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Re: [Fractint] Extended Fermat's Last Theorem - Slightly Off-topic
by Rupert Millard 19 Aug '02

19 Aug '02

Ricardo, >Does someone in the list know if the following conjecture, that includes as >a particular case Fermat's Last Theorem, has ever been posed, and proved >false or true? >x[1]^p + x[2]^p + ... x[n]^p = z^p, for x[i] > 0 and 1 < n < p, has no >integer solutions. >TIA. Yes, this conjecture was made by Euler in 1769. He conjectured "it is impossible to exhibit three fourth powers whose sum is a fourth power, four fifth powers whose sum is a fifth power, and similarly for higher powers." This was first disproven in 1966 by L.J.Lander & T.R.Parkin with: 27^5+84^5+110^5+133^5 =144^5 The first found with fourth powers was done by Noam Elkies in 1988 and is: 20615673^4 = 2682440^4 + 15365639^4 + 18796760^4 Then Roger Frye found: 422481^4 = 95800^4 + 217519^4 + 414560^4 which is the smallest solution for fourth powers. From, Rupert _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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Extended Fermat's Last Theorem - Slightly Off-topic
by Ricardo M. Forno 18 Aug '02

18 Aug '02

Does someone in the list know if the following conjecture, that includes as a particular case Fermat's Last Theorem, has ever been posed, and proved false or true? x[1]^p + x[2]^p + ... x[n]^p = z^p, for x[i] > 0 and 1 < n < p, has no integer solutions. TIA.

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FOTD 18-08-02 (Iterative Teardrops [6])
by Jim Muth 18 Aug '02

18 Aug '02

FOTD -- (Rating 6) Fractal visionaries and enthusiasts: It's Sunday mid-morning here at Fractal Central, and all is well. I have just finished emptying my e-mail box of two large undeliverable e-mails that were returned to me. This is well enough, except for the fact that I never sent the letters in the first place. It's probably another virus, and a clever one at that -- one that works like sending a letter via normal mail with no postage and writing the name of the address you want it delivered to in the 'from' space. Then when the post office 'returns' the letter for lack of postage, they are actually delivering it. I also feel a bit cruel about failing to reply to Baerbel's request for information about unsubscribing from the Fractint list. But it's a bit amusing to see such a request (from someone who already knew how to subscribe) appear three lines below the unsubscribe information in the letter's header. As for today's fractal, (which I have rated at a harmless 6), it's a scene in the fractal that results when 0.01 part of Z^2 is added to Z^(-2), and (1/C) is added to the combination, then the whole thing is iterated with a bailout radius of 100. That 0.01 part of Z^2 is not much, but it makes a world of difference in the final fractal. The parent fractal, which is enclosed in a circle, looks surprisingly like a fractal planet. Changing the logmap of today's image to 0 and doing about 10 out-zooms will reveal this planet in its full glory. As is the case with most fractals that contain a negative exponent of Z, the bailout radius has a great effect on the appearance of the fractal. With the parent fractal on the screen, redraw the image with imag(p3) set to 2400. A totally different image appears. I named today's image "Iterative Teardrops" because of the teardrop shape of the elements surrounding the central midget. These disconnected elements are typical of fractals whose formula contains negative powers of Z. The rating of 6 equals a little above normal on my rating scale -- about the mildest praise I could give to such a mundane image. The redeeming feature is the render time of 6 minutes, and the fact that the completed GIF image file may be downloaded from either of the following web addresses: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Saturday here at Fractal Central was uneventful. The partly cloudy day with a temperature of 95F 35C and moderately high humidity was notable only because it continues the warmer and drier than normal pattern that has prevailed most all summer. Also it was the fourth day in a row on which the weather experts had predicted showers, and the fourth day in a row on which the predicted showers failed to arrive. Those experts are far better at explaining why something did not happen than forecasting what will happen. The fractal cats, who are unconcerned with weather experts, passed the day doing what cats do best -- lazing around the fractal grounds. As for me, it's Sunday morning, and if I really work hard, I might find a way to get through the day without working. And don't laugh. After all, working to avoid work is no more anti- productive than fighting for peace. Until next time, on the 20th, take care, and don't be too lazy. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ IterativeTeardrops { ; time=0:06:12.45--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+3.31533979732890300/+3.380854530622418\ 00/2.718068e+010/1/17.4927412805414235/0.007870415\ 83158384211 params=1/-2/0.01/2/0/0 float=y maxiter=1000 inside=0 logmap=130 periodicity=10 colors=000GLKFNKNUTV`WbgZjnhtml90M_pwcipgbgkWZnPQe\ TNXXKOXHRbJTecVhLfkm_nNmqOctPzvQYqRQlSIgTBcUFdXJe_\ NfbRgeVhhTqpSYwRZwQOwbzocmidhcdcZe0TeUO_TPVTQPTRKT\ SFRTnGwjJtgMndPhaSbZVXWYRT`LQcGWaOa`WgZclYjghsbrwn\ auzLpjKmVJkFIi0Ig6RoBZvHmwMnwJcwHTwFIwD8wSCgfGTuJE\ tLFsMFsOGrPGrRHqSHqTH9WbDYeG_gJajMblPdnSfqVhsYiurk\ wzhtseiscZtf_pdbmbej`gg_jdYlaWoZVqWTtTRwQPwNOwKMwH\ KwEJwDIwCHwBGwAFw9Eu8Ds7Cp6Bm5Ak49h38e38cBDfVEkWCp\ XAuX9wO5pG2gK9lNGpQMtUTwXZw_ewbkwb_wbOwbCwb1wd2we3\ wf4wg5wh6wj6wk7wl8wm9wnAwoAwjRtegjaxadscfnehigjdil\ _knVmpQorLqtGsvBux6wz2wrDujOqbZnVijNsgQUwNWwKYwI_w\ FawDcvAet7gs5ir2kq0lp4fs7`uAVwDUwGVwJWwMXwPYwSZwU_\ wW`wZaw`bwbcwedwgewifwlgwnhwpiwsjwukwwlwymwvnwtowr\ pwpqsnrnlsiitdgu`evWcwRaxM_yIYzMWzQUzTSzXQz_OzcMzg\ LzjJznHzqFzuDzwBzw9zw8zwJzwUzwdzwozwnzwnzwnzwnzwnz\ wnzwnzwozwpzwpzspzopzkpzg } 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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(no subject)
by Baerbel Strauch 17 Aug '02

17 Aug '02

how can i stop getting e-mails about fracint? _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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Fractal Tone-Poems (music?)
by Bill Jemison 17 Aug '02

17 Aug '02

Thanks Miguel! I remember that you had posted some music pars a while ago, in fact I have them saved in a special directory. so please do post some more. I like Nocturn as well. the orbits are rather hypnotic along with the music. Lotus is probably my favorite, due to the way that the unfolding of the "petals" follows the tonal patterns. It's not particularly "melodic" but I feel that it has merit anyway. That's why I am inclined to call them tone poems rather than music, although one might be able to argue that there isn't much difference. Bill

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Re: [Fractint] Fractal Tone-Poems (music?)
by Franktal Gallery 16 Aug '02

16 Aug '02

Bill, I believe Nocturn is one of the best music PARs I ever heard ! I used to post music PARs a couple of years ago, and I'll do it again when inspiration strikes me... ;-) For those of you who may never heard them, here's a link to my music PAR collection : http://www.geocities.com/franktal2002/sounds.html Regards, Miguel >From: Bill Jemison <fishburnIII(a)compuserve.com> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >Subject: [Fractint] Fractal Tone-Poems (music?) _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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Fractal interstellar gas
by David Jones 16 Aug '02

16 Aug '02

Fractal interstellar gas at end of a star's life: http://hubblesite.org/news_.and._views/pr.cgi.2002+15 David gnome(a)hawaii.rr.com

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Re: [Fractint] FOTD 08-08-02 (Odd Mandelbrot [5])
by gnome＠hawaii.rr.com 16 Aug '02

16 Aug '02

I firmly believe that cat fur is fractal - explains why such small animals can shed so much fur everywhere without visibly losing any fur. ;-) David gnome(a)hawaii.rr.com >>On Tue, 13 Aug 2002 19:07:34 -1000, David Jones wrote: >> >>>Besides, some of us think that Jim is really just a virtual >>> identity of the cats. >> >>You mean a fractal manifestation? >> >>:-) >> >>John >>-- John Lewis, jlewis(a)clara.net on 08/14/2002

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FOTD 16-08-02 (Papillon [6])
by JimMuth＠aol.com 15 Aug '02

15 Aug '02

FOTD -- August 16, 2002 (Rating 6) Fractal visionaries and enthusiasts: Having posted several consecutive FOTD's that were faster than the speed of light, I now post one slower than...well...a fractal cat. The slowness is a result of the magnitude of the image, which takes us into the realm of arbitrary precision math. It's a slow trip into the Mandelbrot set to the location of today's image, but a trip well worth taking, for the midget in the image is unlike any I have previously seen in a fractal as mundane as the M-set. The scene pictured in the image is located in a remote valley of the largest midget on the west branch of the filament extending from the large period-3 northern bud of the M-set. I named the picture "Papillon", which is the French word for 'butterfly'. While studying the image, I saw purple butterflies all through it, but since I have used this name several times in the past, I decided to use the French word for that insect instead. The rating of 6 is nominal. The scene displays a curious mixture of total chaos and areas of organization, which is rather unusual for at least the lower magnitudes of the M-set. A rough version of the image can be seen in 3 minutes by striking the < g > key and entering the command < mathtolerance=/1 > before running the parameter file. This will force the program to calculate the scene using conventional math. But to see the image in its fully-resolved glory, a wait of 5 hours will be required. All is not lost however, for the completed and fully-resolved image will soon be available on the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Thursday here at Fractal Central was once again warm and humid -- the kind of day that brings out the laziness in cats. The temperature of 95F 35C kept the not-very- dynamic duo confined to quarters until the sun went down, and even then, they ventured out only briefly. Luckily for me, modern science has provided relief from the heat in the form of air-conditioning, which I took advantage of all day as I tended to the work that needed to be done. Tomorrow promises to be a bit cooler, with at least a chance of showers, another ideal day for working. So until next time, which will arrive on Sunday the 18th, take a moderate amount of care, but not so much care that life ceases to be fun. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Papillon { ; time=4:56:06.77--SF5 on a P200 reset=2002 type=mandel passes=1 center-mag=-0.1534230146723439126/1.03855500630879\ 9133/9.504526e+013/1/-27.3516134375319133/3.885780\ 58618804789e-016 params=0/0 float=y maxiter=30000 bailout=6 inside=0 symmetry=none periodicity=10 colors=000gCcgAff7hf5jg8kgBkgDkgGkgIkgLkgOlgQlgTlg\ VlgYlg_ljT_mNOpHCqIBrJArK9sL8tM7tN7uO6vP5vQ4wR3xS2\ xS2wU3vV4uW5tX6sY6rZ7q`8pa9ob9ncAmdBleCkfCgUAcH8`4\ 6_39_3B_3E_3G_3J_3L_3O_3Q_3T_3V_3X_2`_2b_2f_2h_2k_\ 2m_2q_2s_2v_2x_2zZ3wZ3tZ4qZ4nY5kY5hY6eY6bX7_X7XX8X\ X8UVASUBRTDQSEORGNPHNOJNNKMMMMLNMJPLIQLHSLGTLFVKDW\ KCYKBZJA`J9aJ8bJBaID`IF`IH_IJ_HMZHOYHQYHSXGUXGWWGZ\ VG`VGbUFdUFfTFiSFkSEmREoREqQEsQEoTGkVHhXJdZKa`MYbN\ VdPRfQNhSKjTGlVDnW9pY6rZBm`GhaLccQZdUUeZPgcKhhFjmA\ kq6lkEneMocLpaKq_JqYJrWIrVHsTHsRGtPFuNFuMEvKDvIDwG\ CwEBxDBxJGqOLjUQcZVXd_QidJnhDleGkbIj_KiXMhUPgSRfPT\ eMVcJYbG_aEa`Bc_8fZ5hY2jX0lW3jW5iV7hV9gUBfUDeTFdTI\ bSKaSM`RO_RQZQSYQUXPXVPZUO`TObSNdRNfQNhPPiORjOSkNU\ kNWlMXmMZmL`nLaoKcoKepJfqJhrIjrIksHmtHotGpuGrvFsvF\ mtGhrHcqHZoIUmIPlJKjJFhKAgK5eL0dL0bI0aGEFvDKrCOoBS\ lAWh9_e8cb7g_Dd`JbaO_aUYb } END PARAMETER FILE=========================================

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Fractal Tone-Poems (music?)
by Bill Jemison 15 Aug '02

15 Aug '02

<<Oh, no colourmap, then :( :)>> Never will be from here, but sometimes I do use colormaps ;}. However, as I said, some of these have no image, so there's not much need for any colors <g> Bill

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