internet. ; If the goofy fractal cats do anything exceptionally goofy, I'll ; tell about it however. (Yes, FL did have something to do with ; my decision to stick more to the topic.) ; ; Today's image shows some of the unexpected stuff that goes on in ; the fractals created by the formula Z^(1.075)+C. The most ; surprising thing about these almost-linear fractals is that they ; actually contain fiercely detailed Minibrots, which can be ; easily found with my 'secret' method of finding minibrots. ; ; One of these unlikely minibrots lies at the center of today's ; image, at the very limit of resolution. I have not gone deep ; enough to make the minibrot visible in today's image because at ; that depth, the surrounding pattern breaks down into near total ; chaos. ; ; At the modest magnitude of today's image, the pattern is far ; more interesting, rather resembling a ratchet wheel surrounded ; by a lacy network of lightning. I named the image "Ratcheting ; Onward" because of the ratchet pattern. This heavily fractured, ; circular effect is typical of the minibrots in fractals of such ; a low order. ; ; The rating of a 6 is what I think the image deserves. The ; calculation time of 1-2/3 minutes is a real bargain. An equal ; bargain may be found at the FOTD web site at: ; ; ; ; where the finished GIF image is posted. ; ; Until next time, take care, and keep a stiff upper fractal. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Ratcheting_Onward { ; time=0:01:41.60-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=-14.94607802098338/-2.324758141946301/\ 8252035/1/-162.5/0 params=1.075/0/18/1500 float=y maxiter=1800 inside=0 logmap=131 periodicity=10 colors=0009G06H0AI6DJFHDKKKZOPdRVmUfuZitzksonrwnqz\ uphVsZ9uX8pV7lU7hS6dR6`P5XU5Tc6Nm6Zr6Zz6Zz6ZIlq3Wp\ BafIguPmuWruVzuUzuTluShuRhuQfuPduOcuPiuQnuRsuOmuMg\ uKUuLUuMUuNUuPUuQUuRUuSUuTUuVUuWUuXUuYUu_Uu`UuaUub\ ZucZueYufXugWuhVuiUukTulcUmcVncVpcWqcXrcXscYtcYvcZ\ wc_xc_yc`zc`ycaycaycbycbyccxccxccxcdxcdxcewcewcfwc\ fwcfwcgwcgvchvchvchvcivciucjucjuckuckuckucltIltImt\ ImtIntInsInsIosIosIpsIptHqsIpsIpsIprIprIprIorIoqJo\ qJoqJoqJopJnpJnpJnpKnoKnoKnoKmoKmnKmnKmnLmmLlmLlmL\ lmLllLllLllMklMkkMkkMkkMkkMkjMjjNjjNjjNjiNjiNiiNih\ NihOihOihOigOhgOhgOhgOhfPhfPhfPgfPgePgePgePgfIkePg\ eVcda_dgWcnSctOczKbZ8a60b70c80d91dA3eB5fB7fC9gDBhE\ DhFFiFHjGJjHLkINlJPlKRmKTnLVnMXoNZpO`pOamPbjQbhRbe\ SccSc`TcYUdWVdTWdRWeOXeMYeJZfG_fE_fB`g9ag6bg1bf3bg\ 4bg6bg7bg8bgAbgBbgCbgEbgFbgHbgIbgJbhLbhMbhNbhPbhQb\ hRbhTbhUbhWbhXbhYbh_bh`bi } 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|