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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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 20.0 PAR-FORMULA 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 20.0 PAR-FORMULA FILE==================================