From: owner-fractint-digest@lists.xmission.com (fractint-digest) To: fractint-digest@lists.xmission.com Subject: fractint-digest V1 #607 Reply-To: fractint-digest Sender: owner-fractint-digest@lists.xmission.com Errors-To: owner-fractint-digest@lists.xmission.com Precedence: bulk fractint-digest Monday, October 29 2001 Volume 01 : Number 607 ---------------------------------------------------------------------- Date: Tue, 23 Oct 2001 22:22:04 +0500 From: "Tony (Anthony) Hanmer" Subject: Re: (fractint) FOTD 23-10-01 (Maltese_Minibrot[7]) Jim, the ONLY unsuccessful thing about this image is your rating of it: too bad you're not as "clever" with real integers as you are with complex numbers! Try a 9. I'm so glad that Sept. 11 didn't permanently knock you out of interacting with all of us in your amazing way. Thank you. Tony Hanmer Tbilisi, (Republic of) Georgia _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 24 Oct 2001 10:58:55 EDT From: JimMuth@aol.com Subject: (fractint) FOTD 24-10-01 (Mandelbrot Mania [6]) FOTD -- October 24, 2001 (Rating 6) Fractal visionaries and enthusiasts: Once again I must let down my faithful readers, who were (hopefully) waiting with bated breath for further adventures on the hypersphere. Unexpected work arrived, leaving me no time to write. But I did find time to dredge up a quickie fractal. (In the future, I will not promise an article until I actually have it written and composed.) The formula of today's fractal subtracts 1.3 parts of Z^(0.9) from 1.3 parts of Z^(-1.1) and adds 1/C, producing a 3-lobed figure that is quite sensitive to the bailout radius. The scene of today's image is deep on the left side of the right valley. I named the image Mandelbrot Mania because of the appearance of the parent fractal more than the appearance of the image itself. I rated it a 6 because it's a little better than a 5 and not quite worth a 7. The render time of 44 minutes is a bit much to ask for an image that rates only a 6, so I recommending downloading the GIF image from: or from: where the image will soon be posted. The day began cloudy and foggy here at Fractal Central, but by noon the sun burned off the dampness, leading to a warm afternoon with a temperature of 79F 26C. The fractal cats enjoyed much of their time outdoors, but still managed to find something to fight about. All ended well however, with the dynamic duo sleeping together peacefully on the porch. (For a bit of philosophy, check the philofractal list.) With a day's work waiting to be done, I must now close the FOTD and get busy on other matters. But I'll return in the proper time. Until then, take care, and hope for the best. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Mania { ; time=0:45:23.09--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.07345537336418037/+0.042097568866235\ 17/3.724103e+007/1/-115.000000007003862/5.70113192\ 766008581e-009 params=1.3/-1.1/-1.3/0.9/0/50 float=y maxiter=6000 inside=0 logmap=745 colors=000WffVjmVjkVjjUjiUjhUkfTkeTkdTkbSkaSk`Sk_R\ lYRlXQlWQjUQhTPfSPdRTbSU`TUZUVXVWVWXTXYRYYP_ZN`_La\ `JbaJcaJdbJecKfdKgdKheMifOigQihSjiUjjWjkYjkZkl`kmb\ kndkoflphlqjlrmmqklpiloglnekmcklbkk`kjZjiXjhVjhUjg\ SifQieOidMhcKhbJhaHh`Fg_DgZBgY8hZAgZBfZDf_Ee_GdXHb\ `Jc`Kb`MbaNaaP``PaaQ`aQ`aR_aR_aS_aSZaTZaTZbTYbUYbU\ XbVXbVXbWWbWWbWWcXVcXVcYUcYUcZUcZTc_Tc_Td_Sd`Sd`Rd\ aRdaRabQZUQWbQTbQQ`INZALXCIVDJTEJRFKPGLNIMFJMGKNHL\ OIMPJOPKPQLQRMRSNSSOUTPVUQWVRXVRYXQWYPVYOUXNTWNRWM\ QVLPXKOPFNZJL`IKaHJcGIdGGUFFZEEhDDiDChFE`HFbJHfLIf\ NJePLaRMeTOfVPfXQgZSg`ThbVhdWifXihZjj_ilainbhpchre\ gtfetdgsgiqjkllmgoobrpXsqYtjZob_jW_eO``HaW9bR2aL2b\ M3cN4cN5dO6dO7eP8fQ9fQAgRBgRCiSDjSElTFnUGoUHqVIrVJ\ tWKvXLwXMwYNvYOwZOw_OuZ2tS2rT3rU4rV5qV6qW7qX8oY9oY\ AnZBn_CmbDmgEllFlqGlvHlzIlzJlzKlzLkzMkzNkzOkzPkzQk\ zRjzSjzTjzUjzVjzWjzXizWjz } 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================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 25 Oct 2001 09:39:11 EDT From: JimMuth@aol.com Subject: (fractint) FOTD 25-10-01 (Threads of Infinity [6]) FOTD -- October 25, 2001 (Rating 6) Fractal visionaries and enthusiasts: It's another very busy day here at Fractal Central, which means another brief FOTD discussion. I view such days with mixed emotions, of course. On the one hand, busy days mean more money to buy a faster fractal-finding machine, but on the other hand, busy days mean little time to actually search for the fractals. Also due to the rush, the continuation of the misadventures on the hypersphere will have to wait at least two more days. Today's fractal, which takes 13 minutes to render, took about 1/2 hour to find. This is about the average time that passes between going into fractal mode and actually finding the midget of the day. To this time must be added the render time of the image. Luckily, I can write the discussion on a separate machine. The formula that created today's image takes 10 parts of 1/Z and subtracts one part of Z before adding 1/C. The resulting parent fractal appears as a half-obscured Mandeloid standing on its nose. The midget in today's image is located in a spiral on the left shore of the East Valley of the Mandeloid, which in today's case is actually a North Valley. The elements of the spiral are unusually rope-like, inspiring the name "Threads of Infinity". The name also could have been inspired by the name of an old TV program about fractals, which is titled "Colors of Infinity". The image rates a 6, and renders in 13 minutes. The GIF image downloads in only one minute. The image may be found at the URL's: and: The fractal weather today was very summer-like, with warm sun and a temperature of 83F 28C. The fractal cats, who have been quarreling lately, enjoyed an afternoon in the yard, and actually managed to get through the entire afternoon without getting into a fight. And I'm about to 'enjoy' a busy day, so until next FOTD, take care, and the less you try to make sense of things, the more sense they'll make. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ ThreadsOf_Infinity { ; time=0:13:19.83--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.00007793807533362/+0.112392194825511\ 90/5.776346e+008/1/22.5000000881690916/-2.05411887\ 214956845e-007 params=10/-1/-1/1/0/0 float=y maxiter=1200 inside=0 logmap=178 colors=0000JdTWYegThfMldHpcAsc5ig6`j6VgCOdHIbMC`Q5\ ZV0W`0Te0Si0Vf1Xd2_a9``FbZLbYQcXXdVadUhfTmgSsgSh_U\ YTXONZDG`CGXCGUCGQCGNCGJCGHCGDCGACG6CG3CG0CG0BL0BR\ 0BW0B`0Bf0Bk0Bp0Bv0By0By0By0Dy0Gx0Is1Ll6OfCQ`HTVMW\ OSYJX`Caa7eeChhGikKjmOlpSmtWpw_qxcrxgtxkuxjttjtojt\ ijtdjt_jtVjtPhrKhrFhr9hr4hr0hr0hr0fp2dn6clB`jD_hHZ\ fLXePVbTTaWSZ_PYcOVgNUiLTkNQlNNlOMmOJmPIoPFoREpRCp\ SAqS8qT6sT3uV2xV0xX0x_3xW9xPDwOIsNMpKSpJVpH`oGdoFi\ oEmhCeaCYXBQQBIK9AF92880280B70I73Q7AY7Id7Pl7Xt7bx7\ jx7qxClxGfxKbxOYxTUxXPx`LxdFxhCxcFwZIsTLmONiJQdET`\ BVWEYSG`PJbMLeKOhMRjPTmSWpW_rX`rYbu_cu`duafucgudhj\ ejagkShlIimNkoJlpHmqEosApt8qv5sw1tw0wv0xv0xt0xt0xq\ 0up1qm3ml6ij9ehCafEYdHVbJQ`MO_PQ_ST_UW_XY_Z__aa_dd\ _fg_ih_lk_nm_qp_tq_ulZuhZud_u``uXbuScuSduSfuSguShu\ TjuVkuWluXmuYou_pu`quasuctudvudvudvudvudvudvudvudv\ udvudvudvuevugvuhvuivukvu } 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================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 26 Oct 2001 11:06:45 EDT From: JimMuth@aol.com Subject: (fractint) FOTD 26-10-01 (A Chilling Chiller [6]) FOTD -- October 26, 2001 (Rating 6) Fractal visionaries and enthusiasts: Another rushed day brings another short discussion. I gave today's image the name "A Chilling Chiller" because of the somewhat ominous feeling it produces. This effect would work as the starting point for the cover of a cheap horror novel. The brownish elements around the midget, with their sharp points, have a vague resemblance to a colony of roosting bats, and with the lack of strong reds, the remaining blues and greens add to the ominous overall feeling. The formula of the parent fractal is a simple Z^(2.1)+C, with the resulting figure being sliced a bit up the infinite logarithmic spiral. The rating of 6 is perhaps a bit high for this hasty image, which rendered while I tended to other tasks. The render time of 34 minutes is slow enough to make a trip to Paul's web site at: or Scott's site at: worth the effort. The fractal weather today was once again summer-like, with blue skies and a temperature of 77F 25C. But the brisk winds had the fractal cats uneasy, cutting their outdoor time by well over half. It's now time to return to the daily grind, and do what needs to be done. One of these days I'll get around to that hypersphere, but today is not the day. I shall return tomorrow however, with the next FOTD. Until then, take care, and worry not. (If possible) Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ A_Chilling_Chiller { ; time=0:34:43.34--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-0.47311802838614140/+0.585934696010908\ 20/1.223377e+010/1/-122.5000875222524/0.0002730490\ 83844949247 params=2.1/0/0/0 float=y maxiter=10000 inside=0 logmap=790 periodicity=25 colors=000TawRcwPewNgvLiwJlwHowJlzLjeNhcOdaQaZSZXU\ VUVSSXPPZLM`IKaFHcBEe8Cg59h27i5Aj7Dk9GlBJlDMmFOnHR\ oJUoLXpN_qPbrRdrTgsVjtXmuZpu`rr_rp_rn_rl_rj_rh_rf_\ rd_rb_r`_rZ_rX_rV_rT_rR_rP_rN_rL_rJ_rH_rF_rLUoQOmV\ Ij_Chd6fc8gc9gbAhbBhbCiaDiaEjaFj`Gk`Hk_Il_Jl_KmZLm\ ZMnZNnXMmWLlULkTKkRJjQJiOIhNIhLHgKGfIGeHFeGEdEEcDD\ bBDbACa8B`7B_5A_49Z29Y18X08XCFQOLJ_SCkY5gW4dU4aT4Z\ R4WP3TO3QM3NL3MO5MR7MU9LWBLZDLaFKcHKfJKiLKkNJhMIfL\ IdKHbJG`IGYHFWGEUFESEDQDDOCCLBBJABH9AF89D79A688576\ 474362260155A49I3EQ3IZ2Nf1Rn1Vv4`t7er9jqCooFtmZzlL\ tbPmUNhTLcSKZRIYQHYPFYOEZNCZMAZL9_K7_J6_I4`H3`G1`F\ 0`E4bI7cLBeOEfRHhULiYOk`SlcVnfYoiapldpngqqkrtnswqs\ yoqxmoxkmwikwgjwehwcfwadw_cwYcwWcwUcwScwQcwOcwMcwK\ cwIcwGcwIcwJcwLcwMcwNcwPcwQcwScwTcwUcwPcwKcwFcwAcw\ 5cw0cw1cw2cw3cw4cw4cw5cw6cw7cw8cw8cw9cwAcwBcwCcwCc\ wDcwEcwFcwGcwGcwHcwXcwVcw } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z| The elements of the spiral are unusually rope-like, inspiring > the name "Threads of Infinity". The name also could have been > inspired by the name of an old TV program about fractals, which > is titled "Colors of Infinity". Was this program narrated by Arthur C. Clarke? The first time I ever heard of fractals was a show on PBS about them. All I remember was a zoom into the Mandelbrot set with Arthur C. Clarke talking. A few months later, I got internet access and came across a (not very good) Mandelbrot explorer almost by accident. I remembered the word Mandelbrot from the show, downloaded it, and I was hooked. If anyone can name the show based on this vague description, tell me. Jon K. ________________________________________________________________ GET INTERNET ACCESS FROM JUNO! Juno offers FREE or PREMIUM Internet access for less! Join Juno today! For your FREE software, visit: http://dl.www.juno.com/get/web/. - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 27 Oct 2001 12:57:08 +1300 From: "Morgan L. Owens" Subject: Re: (fractint) FOTD 25-10-01 (Threads of Infinity [6]) At 16:44 26/10/2001 -0500, the_juggernaut@juno.com wrote: > > The elements of the spiral are unusually rope-like, inspiring > > the name "Threads of Infinity". The name also could have been > > inspired by the name of an old TV program about fractals, which > > is titled "Colors of Infinity". > >Was this program narrated by Arthur C. Clarke? The first time I ever >heard of fractals was a show on PBS about them. All I remember was a >zoom into the Mandelbrot set with Arthur C. Clarke talking. A few months >later, I got internet access and came across a (not very good) Mandelbrot >explorer almost by accident. I remembered the word Mandelbrot from the >show, downloaded it, and I was hooked. > >If anyone can name the show based on this vague description, tell me. "Colours of Infinity: Exploring the Fractal Universe", published in 1994 (with a soundtrak by David Gilmour). It grew out of a speech Clarke had given in 1989. An extract of the speech is at the end of Clarke's 1990 novel _The Ghost From the Grand Banks_, where he introduces it thus: In November 1989, when receiving the Association of Space Explorers' Special Achievement Award in Riyadh, Saudi Arabia, I had the privilege of addressing the largest gathering of astronauts and cosmonauts ever assembled at one place. (More than fifty, according to Apollo 11's Buzz Aldrin and Mike Collins, and the first "space walker" Alexei Leonov, who is no longer embarrassed at sharing the dedication of _2010: Odyssey Two_ with Andrei Sakharow.) I decided to expand their horizons by introducing them to something _really_ large, and, with astronaut Prince Sultan bin Salman bin Abdul Aziz in the chair, delivered a lavishly illustrated lecture "The Colours of Infinity: Exploring the Fractal Universe". The material that follows is extracted from my speech; another portion appears at the beginning of Chapter 15. I'm only sorry that I cannot illustrate it with the gorgeous 35-millimetre slides - and videos - I used at Riyadh. Try "http://klru.worldpost.com/publicarea/ViewProgram.asp?VsnID=45398" Morgan L. Owens "Yet the most astonishing feature of the M-set is its basic _simplicity_." - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 26 Oct 2001 20:38:50 -0500 From: "Paul N. Lee" Subject: Re: (fractint) FOTD 25-10-01 (Threads of Infinity [6]) the_juggernaut@juno.com wrote: > > Was this program narrated by Arthur C. Clarke? > ........ > If anyone can name the show based on this vague > description, tell me. I acquired a copy of the video quite some time ago, but I hear that it can now be purchased from the following (at a much higher price): http://www.films.com/item.cfm?bin=4976 Sincerely, P.N.L. - -------------------------------------------------------------- http://www.fractalus.com/cgi-bin/theway?ring=fractals&id=43&go - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 27 Oct 2001 10:17:12 EDT From: JimMuth@aol.com Subject: (fractint) FOTD 27-10-01 (Electric Minibrot [9]) FOTD -- October 27, 2001 (Rating 9) Fractal visionaries and enthusiasts: Due to the continuing rush, the discussion will once again be short. But the rush is nearly finished, so hopefully, in the next FOTD, I'll return to the hypersurface (curved 3-D space) of the hypersphere to explain how one might find their way from one place to another. Today's FOTD is not a total loss however, for the image is one of the select few to have rated a 9. The formula behind the image adds a tiny negative portion of 1/Z to a much larger portion of Z, then adds 1/C. The resulting parent fractal is a curious Mandeloid with broad bands of chaos on its east side, but only very narrow bands on its west side. Today's midget is located near the tip of a meandering, curving chaotic area in the narrow band of chaos on the northwest shore of the main west bud. I named the picture "Electric Minibrot" when the zig-zag filaments reminded me of stylized lightning. The glowing white balls could also be seen as samples of those rare glowing blobs of plasma known as ball lightning, which by the way I have never observed. Whether the rating of 9 is justified is up to the viewer to decide. The 13-minute, 13-and-13-hundredths seconds render time, which consists of a string of unlucky 13's, is a bit slow. The wise and lucky choice would be to download the GIF image from: or from: The fractal weather today (Friday) here at fractal central was chilly and blustery. The temperature of 59F 15C was not too cold, but combined with the brisk wind, it was enough to keep the sensitive cats house bound. The cats got grouchy. As for me, I'm going to wrap up the last of the serious work so that I can get to the even more serious work of searching for the next fractal. That next fractal will appear as tomorrow's FOTD. Until then, take care, be patient, but not so patient that you become a patient. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Electric_Minibrot { ; time=0:13:13.13--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+2.396786690594519/+1.241589333886222/3\ .216269e+011/1/107.489681409293439/0.0032344174442\ 0335797 params=-1.05/1/-0.000315/-1/0/0 float=y maxiter=1200 inside=0 logmap=245 mathtolerance=/1 symmetry=none periodicity=0 colors=000zzz5VG8UHBSJDRKGPMJONLMOOLQRJRTITWGUZFW`\ DXcCYfA_h9`k7bn6cp5dm4bk4ai4`g4Ze4Yc3Xa3V_3UY3TW3R\ T2QR2PP2NN2ML2LJ1JH1IF1HD1FB0E90DB2ED4EE6FG8FH9FJC\ GLBGMEHOFHPGHRGGSHFTHEVHDWICXIBZKB_KA`L9aL8cM7dM6e\ M5gN5hN4iN3kN2lN1mN0nN0oM1pM1pM2qM2qM3rM3sL3sK4tJ4\ tI5uH5uH5tJ8tLBtNEsPHsRJsSMsUPrWSrYUr_Xqa_qbbqdeqf\ jphopjtplzpmzmhzjcwgZrdUmbTh_WcXZZVbUSfPPjINnGKrFH\ vFFvFHsLJnQKiVMe_O_dPViRSnSQsVTpXVn_Yla_jdahfbficd\ kebnf`phZsiXujVokQikMckIYkDSk9Nk5hlfnibtf_ycXwaWu`\ Wt_WrZWqYWoWWnVWlUWkTWiSWhRWfPWeOWcNWbMW`LW_KWaPTb\ TRcXOd`MedKfhHglFhpCitAjx8iu9irAioBhlChiDhfEhdFgaG\ gZHgWIfTJfQKfNLfLMeINeFOeCPd9Qd6Rd3Sd1Te6ReAQfEPfJ\ OgNNgRMhWLh_KicJigIjhPjiWkjbkkillpllwkfojahiWahUVg\ UOfUHeUAdU3eU5fT7gW9gYAh_CiaEicGjeHkgJkhLliNmjOnkQ\ nlSomUpnVpoXqpZrq`rrassastasuatvatwatxarybqzcpzdoz\ enzemzflzgkzhKzVGzQBzM6zI } 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================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sun, 28 Oct 2001 09:56:52 EST From: JimMuth@aol.com Subject: (fractint) FOTD 28-10-01 (Midget in the Woods [8]) FOTD -- October 28, 2001 (Rating 8) Fractal visionaries and enthusiasts: My first impression of today's fractal scene was one of a mass of dense alien foliage, perhaps starting to turn yellow with the approach of alien Autumn. Then, when I saw the Mandelbrot midget in the midst of the brush, I named the image "Midget in the Woods". The most unusual feature of the 8-rated image may be the totally different nature of the areas north and south of the midget. North of the midget, the surroundings appear solid, like a more or less normal fractal scene. But to the south, the features resemble an archipelago of islands interlaced with open areas of water. The dividing line cuts straight through the center of the midget. This dividing line is explained by examining the parent fractal, which is a circular open hole filled with fractal debris. The chains of debris extend beyond the open area and continue well into the solid area surrounding the hole. The size of the hole is dependent on the bailout, which is specified by the imag(p3) parameter. The greater the bailout value, the larger the hole. Knowing that the size of the hole varies with the value of the bailout, I found it simple to take a reasonably interesting midget on the outside of the open area and increase the bailout until the edge of the open area expanded to cut straight through the center of the midget. It took a few trials to find the exact bailout, but the image is a very fast one, so this was no problem. Once I had fixed the bailout, it was only a matter of finding a reasonable color palette. Not counting the set-up time, the attached parameter file runs in 1-1/2 minutes. Not counting the time required to go on-line, retrieving the GIF image will take about the same time. Those who decide to download the GIF image will find it waiting at: and at: But before going there, give Paul and Scott a few minutes to render and post the image. The fractal weather today was quite chilly, with brisk winds, heavy clouds, occasional spits of rain, and a temperature of 52F 11C. These conditions limited the fractal cats to only a few minutes outdoors, but they didn't complain too much, and were actually rather refined cats most of the day. I've been thinking much (a rare event) about the fourth dimension and the hypersphere lately, and have decided that the best place to start is at the surface. The surface (or hypersurface) of a hypersphere is a three- dimensional space of constant positive curvature. Limited portions of this curved space appear exactly like our familiar 'real' space, though as the range of vision grows larger, strange differences appear. One of the most intuitive features of the 'real' world is that the farther away an object lies, the smaller it appears, until it finally disappears altogether. To our everyday minds, it must be this way. Common sense dictates that it could not possibly be any other way. If our space were the surface of a hypersphere however, common sense would lead to a wrong conclusion. An object would first appear smaller with increasing distance in the expected manner, but then, once it passed beyond a distance of one quadrant (90 degrees), it would begin to appear larger, until it reached the antipode (opposite point) of the hypersphere, when the object would appear horrendously magnified, surrounding us in all directions. Of course, the motion of objects, the finite speed of light, and the ripples in space caused by the presence of mass would prevent the ultimate view from being the back of our own head. But the apparent increase in size with increasing distance should easily be observable. To my knowledge, we have not observed this effect in our universe. This may be because we cannot observe a large enough volume of space, but most likely it is because our universe is not shaped like the hypersurface of a hypersphere, but rather more like a pseudosphere. But a pseudosphere is a different animal entirely, which makes a different story. We'll not get into that story -- at least not yet. In the next FOTD I'll lay out the latitude, longitude and altitude grid on the hypersurface of a hypersphere. Until then, when we'll all have our bearings, take care, and don't get lost. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ MidgetInTheWoods { ; time=0:01:31.61--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+1.81788303560401100/+0.010023098963900\ 95/3360.9/1/80.0000000001628422/-1.592690701546217\ 72e-010 params=1/-1.5/2/-15/0/245400000 float=y maxiter=275 inside=0 logmap=20 colors=000dSWh`XifVilTjrRjxPdrM_lJVfHP`EKVCFP9AJ7I\ J6QJ5YJ4jJ3rJ3zP7mUAgZDedHciKbnNWgOQaPKWQJTRIRSHPT\ HNUGLVFJWEHXEFY7EX0EW5CXABYF9ZK8_P6`U5aY4bV6cS7dQ9\ dRAeSDeTGfUJgVMgWPhXShYVgZYf_Ze`_daacbbbccadd`ee_f\ cZgaYiZXkXWmUVoSVqPVsMWuKXwHYyFZzC_zA`zCazDazEazGa\ zHazIbzKbzLbzMbzObzPczQczSczTczUczVczXezYfzZgz_hza\ izbjzclzdmzfnzgozhpziqzjrzkkzldzmbzn`znZzoXzoVzpUz\ pSzqQzrOzrMzsLzsJztHztFzuDzuCzvDzvEzwFzwGzxHzxIzyJ\ zyKzzLzzMzzNzzOzzPzzPzyNzwMzuLzrKzpJznHzlGziFzgEze\ DzcCzbBzaAz`Az_9zZ9zY8zY8zX7zW7zV6zU6zT5zT5zcJzmXz\ kWziWzgWzfVzdVzbVzaUz_UzYUzXTzVTzTTzSSzQSzOSzNSzKW\ zI_zGczEgzBkz9oz7sz5vzArzFnzKjzPfzUbzYZzbVzgRzlNzq\ JzoFzlAziJzfSzc`z`izYqz`kzcfzfazhXzkSznNzqIzoDzmKz\ hQzcXzZbzUizPozNpzKqzIrzGszDtzBuz9vzJmzTezaYzXUzTR\ zPOzLKzHHzDEz9BzCEzEGzGIzIKzKMzMOzOQzQSzSUzUWzWYzY\ _z_bzadzcfzehzgjzilzknzmp } 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================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Sun, 28 Oct 2001 16:39:02 -0500 From: "Phil DiGiorgi" Subject: (fractint) Fractint on Windows XP Is it possible? I've been unsuccessful so far. I still have a win 98 partition I can boot with, but don't need it for anything else anymore. Anyone? - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Mon, 29 Oct 2001 13:09:38 +0000 From: "Andrew Coppin" Subject: Re: (fractint) FOTD 28-10-01 (Midget in the Woods [8]) >From: JimMuth@aol.com >Reply-To: fractint@lists.xmission.com >To: fractint@lists.xmission.com >CC: philofractal@lists.fractalus.com >Subject: (fractint) FOTD 28-10-01 (Midget in the Woods [8]) >Date: Sun, 28 Oct 2001 09:56:52 EST > >FOTD -- October 28, 2001 (Rating 8) encore! encore! Thanks. Andrew. _________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Mon, 29 Oct 2001 10:54:39 EST From: JimMuth@aol.com Subject: (fractint) FOTD 29-10-01 (Randomized Colors [6.5]) FOTD -- October 29, 2001 (Rating 6-1/2) Fractal visionaries and enthusiasts: I named today's image for its basically random color palette. Except in the areas near the center, where I emphasized the midget's surroundings with a soft green glow, the entire scene is colored with one on the random palettes created with the key. The resulting fractal is vivid, though the disorganization of its colors holds its rating to no more than a 6-1/2. The name "Randomized Colors" needs no explanation. The parent fractal of today's scene has perhaps the most irregular shape that I have yet come upon, and likely will produce several more FOTD's before being discarded to the fractal archives. It is well worth an outzoom and a look. But before doing an outzoom, reset the logmap to 0. The 17-minute render time from the attached parameter file is a bit trying. The better choice is to download the GIF image from Paul's web site at: or from Scott's site at: With the fractal image under control, it's time to return to the four-dimensional abstraction known as the hypersphere. Like a spherical 3-D planet, a hyperspherical 4-D planet has an equator, a great circle that lies in the plane of rotation. But unlike a 3-D planet, a hyperplanet also has a polar great circle. This polar circle marks the axis of rotation. As the hyperplanet rotates, the points of the equator rotate in the normal 3-D manner, but every point along the polar circle turns on itself, remaining fixed in position exactly like the two polar points of earth. In the case of a 3-D planet, the rotation is simple. Due to the gyroscopic effect, the axis and its orientation will remain fixed unless an outside force is applied, which will cause the axis to rotate. With a 4-D hyperplanet however, the situation is far more complicated. The simple single rotation is a special idealized case, which would almost never be realized. The complication lies in the polar circle, which, even while acting as the axis of rotation of the equator, may itself begin rotating exactly as the equator is already doing, putting the hyperplanet into an entirely new state known as a double rotation. If the two rotations are equal, every point of the hyperplanet but the center point moves in a circle, while the center point remains fixed. If the rotations are unequal, every point spirals around and moves along a circular line, in a screw motion, tracing out a path known as a surface of double revolution, which is a two-dimensional surface curved in four dimensions. This surface somewhat resembles a doughnut. This hyperdoughnut shape is also the shape of the latitude surfaces of a hyperplanet. And in the next FOTD we'll actually lay out a latitude, longitude and altitude grid on our hyperplanet. The fractal weather today (Sunday) was brilliantly sunny but with a chilly temperature of 51F 10.5C. The winds were lighter however, and this permitted the fractal cats to sleep for over an hour in the warm sun of the porch. Unfortunately, being neither a fractal nor a cat, I cannot sleep in the sun. Instead, I find myself with a day's work that needs to be done before I turn to the fantasy world of fractals and hyperspace. But despair not, for the probability is 99.975325 percent that I shall return tomorrow around this same time with another glorious fractal and a few words not quite as glorious. Until then, take care, and if you take perfect care, nothing more will be needed. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Randomized_Colors { ; time=0:16:53.15--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.02460269414871400/+0.015803598960749\ 27/7397888/1/37.5000008972091194/-4.40023098798036\ 916e-007 params=0.439/2.466/1.265/1.372/0/0 float=y maxiter=1800 inside=0 logmap=315 colors=000PcnLXcHPUCKKXEco7vz1zl0rU0Y90CMEMYRVhcds\ olZprFrw7nz1kz0nz0pz4050as0O`09HdzhIcL0zz0iw0Uc0CI\ FKAzszzdxdPdI9ILzv7`SzH2wA0c40I00UaSCICPmXAIEziMoU\ EOC4zPOa99RzOPhzAKYFhz9Xo4KY05FAzA4h40K0zzzsix`UdH\ CItA70zn0t`0`O0F9Uz1Io05O0Enz7Xd1EIzolz4zp1tZ0aF0H\ E7r92Z40M009Aex4Rc0AI0zS0XC9oh4aX1OL097g0zV0nK0X70\ EzFHVOzMHoE9Y41Fo54a21O00900zKza5Vxz0U`0t00`00H00x\ 9Y0Vz0Lo0CY02FMIz95VzUzsKx`AdH1Iz0zzwzVScA0`40M009\ ozzYgsFKRIzz5ZY0HI0AC045000rAsP1R`0EPEztY9`L4H700v\ 00R0MezFUl9IX15E91r40c10P00AKAz71c0Ve0CKzzaHzV5XE7\ t41R01zzszz`peHOKzz1sp0RO0zKnwC`c5OI09rF7P417zc2dP\ 0IAE1a90R40H0055IV19K017zCpi5YL0FIV0CL05C0020OcgHK\ V9MK1O7zPrxdPlSwMUSMVz9XXzYzhZgL`KCaP2cA2dz0ew0gc0\ hI4ig1kS0lCsnz`odHpIZrRPsIFtA4v25wpixwrzFZz7Fz1Vz1\ gzzzzzvzwazcHzIOzsEz`4zHczpzzMezEKz4SzzSzdHzP5zAzz\ 0azxRzhHzU5zC0zzzz`czHzzt } 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================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Mon, 29 Oct 2001 21:59:44 +0100 From: Guy Marson Subject: Re: (fractint) Fractint on Windows XP At 16:39 28/10/01 -0500, you wrote: >Is it possible? I've been unsuccessful so far. I still have a win 98 >partition I can boot with, but don't need it for anything else anymore. > >Anyone? but Fractint don't run very fast under Win XP, I must push [Enter] when generating a fractal, then it run fast for c. 10 lines and slow down until the next [Enter] get pushed... cheers, Guy > > > >-------------------------------------------------------------- >Thanks for using Fractint, The Fractals and Fractint Discussion List >Post Message: fractint@lists.xmission.com >Get Commands: majordomo@lists.xmission.com "help" >Administrator: twegner@fractint.org >Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" > - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Mon, 29 Oct 2001 17:35:31 -0500 From: "Multiple Bogeys" Subject: Re: (fractint) FOTD 23-10-01 (Something Different [7]) - ------=_NextPart_001_0001_01C160A0.1BF724A0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable Two problems with that description. First of all, if a hyperplanet accret= ed in 4-space it would most probably have angular momentum about every po= ssible axis -- a rotation matrix like | cos a sin a 0 0| |-sin a cos a 0 0| | 0 0 cos b sin b| | 0 0 -sin b cos b| describes a rotation a 4-sphere with no fixed points on the surface. Such= a planet would have no poles at all. The more serious problem is that it would spiral into its sun in finite t= ime, or spiral away into deep space. There are no stable orbits in a four= - -space (inverse-cube) gravity.
Get your FREE download = of MSN Explorer at htt= p://explorer.msn.com
- ------=_NextPart_001_0001_01C160A0.1BF724A0 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
<snip>
 
Two problems with that description. First of = all, if a hyperplanet accreted in 4-space it would most probably have ang= ular momentum about every possible axis -- a rotation matrix like
<= DIV> 
| cos a   sin a    &n= bsp;  0       0|
|-sin a&nb= sp;  cos a       0   &n= bsp;   0|
|     0   &n= bsp;   0   cos b   sin b|
| = ;    0       0  -s= in b   cos b|
 
describes a rotation= a 4-sphere with no fixed points on the surface. Such a planet would have= no poles at all.
 
The more serious problem i= s that it would spiral into its sun in finite time, or spiral away into d= eep space. There are no stable orbits in a four-space (inverse-cube) grav= ity.
 


Ge= t your FREE download of MSN Explorer at http://explorer.msn.com
- ------=_NextPart_001_0001_01C160A0.1BF724A0-- - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ End of fractint-digest V1 #607 ******************************