FOTD 12-02-04 (Unwatched Watchtower [4])
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==================================
Subject-Was: Re: [Fractint] FOTD 12-02-04 (Unwatched Watchtower [4]) I'm not sure that I understand the comments about para, obl, rect and elip. Trying to integrate Julia with Mandelbrot in some fashion, I understand -- Mandelbrot types jenerally hav more control over the inside of the set or the jeneral shape of the imaje -- Julias are more pleasing. I _was_ going to point out the difficulties in that. Instead, I started with this: z=z^((1,1)/pixel) +c as a theory and something much more interestig by the time I was done imitating most of the usual flexibility. I apologize for the APPLICATION/octet-stream, but Application/XFractint isn't rejistered on this system as a mimetype, yet, and no, I don't think it should hav a dash in it. It's open-source, so there aren't any worries about source-leakage causing viruses. As a final note, I call the map diag. It still makes more noise than a simple gray-scale with outside=atan, but at least it highlights the fact that the maximal difference is between an inside point and a point that escapes on the first iteration. _______ My Cat, Bogus, who died in a mysterious accident involving a slej hammer and a blander shall remain nameless in the interests of covering up his part in the public misinformation campaign for acquiring control of Iraq.
On Fri, 13 Feb 2004, SherLok Merfy wrote:
I apologize for the APPLICATION/octet-stream, but Application/XFractint isn't rejistered on this system as a mimetype, yet, and no, I don't think it should hav a dash in it. It's open-source, so there aren't any worries about source-leakage causing viruses.
Come to think of it, TEXT/XFractint might work nicely for visibility of the comments. Ideally, any program that didn't know the best way to display a particular kind of ASCII would hav a default mode.
This is a 16 colour B&W, but it won't work in a 16 colour mode, because the map is more complicated. Like I said elsewhere, this is part of a project, so jenerating an inaccurate fractal was not my intention. My little formal training in computing told mee that sometimes accuracy involves iterations on the function that is in the CPU. The Sine is a case in point. I rekt an assignment over a decade ago, because I discovered that IBM 370s hav not two, but three levels of precision: single, double, and extended. In fact, the textbook, in equating double with extended, was more confused than I was. On a tanjent, you may hav noticed that I _don't_ spel. For me, spelling reform is no where near the political topic it was for Webster. And in case your interested, Mark Twain, Benjamin Franklin, and G. Bernard Shaw were all spelling reformers and vejetarians. Shaw commissioned a set of glyphs to encouraje phonetic spelling. Franklin re-ordered the alphabet to highlight the most similar sounds, and Twain tried to sell the public on a font. I'v bn tld tht my own font resembles Cree. And I gather that this is _phonetic_ Cree (It has some very strong hints for the deaf who wish to speak, especially if the _map_ is as good as mine). Speaking of the essential map that lets humdrum fractals look decent... Some skipping (erroneous inclusions to the inside set) are in this that tesseral makes good work of, yet passes=1 doesn't help, nor does arbitrary precision. [Maybe symmetry should go in the parameter file, instead of dhu formula, along with BFDIGITS, because a lot of formulas _can_ hav symmetries.]. I figure that as long as old versions know well enough to ignore parameters dhat dhey don't understand, dhen dhe backward compatibility issues hav been addressed, here, bt furdher along the path you'll remember the mess that is Ingglish speling is nicely summed in a name for the letter Guu that also fits a very neat pattern for names of the letters that are like "Alpha, Tango, Zuuluu" in one syllable. I orijinally hit upon something much more elaborate for Clubs with the same formula, but I couldn't make it work in black and white. Well...maybe I could, but I doubt that it will make the production. (That's funny...sometimes my Telco skips what I should be skipping in my speling). Now, by "same formula", I'm not referring to what I might write in V19.6, which had a neg function. It didn't work in the formulas, because you were supposed to use the minus sign for everything but parameters. A backward compatibility issue _is_ when you fail to support old parameter files, to say nothing of the fact that this formula may seem unworkable with the minus sign as a constant. _______ Animal, Vejtable, Mineral, Tool: Six 9-up, double-sided pages of glossy card paper for twenty questions -- $18 for the first copy -- less than $2/each for lithography. Some people aren't sure whether computers are more like animals or minerals. Any comp-Sci would likely put them in the vejtabl category, but the only clear category for them and the programs they run is tool.
participants (2)
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Jim Muth -
SherLok Merfy