; Date: Sun, 27 Jan 2013 19:44:45 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 27-01-13 (The Lost Spiral [7+]) ; Id: <1.5.4.16.20130127194307.3897897e@earthlink.net> ; --------- ; ; FOTD -- January 27, 2013 (Rating 7+) ; ; Fractal visionaries and enthusiasts: ; ; Today's image shows a slice of a spiral that lies in the ; Seahorse Valley area of the Z^2+C Julibrot, a fact that is ; confirmed by the name "The Lost Spiral". But the image holds no ; spiral. Instead, it shows a series of concentric rings which ; break apart into two separate spirals near the center. ; ; So what is wrong here? Where is the spiral? Actually, we are ; looking at a slice of it. Everything in the image is a part of ; the same great spiral, but sliced in an odd direction. Fractal ; spirals are four-dimensional things that twist and turn in ; unimaginable ways, and when sliced in odd directions can produce ; the most unusual cross-sections. ; ; The full 4-D 'object' that is sliced by today's image does not ; actually appear on the screen. It lies in the nearby hyper- ; space. The two small spirals at the center are actually two ; slices of the same hyper-object, which is twisted in 4-D space ; so that today's image slices through it two times, exactly as ; a slice through the center of a single donut would produce two ; apparently separate circles. The outer rings correspond to the ; rings produced by a slice through a set of nested spheres. ; ; The image rates a little over a 7. The plus sign is due to the ; minor math interest, which adds very little to the artistic ; worth. ; ; Incidentally, the image has been stretched and skewed to a ; significant degree to clarify the features. ; ; The coloring detail of the image was created by rendering it ; with the outside set to 'tdis'. ; ; I would be the first to agree that the calculation time of 7-1/2 ; minutes is slow. ; ; Have no worry when nothing appears on the screen for a minute or ; two. It takes a while for the calculation to reach the rings, ; which do not intersect the edges of the frame. All these ; problems can be avoided however by visiting the web sites. ; ; The fastest way to view the spiral fragment is to view it on the ; official FOTD web site at: ; ; ; ; High definition variations are posted at: ; ; ; ; Though with such slow images as we have had recently, there ; might be a delay in calculating and posting them. ; ; The historic back images are available at: ; ; ; ; The day here at Fractal Central began with a very chilly temper- ; ature of +5F -15C. But with clear skies, light winds and an ; unusually strong sun, it rose to an afternoon high of a rather ; pleasant freezing. The fractal cat took full advantage of the ; sun, spending the entire afternoon on his shelf in the southwest ; window. The humans, meanwhile, took it as easy as possible. ; ; The next FOTD will be posted in a minimum of 24 hours, a maximum ; of who knows what. Until whenever arrives, take care, and first ; we have inventions, then the inventions become luxuries, and ; then the luxuries become one more technology-based necessity ; that we could not possibly survive without. ; ; ; Jim Muth ; jimmuth@earthlink.net ; ; ; START PARAMETER FILE======================================= The_Lost_Spiral { ; time=0:07:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t center-mag=-0.09292496257779437/-0.094383497537425\ 95/104097.2/0.01534/-28.0422538333465177/-74.32609\ 02171528954 params=78.41120639667959/58.8488418225\ 6538/89.81383709219642/-44.26099429303873/-0.7537/\ 0/-0.5/0/2/0 float=y maxiter=3600 inside=0 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000Z8eb7bf6_j6Xn5Ur4Rv3Ow7Qz3Lz9IzEFzKDzPAz\ V7z_5yb7ye9xhAxkCwnEwqFvtHvwIpqJkkJfeJ``KWVKRPKGGG\ MKKRONWSRaWUf_Yngkkb`hYQfTFxrRjrSXrTJrU2sZ5rV7qRAq\ OCpKFoGHoDkaKjbHicFhcCfcAfbEfaIe`Me_QdZUdYYdXacWec\ UibTmbSqbRucPscOqdNodMmeLkeKjcMkbNl`Pl_QmYRmXTnVUn\ UWoSXpRYpP_qO`qMarLcrJdsIftGgtFhuDjuCkvBlvJgrRboZY\ lfThnOeuJbn`7lcAkfDjhGikJhmMgpPfsSeuVdxYcz`YyXSxTM\ wPGwMDuPAtS8rV5qY3p_4lU4iP5fK5cF5`A9aDDbGHbJKcMOcP\ SdSQeXVdVZZRaTNcOKcIGcF7cDD`BJR9PG2bI8VKEOMKHJF2NP\ ARZIVhQapUZqYXraUseStiPumLxwNvpOuiQsbRrWSqQQkTOeWM\ _ZLVaJPdHJgFDjE8lEiwGdqI_kJVeLQ_NLUJ3JOGOTTSXeWa`X\ fWXjRYoMYtHZxDZbjiZjkWjmTjoPjqMjsJjtLcuMYvOSwPMxeK\ XuI5xe3pdCicKbcSWb`PbhIapBaxA`rA_l9_f9Za8ZW8YQ0ZM8\ YLGYLOYLWXKcXKkXKrXKs_IsaHsdFsfEshCskBsm9so8mn9hm9\ clAZkAUjBPiBKhCFgCMeFTcHZbJe`LlZNrYPk`NebMZdLTfKMh\ JGjIJdMMZPPUTROWUJ_XDbV9h } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } ; END PARAMETER FILE========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;