; Date: Thu, 12 Feb 2004 10:08:17 -0500 ; From: Jim Muth ; Subject: [Fractint] FOTD 12-02-04 (Unwatched Watchtower [4]) ; Id: <1.5.4.16.20040212101050.2a9f988e@pop.mindspring.com> ; --------- ; ; FOTD -- February 12, 2004 (Rating 4) ; ; Fractal visionaries and enthusiasts: ; ; What evil has befallen the splendid midget that appeared as ; yesterday's FOTD? Where we once had a lovely, perfectly ; symmetrical pattern, we now have a mis-shapen, distorted thing ; that is downright stressful to look at. I have used the same ; color palette, so what could have caused this abomination? ; ; Actually nothing evil was done to the glorious scene of ; yesterday. I simply shifted my point of view, took a ; 'photograph' of the same scene from a different direction, ; and named the picture "Unwatched Watchtower". ; ; As I have said often in the past, the Mandelbrot set, the ; perturbed M-sets and the Julia sets are slices of a single ; four-dimensional object known as the Julibrot. Since this ; Julibrot object is four-dimensional, it may be sliced in new ; ways that produce neither Julia nor Mandelbrot sets, but ; entirely new aspects of the familiar Julia and Mandelbrot ; scenes. Today's image illustrates what happens to yesterday's ; "Watchtower" image when it is seen from one of these new ; directions. ; ; Some slices taken in new directions reveal aspects that are ; virtually the same as the familiar Julia and Mandelbrot aspects; ; other slices reveal grossly stretched and distorted aspects such ; as we have in today's image. In order to fully comprehend why ; this is so, it would be necessary to visualize the entire inside ; of the Julibrot, which would be difficult for even a four- ; dimensional person, not to mention a mere three-dimensional one. ; ; To try to understand what is happening in images such as today's ; I reduce the problem to three dimensions and imagine taking a ; blob of white silly-putty and a blob of black silly putty, and ; combining them into a single lump. Then I knead the lump ; slightly, so that the black and white putties just start to ; blend, forming well-defined arms and filaments that twist and ; turn through the interior of the combined blob. Then I cut the ; combined blob in half to reveal inside features much like those ; in today's image. The features have not really been stretched, ; the apparent stretching is due to the angle at which some of the ; twisting and turning features have been sliced. ; ; All this stretching and distorting has taken its toll on the ; superb original image. Today's version is worth no more than a ; humble 4, which equals slightly below average. Considering the ; render time of 7-1/2 minutes, this results in an overall value ; of 52. The 7-1/2 minute wait while the parameter file runs can ; be avoided by downloading the completed GIF image from Paul's ; web site at: ; ; ; ; The weather on Wednesday here at Fractal Central was very ; average, with lots of sun but a chilly temperature of 39F 4C. ; The cats' behavior was also very average. After an uneventful ; hour in the yard, they came inside and settled by the heat for a ; long sleep. Today is starting cloudy and cold, with snow not ; far to the south. As long as it stays to the south, the cats ; will not be worried. ; ; My only concern is to get the waiting work finished, a task that ; will take about two hours to accomplish. Then I'll see what I ; can find in Fractal Land. The best of what I find will appear ; as tomorrow's FOTD. Until then, take care, and watch for ; lurking Julibrots. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ UnwatchedWatchtowr { ; time=0:07:39.12--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000000227835/+0.000000000001655\ 24/9.466954e+011/0.07488/-42.1987606685050665/-86.\ 2801728293503629 params=19.055/-104.667/2/0/-1.861\ 19088257009/0.000407298011669/-1.86119088257009/0.\ 000407298011669 float=y maxiter=7500 inside=0 periodicity=10 colors=000NleRuhVzkTzlRxmQunOroMopL\ lpJiqIgrGdsEatDZtBWu9Tv8Qw6Nx5LxJT_W_CUZGTZJRZMQZP\ OZSNYWLYZKYaIYdHYgFXdEXbDW_CWYBWVAVT9VQ8VO7UL6UJ5U\ H5UI5TJ5TJ7JY7JY7JY7JY7KY7KY7KY7KY7KY6LX6LX6LX6LX6\ MX6MX6MX6MX6NX6NX6NX6NX6NXyHvwIuvItuIttIssIsrIrqIr\ oIqnJqmJplJpkJojJoiJngJnfJmeKldKlcKkbKkaKj_KjZKiYK\ iXLhWLhVLgULgSLfAAAAAAAAAAAAAAAAAAAEAAEAAEAAEAAEAA\ EBAECAEDAEEAEFAEGAEHAEIAEJAEKAELCEMFENIEPLGROIURKW\ UM_WOcZNicMnhLrmOwrRywUzzWwwbrrgmmjhmmcmoZmqUmsUnu\ WowYqyZsz`uzawzbuvbrqbmlchgcc`cZYcUVdPTeNRfRPgWNh_\ LicJjgHklFlpDmtBnx9nvHdtPVsXMqdCpl3kk6fj9aiCYhFTgH\ OfKKeNFdQAcT6cV7bW7aX8`X8_Y9ZZ9YZAX_AX`BW`BVaCUbCT\ bDScDRdDRdFVgGYiHakIdmJhoKkqLgmMcjN_gOWdPSaQOZRKWS\ GTTCQU8NU5KSISRU_PfgOrnNsoNspNsqNsrMssMstMttMtuLtv\ LtwLtxLtyLtyNnvOitPdrQZpRUnSPkTJiUEgV9eW4c87mEEmKL\ mQSmWZmadmYajV_hRXfOVdLSaHQ_ENYBLWFV_Jcb } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } ; END PARAMETER FILE================================== ;