; Date: Sat, 08 Feb 2003 10:10:10 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 08-02-03 (Lava-Ring [5]) ; Id: <1.5.4.16.20030208101318.391fa0c6@pop.mindspring.com> ; --------- ; FOTD -- February 08, 2003 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; Today's image is yet another of my evaporated ones, created this ; time by subtracting a portion of Z^(-7.17) from an equal portion ; of Z^(-1.717) before adding 1/C. The scene was then ; 'evaporated' by raising the bailout radius to one-googol and ; rendering the resulting blank screen with the inside option set ; to < bof61 >. ; ; The real(p3) parameter is so awkward because its value was ; determined using the evolver feature. I use this feature in my ; fractal travels more often than is apparent, but in most cases I ; round off the value to something more aesthetic. In today's ; case, I was searching for the point where the entire fractal ; expands to infinity and returns from the opposite direction, and ; once I had found this point with the evolver, I did not bother ; with the rounding. ; ; Infinity is a curious concept, in some ways quite counter- ; intuitive. The arithmetic of infinity is very simple -- ; regardless of what is done to it, infinity remains unchanged. ; When geometry is expanded to infinity, some even more surprising ; things happen. An infinitely long line has a single point at ; infinity. It does not have the two points that intuition would ; demand. ; ; This can be better understood by thinking of two infinitely long ; parallel lines lying in a flat Euclidian plane, which can be ; considered either as never intersecting or as intersecting at ; infinity. (This is two different ways of saying the same ; thing.) Then imagine a finite point where the two lines ; intersect. It is only a single point, but as the lines are ; rotated, this point of intersection moves off in one direction, ; reaches infinity, then returns from the opposite direction. The ; point at infinity of the line lies in both directions. At no ; time during the rotation does a second point of intersection ; magically appear. ; ; The same situation prevails with an infinite plane, which has a ; straight line at infinity. Points that go off in any one ; direction and pass beyond infinity return from the opposite ; direction. (Actually, we're getting into projective geometry, ; and such a plane is actually a projective plane, but that's a ; different topic.) ; ; I named today's image "Lava-Ring". If enough imagination is ; used, the boiling pit of molten lava can actually be seen. But ; since molten lava is not my favorite substance, I could rate the ; resulting image no higher than a 5. The 24-minute render time ; also holds down the rating, but this wait can be avoided by ; downloading the completed GIF image from: ; ; ; ; or from: ; ; ; ; The snow ended by noon on Friday, but the damage had already ; been done. With 8 inches 20cm of ice-crystals covering the ; yard, and a temperature around freezing, the fractal cats were ; confined to the near side of the porch, under the cover, where ; only a dusting of snow had settled. With such cramped quarters ; and cold paws, they stayed outside only a few minutes. The snow ; is still there this morning, so I suppose it will be another bad ; day for the aging duo. ; ; For me, it will be a passable day, but only if the small amount ; of work goes well. But regardless of how the work goes, I shall ; return in 24 hours with the next in the near-eternal series of ; fractals. Until then, take care, and be kind to web-footed ; fractals. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ Lava-Ring { ; time=0:24:05.69--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.79396508590478570/+0.640345353073420\ 90/5.261436e+008/1/-15/1.94124406955459294e-006 params=-1/-1.717/1/-7.17/-5.453445844904936/1e+100 float=y maxiter=1200 inside=bof61 logmap=122 periodicity=10 colors=00000X34A3JD3Fc3AQ36f9A`DDXIGSMJOSMJXPF`S9d\ V4jY0o`0sc0xf0za0s_0vX0oS0lP0vM0YI0lF0PC0V70_40P10\ V00T00Q01P01Q09Q3FQALSIQSPXSYcTfiTooTxuTzzSzxSvuSr\ rSmoSlmXgi_cfc_afV_jQVmOSpJOuFLxAGz6Dz19z06z7CzGGz\ PMzXQydVxm`vvduzixufylczd`zXYzOVzGTxJPoLMgMJ_OGQPD\ JQAAS73T44V76YA6_C7`F7cG9dJ9fLGdTOd`Vdgadogdvfcsdf\ pcimall`ri_vfYmcQzaJraJzaJzaJzaJmcJzcJzcJzcJzcJzcJ\ mcJmcJzcJmcJzcJzcJzcJzcJzcJzcJmcImdIzdImdIzdIzdIzd\ ImdIzfIzfIzfIzfImfIzfIzfIzfIygIygIygIxgIxgIxgIvgIv\ gIviIuiIuiIuiIsiIsiIsiIriGrjGrjGpjGpjGpjGojGojGolG\ mlGmlGmlGllGllGclGjlGjmGjmGimGimGimGgmGgmGgmGfoGfo\ GfoGdoGdoGdoGcoGcoFcpFapFapFapF`pF`pF`pF_rF_rF_rFY\ rFYrFYrFXrFXrFXsFVsFVsFVsFTsFTsFTsFSsFSuFSuFQuFQuF\ QuFPuFQuFTsDXoC_gAa`9dT7gM0jF0iC0fG0dL0cP1`V3__4Yc\ 7VgFTlMTpTTr`TsgTuoTusTuxTszVjzXazYTzYMz_Dz`4z`0z`\ 0y`0CmYAlX7jT4iS3gQ3aT3YV } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } ; END PARAMETER FILE================================== ; ;