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Re: [Fractint] FOTD 08-08-02 (Odd Mandelbrot [5])
by Jim Muth 11 Aug '02

11 Aug '02

At 05:11 PM 8/10/02 +1200, Morgan Owens wrote: >At 03:02 10/08/2002, John Wilson wrote: > >>Whoah! That's a real blow below the belt. I am anxiously awaiting >>replies from the mathematicians, but shouldn't this be in the Philofractal >>list?. >> >>John W. > >Perhaps, but Jim would probably complain that it's not "irrationally >mystical" enough. It's the Philofractal list after all, not the >"scientifractal" one. This topic *should* be on the philofractal list, but I suspect that Morgan no longer subscribes to that list. Can't take irrationality and mysticism, I assume. Jim M.

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Hypergeometry
by Andrew Coppin 10 Aug '02

10 Aug '02

Hi folks. I realise that this subject is perhaps *a little* off topic, but I'm posting it here in case anyone else is interested. Jim's talking about the 4th dimension got me thinking... I want to do projections and slices of 4D shapes. But I don't have the software... A while back I managed to write a program to do wireframe projections of 4D figures. It wasn't all that good really! So I sat down and wondered if I could adapt my raytracer to draw 3D slices... But today I managed to get good old POV-Ray to draw it for me! Just took a bit of algebra shifting! A hypercube is the intersection of 8 hyperplanes. Each one is given by ax + by + cz + dw - e <= 0. To convert these into standard POVRay planes (ax + by + cz - f <= 0), just select a value for W, then f = dW + e. Now do a CSG intersection of all 8 planes and bob's your uncle! (Actually my uncle's name is John, but hey...) As I type this I'm doing some animations of various slices. This is where I need some help... I can get the slices to look like ordinary cubes (which vanish/appear at certain W values), but that's not vary exciting. If you cut a normal cube across a corner, you get a triangular section (rather than square). I managed to get a prism-shaped cross section out of my hypercube (by doing a 45 degree YW rotation), but how do I rotate the hypercube so that one of its corners faces along the W axis? (The hypercube starts out aligned to the coordinate axies.) Secondly, what other interesting 4D polyhedrons (?!) are there, and how do I construct them? Thanks folks! Andrew. PS. I say again, if anyone wants to see the POVRay files or just chat about the math, feel free to email me off list (or on list if enough people are interested...) PPS. I'd love to post pictures, but A) no binaries on a mailing list, and B) the animations are a tad TOO BIG to be emailing around anyway! _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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FOTD 08-08-02 (Odd Mandelbrot [5])
by Jim Muth 10 Aug '02

10 Aug '02

FOTD -- August 08, 2002 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a scene in that great abstraction known as the Julibrot. The iterated formula is Z^2+C, which draws our old friend the first fractal of all, the Mandelbrot set. But the same formula also draws a horde of Julia sets, which might have come first, and though they are not as well known, a horde of perturbed Mandelbrot sets can also be drawn by the simple formula. But wait, that is not all. The Z^2+C formula also draws families of sets which have no official names, though I call them Oblate, Parabolic, Elliptic, and Rectangular sets. These six families of fractals represent the six mutually perpendicular orientations through the four-dimensional object known as the Julibrot. Yes, I realize that a four-dimensional object is an absurdity. Such an object could exist only in a space of four dimensions, and a quick glance at the world shows that there is no room for a fourth dimension. Our three familiar dimensions take up all the space that exists. If anyone doubts this, I challenge the doubter to go out to an open area and point his arm to a direction that is not one of our familiar 3-D directions. Yet, the Julibrot figure does not know that it cannot exist, because it is there and it will not go away. I know it is there because I can calculate and then see slices through it, and I can rotate those slices in most any direction I desire. Today's image for example is one of a midget on a filament in the east suburbs of the large midget at -1.75 on the negative stem of the M-set. But it does not look like a Mandelbrot midget. Nor does it look like a Julia set for that matter. In fact, it is none of the four other types of sets either. It is a nothing set -- a slice through the Julibrot at the point of the Mandelbrot midget, in a totally oblique direction. But sometimes, even nothing can be something, and today's nothing set makes a picture which contains much of the character of the Mandelbrot midget of which it is an odd slice. Because it is an odd slice of a Mandelbrot midget, I named the image "Odd Mandelbrot" The rating of a 5 seems about right, and the render time of under one minute is certainly right. As always, the completed GIF image ia available on the WWW at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Wednesday was almost perfect. The blue skies, gentle winds, and temperature of 80F 27C kept the fractal duo outdoors for a good part of the day. And when it was finally time to return indoors, they did so reluctantly. I now find myself with a moderate amount of work that needs to be done. Since it's always better to have work behind one rather than before, I'll have to get the work behind me. Until next FOTD on Aug 10, take care, and prosper. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Odd-Mandelbrot { ; time=0:00:50.09--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new center-mag=-0.00000\ 000000474777/+0.00000000001270966/3.405492e+010/0.\ 1549/64.5600772360675847/76.4411018546430654 params=45/-45/2/0/-1.746325272478873/0.00829666984\ 6033399/-1.746325272478873/0.008296669846033399 float=y maxiter=1500 inside=0 logmap=132 colors=000c83d82e82fB5gD7gG9hICiKEiNGjPIkRLkUNlWPl\ ZRm`UnaWncYod_mebkgdihfehfbg`_eTWcMI`IGZEEWACU6AS3\ HO4NK5UG6_C7f88l59i68g68e67c77a76_76Y85W85U84S84P9\ 4N93L93JA2HA2FA1DB1BB09B07B0BI2FO3JU4N_6Re7Vk8Vo8S\ jCSjCPeGNaKKXOHTSFOWCK_9Fc7Bg46k22o76kC9gHDdLG`QKX\ VNU_RQcUMhYJm`FqcCeWCUOCIGC69CM5E`1Fh3Dp4Bw5Ar4Bn4\ Ci4Ce4Da4DX4ET4EO4FK4FG4GB4G74H34H78JBBKEFMIINMLOP\ PQTSRXWT_ZUcaVgeXjhYnl_ro`urarp_ooZlnYjmXglWdkVajU\ _hTXgSUfRReQPdPMcOJbNHaML_LOYLRXLUVLXUL_SLbRLePKhO\ KkMKnLKqJKtIKwGKzFKyGMxHNwIOvJPuKQtKRsLTrMUqNVpOWo\ PXnPYnOZoNZoM_pL_pK`qJ`qHarGbrFbsEcsDctCdtBduAeu9e\ v8fv7fw7gx6hy6iz6jz6kz6lz5mz5nz5oz5pz5qz5rz4sz4tz4\ uz4vz4wz4xz3yz3zz3zz3zz3zz2zz2zz2zz2zz2zz2zz1zz1zz\ 1zz1zz1zz1zz0zz0zz0zz0zz0zz9zz8zz8zz8zz8zz7zz7zz7z\ z7zz7zz6zz6zz6zz6zz6zz5zz5zz5zzdzzczzbzz`zz_zzZzzY\ zzWzzVzzUzzSzzRzzQzzPzzNz } 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==================================

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FOTD 10-08-02 (Levanter [6])
by Jim Muth 10 Aug '02

10 Aug '02

FOTD -- August 10, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's image is named "Levanter". If I remember correctly, a levanter is a strong wind on the Mediterranean Sea. I have no idea why I gave today's rather harmless fractal such an unlikely name. I guess I simply liked the sound of the word. Actually, when I began trying to think of a name, my thoughts were of politics and had drifted to the Middle East. I had done a lot of thinking earlier Friday, trying to convince myself that the U.S.A. is not about ready to launch a war in the Middle East, the purpose of which would be to secure the oil fields in an effort to boost its lagging economy. I might be imagining all this neo-imperialism, but the older I get, the more I realize that the only problem with my cynicism is that I'm usually not cynical enough. Remembering my resolution never to discuss politics, I will now confine my comments to the fractal at hand. The iterated formula, Z^(10)-10(1/Z)+C, is another whimsical expression I entered into the M-Mix4 formula at random. It draws a tiny M-set far beyond the right edge of the default screen. This M-set is surrounded by even tinier cut-off M-sets, like our galaxy is surrounded by globular clusters. Today's scene, with its obviously cut-off features, reveals one of these tinier 'globular' M-sets. When calculated with the normal equal-iteration bands on the outside, today's image was dull and flat. To add a little life, I re-calculated the scene with the outside set to <tdis>, and tweaked the colors a bit. The resulting picture improved from a 4 to its current rating of a 6. Perhaps the best feature of the image is its super-rapid render time of 44 seconds. Even the download of the completed image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> can't beat that time. The fractal weather Friday was wonderful here at Fractal Central, with a temperature of 86F 30C, sapphire blue skies decorated with cottonpuff clouds, low humidity and a gentle breeze. The fractal duo approved heartily by actually romping in the yard a few times in between their bouts of sleeping on the porch. They are indeed in touch with their inner kittens. As for me, I'd best get in touch with the work that needs to be done. I know it's Saturday, and Saturday is supposed to be an off day, but when a job comes in on Friday afternoon and needs to be delivered Monday, it means working on the weekend, especially since the customer is paying extra for rush service. So until next time, which will arrive on the 12th, take care and for peace's sake, avoid politics. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Levanter { ; time=0:00:44.65--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+11.48064466578638/-2.778123424321501/2\ .234309e+008/1/15/-0.000284086357036986148 float=y params=1/10/-10/-1 maxiter=270 inside=0 outside=tdis colors=000MnzMmzMlzMkzMjyNixNhwNgzNfyOexOdw000MHRV\ KPbOMmQJzUHpPKlLMkHPjDRi9TaJaVSiNaqGjyMixShwYhwcgv\ ifunfuofupfupguqgurhushushuritqitpitojtnjtnjsSpmmj\ slkskksjksilsilrhlrglrfmremrdmrdnqcnqbnqanq`oq_oq_\ opZppYppXppWppVqpVqoUqoTroSroRrotvvquunutktshtsetr\ bsq_sqXrpUrojVxiWwiWwhXwhXwgYwgYvgZvfZvf_ve_ve`ue`\ udaudaucbucbucctbctbdtadtaetaes`fs`fs_gs_gsZhsZhrZ\ irYirYjrXjrXkqXkqWlqWlqVmqVmqVnpUnpUopTopTppTpoSqo\ SqoRroRro5T46U67V78W98XA9YCAYDAZFB_GC`ICaJDaLEbMEc\ OFdPGeRGeSHfUIgVJhXJiYKj_Lj`LkbMlcNmeNnfOnhPoiPpkQ\ qlRrnd36c58c69c7Ab8Bb9CbADaCEaDFaEG`FH`GI`HJ_JK_KL\ _LM_MNZNOZOPZPQYRRYSSYTTXUUXVVXWWWYXWZYW_ZV`_Va`Vb\ aVcbUecUfdUgeThfTigTjhSliSmjSnkRolRpmRqnPAIQGNQMRQ\ RVQXZRbcRggRmkD2oE3oE4oE5oE6oF7oF7oF8oF9oFAoGBoGCo\ GCoGDoHEoHFoHGoHHoHHoIIoIJoIKoILoJMoJMoJNoJOoJPoKQ\ oKRoKRoKSoKToLUoLVoLVoLWo } 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 20.0 PAR-FORMULA FILE==================================

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FOTD 06-08-02 (Blackberries [6])
by Jim Muth 06 Aug '02

06 Aug '02

FOTD -- August 06, 2002 (Rating 6) Fractal visionaries and enthusiasts: Fractal Central has suffered two more power failures since I posted my most recent letter. (But still the fractals keep coming.) This most recent outage was the tenth since Saturday morning. I know this to be an accurate count because every time the power cuts off and comes back on, my fax machine spits out a 5cm strip of paper. There are 10 strips now lying beside the fax machine. The local electric utility, always with a handy excuse, claims that broken trees are continuing to fall. This is well and good, except that they also advertise their professional tree- trimming program which they claim is designed to prevent such outages. The newer suburban subdivisions in the area are being constructed with the power lines underground, which does cut back on the number of outages, but this creates another problem. Fractal Central lies in a lightning-prone area, and the above- ground power grid acts as a rather effective, if unintentional, lightning rod. After almost every lightning storm, there is news of one or more of these new high-priced houses in one of these new subdivisions without overhead power lines being struck by lightning and set afire. I guess I'd rather have a few power outages per year than have my house burn down. And finally, what ever happened to those old-fashioned but effective lightning rods on the rooftops? As for today's fractal, I entered a lot of ones into the M-Mix4 formula and came up with a basket of blackberries. The fractal berries actually have me hungry. Not surprisingly, I named the image "Blackberries". It's an acceptable image, maybe a little above average. As such, it was rated a liberal 6. Spending 39 minutes to render a single 6-rated fractal is a bit much to expect of even the most avid fractalist. For increased happiness, I suggest a download of the completed GIF image file from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday here at Fractal Central was hot and humid, with a temperature of 95F 35C, which was just hot enough to keep the dynamic duo confined to quarters. In the evening a light shower passed over, followed by a cooling breeze to make the evening end pleasantly. Today promises to continue the cooling trend, but before I can enjoy the pleasant conditions, I must finish some work, while hoping the power stays on. And before I finish, I must begin. So until next time, (on the 8th), take care, and strive for perfection. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Blackberries { ; time=0:39:01.75--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.13984727490430700/+1.592634280290241\ 00/1.003849e+007/1/-127.499999891903641/-2.5538621\ 2705266402e-007 params=1/1/-1/-1/0.1/0 float=y maxiter=5000 inside=0 logmap=675 periodicity=10 colors=000QKibWCaZD``E_cFZeGYhHXkIWmJVpKUsLTuMSxNR\ zNOuMLqMIlMGhMDcMA_M8VM5RM2MM0IM2HP4GR5FT7EV8DXACZ\ BB`DAbF9dG8fI7hJ6jL5lM4nO3pP3rSFnUQjXagZlc`w`ctafq\ ahoaefdcYg`PjZHmMzTRuRWqP_lNdhMhcKm_IqWHoZLnaPmcTl\ fXji`ikdhnhgpkiojkoimoioohqohsoguogwofxoftmepkdljc\ hhbdgaae`Yd_UbZQ`YM_XJYWFXVBVU7UT3SS0RS2QT4QT6QT8Q\ TAQTCQTEQTGQTIQTKQTMQTOQTQQTSQTUQTVQTXURYXQ_`OadMb\ gKdkIfoGgrEivCjyBRmzQkyQixPhwPfvOduOctNasN`rNZqMXp\ MWoLUnLSmKRlKPkKOkLMjLLiLKhLJhLIgLGfLFeLEeLDdLCcLB\ cNEbOGaPI`QK_RMZSOYUQXVSWWUWXXVYZUZ`T`bSadRbfQchPd\ jOelOcjNahM_gLYeKWdJUbIS`HQ_GOYFNXELVDJTCHSBFQADP9\ BN89L77K65I54H45G65G76G96GA7GC7FD8FF8FG8FI9FJ9ELAE\ MAEOBEPBERBESEFTHFTKGTNGUQHUTHUWHUXJWXKXXLZYN_YO`Y\ PbYQcZSdZTfZUgZVh_Xj_Yk_Zm``n`ao`bq`craesafuagvahw\ djsflohnkjpglrcnt_pvXmwYjwYhwYewYcwY`xYYxYWxYTxYRx\ YOyYLyYJyYGyYEyYIsZMmZPh_ } 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 20.0 PAR-FORMULA FILE==================================

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Re: RE: [Fractint] FOTD 04-08-02 (Screw Propeller [5])
by harrybissell＠prodigy.net 05 Aug '02

05 Aug '02

Downed power line OFTEN lay on the ground sparking... The sparks may only be 10's of amps and the conductuctors are good for hundreds or thousands of amps... so there is little chance of a breaker trip unless the wires contack each other. The power supply will happily arc for days. I had a downed power line in my backyard... slowly sawing (arcing) its way through a large tree. When I called the utility... they said "Call us back when its sawing through a HOUSE.... <click>" Guess they had more important calls to make :^P ??? Harry Bissell <resume lurk> --------Original Message-------- From: schamber(a)uwm.edu To: <fractint(a)mailman.xmission.com> Sent: Aug 5 2002 08:57 Subject: RE: [Fractint] FOTD 04-08-02 (Screw Propeller [5]) >I, too, have seen a live wire on the ground. It was particularly distressing >because at the time I was living in a community house (13 people) and there >were people coming and going at all hours and no way to warn the people >coming home that the back door, which was used most often, wasn't >particulary safe. Also the power company didn't seem too disturbed by >imminent electrocution. Luckily no one was hurt. >============================================ >Deborah Schamber >UW System Institute on Race & Ethnicity >-----Original Message----- >At 14:26 05/08/2002, JimMuth(a)aol.com wrote: >>After a day without power and a live wire sparking and >>sputtering on the ground in the alley beside Fractal central, >That's something I've never understood - if that's a power line you're >referring to then in this country such an insult to the supply would cause >a circuit breaker to jump out and the whole line would've gone dead (and >the line company would be alerted). You just don't see live wires sparking >and sputtering on the ground - after all, that represents lost revenue to >the line company. >Morgan L. Owens >"Safety regulations alone demand it." >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Powered by Wild On Web: Free POP Mail Access - Access your E-mail from Anywhere in the World! http://www.wildonweb.com |Awards|Money|Bank|Credit|Dating|Games|Jokes|Vitamins|Magazines|Diet| |Bookstore|News|Babies|Cards|Homepages|Hobbies|...

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FOTD 04-08-02 (Screw Propeller [5])
by JimMuth＠aol.com 05 Aug '02

05 Aug '02

FOTD -- August 04, 2002 (Rating 5) Fractal visionaries and enthusiasts: After a day without power and a live wire sparking and sputtering on the ground in the alley beside Fractal central, the local electric utility has finally repaired the situation, and things are back to normal. (I wrote the above paragraph around 11am this morning, when I assumed things were under control. Unfortunately, the power went off again before I could post the FOTD, and just now, 10:15pm, has come back on for good . . . I hope.) With no time to search for an outstanding fractal, I had to settle on a run-of-the-mill high-iteration midget located in a remote valley of the Mandelbrot set. I named the image "Screw Propeller". I gave it this name because the elements around the midget remind me of a ship's propeller, and not as an insult to some imaginary fellow named 'propeller'. Since the scene is in the classic M-set, and the midget happens to be the first one I came to, I have rated the picture a perfectly average 5. The only really unusual feature of the image is the high maxiter of 100,000 and the logmap setting of over 13,000. Since its magnitude is still within the range of conventional math, the image renders in 10 minutes. The image will download from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> in even less time however. The fractal weather Saturday started with a violent thunder- storm with 80mph (130kph) winds, over 4 inches (10cm) of rain in one hour, hail and continuous lightning. Trees fell everywhere. The day then continued with heat, humidity and additional but less violent storms. The 95F 35C heat and thunder kept the fractal duo of cats confined to the indoors. The power failure that ensued when a tree across the alley fell on power lines kept me from fractalling and left me with no excuse to escape the task of cutting and collecting the fallen tree limbs that cluttered the front lawn. Today is just as hot, but at least no more storms are in sight. Until the next time on August 06, take care, and fractals may be the answer, but first one must know the question. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Screw_Propeller { ; time=0:10:59.00--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.22509332273260120/+0.758019130508034\ 70/1.25732e+010/1/14.9999752295271485/1.9313561407\ 1707207e-005 params=0/0 float=y maxiter=100000 bailout=6 inside=0 logmap=13255 periodicity=10 colors=000cvzq0Sq0Sq1Sq1Up1Vo1Xo1Zn1_n1am1cm1dl1fl\ 1hk1ik1kj1mj1ni1pi1qj3oj4mj6kj7jj9hjAfkBdkDckEakG_\ kHYkIXkKVlLTlNRlOQlPOlRMlSKlUJmVHmWFmYDmZCm`Ama8na\ 6mb7mb8lb8lb9kb9kbAjbAjbBibCibChbDhbDgbEgbEfbFfbFe\ bGebHdbHdbIdbIcbJcbJbbKbbKabLabM`bM`bN_bN_cOZcOZcP\ YcPYcQXcRXcRWcSWcSVcTVcTVcUUcUUcVTcWTcWScXScXRcYRc\ YQcZQcZPc_Pc`Oc`OcaNcaNcbMcbMccMccLaaL``L__LZZLYYL\ XXLWWKUUKTTKSSKRRKQQKPPKOOJMMJLLJKKJJJJIIJHHJGGIEE\ IDDICCIBBIAAI99I88H56I77I87J97JA7KB7KD7LE7LF7MG7MH\ 7NJ7NK7OL8OM8PN8PO8QQ8QR8RS8RT8SU8SW8TX8TY8UZ9U_9V\ `9Vb9Wc9Wd9Xe9Xf9Yh9Yi9Zj9Zk9_lA_mA`oA`pAaqAarAbsA\ buAcvAcwAdxAdyAdzAcu9cp9cl8cg8cc7cZ7cU7cQ6cL6cH5cC\ 5c85d98eABeBDfCGfDIgELhFNhGQiHSiIVjJXkK_kLalMdlNfm\ OinOlmPlmPmmQnmQomRplRqlSrlSslStlTulTvkUwkUxkVykVz\ kVzkWzjWzjXzjXzjYzjYzjYziZziZzi_zi_zi`zjazkbzlczmc\ zmczmczmczmczmczmczmczmcz } END PARAMETER FILE=========================================

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Re: [Fractint] FOTD 04-08
by Jim Muth 04 Aug '02

04 Aug '02

At 02:46 PM 8/5/02 +1200, Morgan Owens wrote: >That's something I've never understood - if >that's a power line you're referring to then >in this country such an insult to the supply >would cause a circuit breaker to jump out and >the whole line would've gone dead (and the line >company would be alerted). You just don't see >live wires sparking and sputtering on the >ground - after all, that represents lost >revenue to the line company. It was a live 4,500 volt power line sparking and smoking, not actually on the ground, but tangled in the tree which had pulled it down. I suppose the downed line was not grounded solidly enough to trip the breaker. But it was a curious sight as different parts of the fallen tree smoked and burst into flame as the current arced across the breaks in the wood. We first called the fire department, but when the company arrived they said they could do nothing about live wires. They notified the power company, which already had been notified six times. But since over 100,000 lost power in the storm, the power company was overwhelmed. It was 16 hours before the crew finally reached the scene, cut up the tree, restrung the wire and moved on to the next job. Just to keep this on topic, the lightning during the storm traced lovely fractal patterns in the sky. Jim (the enlightened) Muth

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Alibi for a late FOTD
by JimMuth＠aol.com 04 Aug '02

04 Aug '02

Due to another (no kidding) power failure at Fractal Central, the FOTD for August 4 will appear ASAP. (As Soon As Possible.) Jim (in the dark) Muth

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Fwd: Re: [Fractint] Volumetric Fractals, Julia and Mandelbrot mysteries
by Morgan L. Owens 04 Aug '02

04 Aug '02

> >This isn't from the post you're thinking of - I just lifted it from a >private email I sent in April 2000: > > >Evolution mode options: >Evolution mode: yes (of course) >Image grid size: 15 >Grout: no > >Tweak central: >Param 1 real: x >Param 1 imag: y >the rest: no Because one can't (couldn't?) save evolver screens as .pars, it had to be saved as a .gif instead. (The type was "julia", randomness was of course turned off). >I've just started wondering what would happen a formula is written to >allow a displacement parameter à la lyamandel/hypercomplex, so that some >point other than the centre of the Julia set is centred on the Julia's box. Or just use the image coordinate settings :) Any reason why the evolver's grid size might be limited to 51? >Morgan L. Owens "3*17?"

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