; Date: Tue, 19 Oct 2004 09:55:14 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 19-10-04 (The Rage of Poseidon [6]) ; Id: <1.5.4.16.20041019095618.0d6760f4@pop.mindspring.com> ; --------- ; ; FOTD -- October 19, 2004 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; Today we turn to the Halley formula of Fractint, which is one of ; my favorite formulas. It converges on roots of polynomials much ; like the Newton's formulas, but with much more control over the ; appearance of the images. The 'epsilon' parameter controls how ; close to the actual roots the points must come before calcula- ; tion is stopped. The 'relaxation' parameter has nothing to do ; with relaxing after a hard day's work. It controls the amount ; of chaos in the image. A value above one allows more chaos, ; while less than one keeps the chaos under tighter control. An ; imaginary value, such as I used in today's image, twists the ; entire scene. ; ; The colors are determined by the number of iterations needed to ; reach the point where the change is less than the value assigned ; 'epsilon'. The smaller this value, the more iterations will be ; needed, and the greater the opportunity for chaos to sneak in. ; Today's image uses a value of an extremely small 10^(-15), which ; brings out all potential chaos. ; ; In addition to total chaos between roots, some settings of the ; Halley parameters produce total chaos along the borders between ; areas of different numbers of iterations to the same root. This ; is the case in the purplish areas of today's image, where magni- ; fication will reveal that no two adjoining areas actually touch. ; Regardless of the magnitude, there is always chaos along the ; 'borders'. Though it usually consists of only two colors, this ; chaos is interesting in itself. Sometimes, as in today's image, ; it is totally chaotic, while at other times, unexpected geome- ; tric patterns appear. I am not sure whether this chaos is part ; of the formula or an artifact of the math routine, but it is ; curious nevertheless. ; ; One of the early versions of today's image was colored with a ; turquoise theme, and resembled an undersea scene, with air ; bubbles rising toward the surface. I named it "The Rage of ; Poseidon". (If I remember my mythology correctly, Poseidon is ; the god of the sea, who really had it in for Ulysses for ; blinding his cyclops son.) I have since totally changed the ; color scheme to something more like a view down into the pit of ; hell, but I have kept the angry oceanic name. ; ; I would have rated the image at a 7, but I have a certain ; aversion to spirals, of which today's image is a perfect exam- ; ple, so I could rate it no higher than a 6. When the brief ; render time of just under 4 minutes is considered, the overall ; worth equals a humdrum 153. ; ; The image may be rendered from the included parameter file or ; downloaded, already completed, from the FOTD web site at: ; ; ; ; The weather remained uneventful here at Fractal Central on ; Monday. The partly sunny skies and temperature of 59F 15C were ; barely good enough to meet the quality standards of the fractal ; cats, who spent less than an hour lounging testily in the yard. ; Things will be no better for the duo today, since it is ; starting wet and chilly. They will not like this. ; ; The next FOTD is but 24 hours away. Until then, take care, and ; don't surrender to fractal terrorism. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Rage_of_Poseidon { ; time=0:03:54.98--SF5 on a P200 reset=2003 type=halley passes=1 center-mag=14.1471\ /8.14196/0.03333333 params=12/0.9/1e-015/0.59 float=y maxiter=95 bailout=9 symmetry=none inside=bof61 logmap=yes periodicity=0 colors=000pfC_lPZkPXjQWhQVgQUeRTdRJeWScR_aMg`IeYLd\ VNcSQbPSaMV`JX_G_ZDaYAdX7fX2jW4hW6gW8fWAeWCdWEcVGb\ VIaVK`VM_VOZVQYVRXXSWZTV`UUbVTdWSfXRhYQjZQl_Pn`Opa\ NrbMtcLvdKxeJzeJxgIvhHtiGsjFrkEwlAzmKznUzoczpmzqwz\ zzzzzzzzzzzzzzzzwzzmzzczwUzrLzmMzhMzcNzcNzcNwYOtKO\ qEPnAOkANhANcAM_1LX4OW6QW8SXBVXEXYHZZLaZOc_Re_Vh`Y\ kaanafrbjudnzbox`owZovXotWosUorSoqQooOonNomLokJojH\ oiEqiGohHngJmfKleMjdNicPhbQgbSfaTd`Vc_WbZYaYZ_X`ZW\ aYWcXVdWUfUTgTSiSRjRQkQQiRPgRPeRPdRPbRP`RO_ROYROWR\ OVROTRNRRNQRNORNMRNLRNOSQRSSUSVXSX_S_bSa_U`XV`VW`S\ X`QY`NZ`L``Ia`Gb`Dc`Bd`8e`6f`5f`4fa3fa2fa2fa5g`7g_\ AhZChYEiXHiWJjWMjVOjUQkTTkSVlRYlRyqH_mQamPdnOfnNin\ MkoMmoLppKrpJuqIwqHfW7gX8gX8gX8gX8gY8hY8hY8hY8hY8h\ Z8hZ9iZ9iZ9iZ9i_9i_9j_9j_9j_9j`9j`9j`Ak`Ak`AkaAkaA\ kaAkaAlaAlbAlbAlbAlbBmbBmcBmcBmcBmcBmdBndBndBndBnd\ CneCneCoeCoeCoeCofCofCpfC } ; END PARAMETER FILE========================================= ; ;