September 2007 - Fractint - mailman.xmission.com

Triternion and ismand parameter
by GillesNadeau 16 Sep '07

16 Sep '07

Hello all, I spent the night to be played with the formulas triternions of Russell Walsmith and the parameter ismand. Here formulas and of the parameters by hoping that that will interest of people on this list. Gilles

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FOTD 16-09-07 (Dry Valley Ambush [4])
by Jim Muth 15 Sep '07

15 Sep '07

FOTD -- September 16, 2007 (Rating 4) Fractal visionaries and enthusiasts: Today's image is named "Dry Valley Ambush". I gave it this name because I was ambushed by it. Dry valleys are symmetrical features that look like they have a midget at their centers, but when the symmetry is enlarged, it dies out in a flat blank area. A flat blank area is what I found when I eagerly dove into the broad double spiral in today's image, fully expecting to find an unusual midget at its center. Due to my disappointment, I rated the image at a lowly 4. I doubt that it is worth much more. But with its clashing bright oranges and dark blues, there is a certain mischievousness about it that merits publication. So I decided to change what should have been an immediate discard into the FOTD for today. The parent fractal resulted when I combined 0.01 part of Z^(-77) with 0.01 part of Z^(79) and added (1/C). This parent is little more than a thin ring of radius 1 centered on the origin, with the fractal stuff lying in the interior of the ring. At first, the entire ring looks promising, but only the parts of the ring that lie on the X-axis are actually in the critical state. Today's scene is located near the point where the ring inter- sects the negative X-axis. Because of the location, I expected more at the center of the spiral in today's image than I found there. But fractals are unpredictable, and one is sometimes un- expectedly surprised or, as in today's case, disappointed. At least, the image is a fast one, finishing in 53 seconds on the fast P4-2000mhz machine. It would take near 5 minutes on the old P200mhz unit. The finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A slightly chilly but otherwise near perfect day prevailed here at Fractal Central on Saturday. The fractal cats enjoyed the pigeons scrounging for food on the sidewalk. I enjoyed having the work caught up, even though the day's fractal left something to be desired. The next fractal will appear in 24 hours. Until then, take care, and fill in life's blanks with fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Dry_Valley_Ambush { ; time=0:00:52.79-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-1.00587732385816700/+0.000000760828969\ 08/5965409 params=0.01/-77/-0.01/79/0/0/0/0 float=y maxiter=310 inside=255 logmap=50 periodicity=10 colors=0000AK0AK0AK0AK0AK0AK0AK0AK0AK0AK0AK0AK0AK0\ AJ0AM0AP1AR2AU3AU4AU5AU7AU9AUBAUDAUFAUHAUKAUNAUQAU\ TAUWAUZAUaAUdAUfAUiAUkAUmAUoAUpAUrCUtFSvIPwLNxOLyQ\ KzSJzUIzSGzQFvOErMDmKChIAcG9cI8cL7cO6cS8cWAc_CeaEn\ cGnaHo_IoYJpWJpUFmS8jQ8gO8dM8bK8_I8XG8UF7RG7PG7MI7\ PLAUODZRGaUJcXM`_PYbSVeTShTPfTNdTKbTH`TEZTBXT8VTYT\ TfRTgWZl`cudhsbfraeq_doZcnXamW`kU_jTZiRXgQWfOVeNUf\ ORgOPhONiOKiOIjOGkODlOBlO9mMCnLFnJIoILpGNpFQqDTrCW\ rBYpDZoEZmG_lH_jJ_iK`gM`fNadPacQaaSb`TbZVcYWcXXcTV\ fQUhNTjKRmHQoEPqBOsCQsDSsEUsFVsGXsHZsI`sJasC_o6Yk0\ Xg4`d8caBf_FiXIlUMoSPrPTuMWxKTxRRxYPxcNxjLxpPtnTqm\ Xnk`kjchhgegkbeo_drXcnZ`j_Zf`XcbV_cSWdQTfOPgMLhJIj\ HEkFAlD7mB8qv9psAppBpnCokDoiEofFndGnaHn_IjZJgZJcYK\ `YKYYLUXLRXMOXNKWNHWOEWOAVP7VP4VODUNMTMVSMcRR`PVYO\ _VNcSLhPKlMJqJHuGGyDFwCJvBMuBPsASr9Vq9Yp8`n7dm7gl6\ jj5mi5ph4sg4va7sXAqSDoNGm } frm:MandAutoCritInZ {; 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)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 15-09-07 (More than Meets an Eye [6])
by Jim Muth 14 Sep '07

14 Sep '07

FOTD -- September 15, 2007 (Rating 6) Fractal visionaries and enthusiasts: Today's image continues the thread of the past several days, as we continue onward and upward to an exponent of 6. The parent fractal is the expected 5-lobed Mandeloid, with today's image located just off the spike of the negative X-axis, very near the point where the spike joins the main body of the parent fractal. I named the image "More than Meets an Eye". In my imagination I see many more things lurking in the depths of the image. Un- fortunately, these are beyond resolution, unless one wishes to shift to arbitrary precision math, which is uselessly slow with the manzpower formula. To prevent the calculation time from jumping from a lightning-fast 105 seconds to an almost unbeliev- ably slow 34 hours, I have included the mathtolerance entry in the parameter file. As for the rating, I decided to stick with a rating of 6. The image is too close to what would be expected to earn more than this. The calculation time of 1-3/4 minutes is fast enough to prevent the stress of boredom, and in addition, the image is available for instant viewing on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The Friday temperature of 75F 24C was near ideal, but heavy clouds and a threat of rain kept the day from reaching its full potential here at Fractal Central. The fractal cats did reach their full potential for trouble however, when Cassie somehow worked her way behind a loose panel in the bathroom closet and spent the next hour or so exploring the no-man's land between the floor and ceiling. She emerged quite dusty but otherwise satisfied with her adventure. My day was busy enough to keep boredom at bay. Tomorrow is still a question, and there will be the next FOTD fractal to contend with. Until then, take care, and stay alert. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= MoreThanMeetsAnEye { ; time=0:01:45.68-SF5 on P4-2000 reset=2004 type=manzpower passes=1 float=y inside=0 center-mag=-1.10976164061526900/+0.000001168008348\ 63/3.847449e+012/1 params=0/0/6/0 maxiter=10000 logmap=438 periodicity=10 mathtolerance=0.05/1 colors=000A0jA0iA0gA0eA0dA0bA0`A0_A0YA0WA0VA0TA0RA\ 0QA0RA0RA0SA0SA0SB0TC0T71T83U84V85W96X98Y99ZAA_AB`\ ADaBEbBFcBGdCIeCJfCKgDLhDNiDOjEPkEQlESmFTnFUoFVoHW\ mJWlKWkMXjOXiPXhRYgSYfUYdWZcXZbZZa`_`a__c_Zd_Yba_`\ b`_daYecWgdVheTifRkhQliOnjMolLpmJqnIroGspFtpEuqDvq\ CwrBxsAyt9zu8zv7zw6zx5zy2zz5zzAzzFzzKzzPzzUzzZzzcz\ zhzzmzzrzzwzzwzzwzzwzzwzzwzzxzzyzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzvzzmzzczvUzrKvmArh2mc4hZ5cY6_X\ 7WW9UVATVBSUCRTEPSFORGNRHMQJKPKJOLINMHNOFMKELG0FC0\ EI0ERCM_DPcESgEVkFYoK`zfcwcfxcdxUbxKaxJ_xKZxKXyLVy\ LUyMSyPRyUPzhOwUNvPMuLLtLKsKJqKIoJHlJGjIFhIEgHDfHC\ eGBdGAbK9aP8`U7_Z6Zc5Zh4Zm3Zr3`v6az8bzAbzCczEczGdz\ IdzKezMezOezQfzSfzUgzWgzYhz_hzaizcizejzgjzijzkgzie\ zhczg`zfZzdXzcVzbSzaQz`OzZLzYJzXHzWFzVIzULzTOzTRzS\ UzRXzR_zQbzPezPhzOkzNmzNpzLrzKuzIwzHszGozGkzGhzGdz\ G`zGXzGUzGWzKXzN_zo`zn`zl } END PARAMETER FILE=========================================

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FOTD 14-09-07 (Qunitic Conundrum [6])
by Jim Muth 13 Sep '07

13 Sep '07

FOTD -- September 14, 2007 (Rating 6) Fractal visionaries and enthusiasts: The logical step beyond yesterday's quartic minibrot is today's quintic minibrot. To explore the Z^5+C Mandeloid I had to turn to the MandelbrotN formula, which can calculate Mandeloids of any order. Things go a bit slower because the type=formula is not quite as fast as the type=mandel4, but I doubt that anyone will complain about a calculation time of 14 seconds on a fast computer and maybe a minute or two on a slower unit. Though the parent Mandeloid is of order 5, it has only 4 lobes, which is the exponent of Z minus 1. This is true of Mandeloids of all orders. Today's image is located on a small filament extending from a small minibrot near the large northwest bud of the parent. The extreme magnitude of over 6*10^12 requires the mathtolerance entry in the parameter file. I named the image "Quintic Conundrum" though I can see nothing unusually puzzling or punnish about it. The rating of a 6 seems appropriate for an image that required so little effort. The major part of running the included parameter file will be copying it in text format into your Fractint directory and running it as you would any other parameter file. Even this minor task may be eliminated by viewing the completed image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday began with a fog bank hanging overhead, but a warm sun cleared away the mist by 9am and the rest of the day was near perfect, with a temperature of 77F 25C. As is usually the case, the fractal cats paid little attention to the weather, diverting themselves instead with various sorts of mischief, such as over- turning waste baskets and scattering the contents. In my department, the work was mostly finished by mid-afternoon, leaving ample time for the fractal search, not to imply that a major search was necessary to find today's image. The next FOTD will appear in 24 hours. Until then, take care, and before you begin a search for reality, be sure you know what reality looks like. Hint -- it might not be the material universe. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Quintic_Conundrum { ; time=0:00:14.12-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotN center-mag=-0.879513612531\ 7894/+0.584447614384022/6.046e+012/1/-15/0 passes=b params=5/0/0/0/0/0 float=y maxiter=500 inside=255 logmap=58 periodicity=10 mathtolerance=0.05/1 colors=000HFZHFXHFVHFTHERGDPECNCBL9AF6790040000000\ 0zBwz5rz8mw7hr6cm5Zh5Uc4PZ3KU2FP2AK15Fzz3itAZh8N`6\ AT54M3201JzOHuMGpKEkIDfHCbFAYD9TCAOAKJ8UF6cB5m73z3\ 1zO5zJ4zE3z92z41nQziNzeLzaJzYHzTFzPDzLAz_pz`ozanmb\ mcblUckKdjFeiDehCfgBgfAhe9hd8ecAcbB`bDZaEWaGU`HR`J\ P_KM_MKZNIZOMXPPVPSTPVRPYPQ`NQcLQfJQiHQlFRoDRrBRu9\ Rx7Rv8Uu9WsAZrA`pBcoCemDhlDjjEmiFogGrfGtdKqbOn`RkZ\ VhXZeVabTe_RiXPlUNpRLtOKwMHpOEiQCcS9XU7RW4KY2EZ4K_\ 6P`8V`A_aCebEjbGpcIudKzdLzeMzeMzeNzeOzeOzePzePzeQz\ eRzeRzeSzeSzeXzYazRfzKkzDhzCfzBdzAbz9_z9Yz8Wz7Uz6R\ z6Pz5Nz4Lz3Jz3Gz6Ez8CzA9zC7zE5zG8zIBzKEzMHzOKzPNzR\ QzTTzVWzWZzYaz_dzagzbfz_ezYdzVczTbzQazO`zM_zJZzHYz\ EXzCXzARz8Mz6Gz5Bz34z25z1EzPDzNCzzBzzAzz9zz8zz7zz6\ zz5zz4zz3zz2zz1zzkzzhrzezzbzz_zzXzzUzzRzzOzzLzzIzz\ FzzCzz9zz6zz3zz`zzIzzLzzJzzHzzFzzEzzCzzAzz8zz7zz5z\ z3zz1zzgzz_zzTzzMzzEzz000 } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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FOTD 13-09-07 (Deep in a Quartic [6])
by Jim Muth 13 Sep '07

13 Sep '07

FOTD -- September 13, 2007 (Rating 6) Fractal visionaries and enthusiasts: After a string of really great images, today's effort returns us to the lowlands. But these are not the Z^2+C lowlands; they are the Z^4+C lowlands, where boring everyday minibrots are much easier to find, but where the good ones lie far deeper. Today's scene lies unusually deep in its parent Mandeloid, and thereby escapes the boredom. But it is this extreme magnitude that makes the mathtolerance=0.05/1 entry necessary. The image is located on a short filament leading from a bud on the north- east shoreline of a large midget on the negative X-axis of its parent. This midget corresponds to the large midget at -1.75 on the main spike of the Mandelbrot set. Perhaps the most striking thing about today's scene does not become visible until two full outzooms are done on it, revealing a most un-quartic pattern, more reminiscent of the classic Mandelbrot set than the Z^4+C Mandeloid. The name "Deep in a Quartic" describes the location of the scene. Compared to the most recent fractal winners, today's image rates only a 6, but it is actually a rather pleasant diversion, well worth the few seconds needed to calculate the parameter file, which uses the passes=b option and the super- fast mandel4 formula. Though the parameter file is a fireball, it is still necessary to set up the parameter file for calculation. This small inconvenience may be avoided however by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the finished image there. Wednesday was an absolutely perfect late-summer day, with blue skies and a temperature of 73F 23C here at Fractal Central, but due to the heavier-than-expected work, I had no time to take advantage of the conditions. The fractal cats were too busy romping to notice the weather. The climax came when they got into a heated tussle on the stairs and rolled halfway down, cursing each other loudly. After that they took a break to make up. The next FOTD is due in 24 hours. Could it be another 10 or another lemon? Check back then to see. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Deep_in_a_Quartic { ; time=0:00:10.47-SF5 on P4-2000 reset=2004 type=mandel4 passes=b center-mag=-1.219\ 512077076407/+0.00327130420977419/2.715843e+013/1/\ -25/0 params=0/0 float=y maxiter=1200 inside=255 logmap=80 periodicity=10 mathtolerance=0.05/1 colors=000A0KA0MA0OA0QA0SB0UC2WD4YH7`LAcPDfTGiWJka\ RjgZimfhsngyvguuuzzzgIPZHFRG6Y`QcuhWebOQXGBSSDhmEz\ c0mZ4hI7cLB_OEVSHQVLMYOH`RDeYNjcXoiftopyuzxvvwvsvw\ puwmtxjsxgsxdmoTggHb_6ZXCVUHSRMOOSKLXHIaSHMaG7bJGc\ MOdPXeSdXUfOVgMZzLbzKezJizHmpGphFt_EwSKsKPpEUmBZj9\ de7i_4nS2sK0nJ4jO8eSCaXGXWKTWNhfEigDjhCiiBhiBhiBgi\ BfiBfiBeizdizdjzcjzcjzbjzajzajz`jz_jz_jzZkzYkzYkzX\ kzXkzWkzVkzVkzUlzTlvTlrUlmVlhWlcXlZYlUZlP_m7`m7am7\ bm6cm6dm6em6fm6gn6hn6in6jn5kn5ln5mn5nn5on5po5qo4ro\ 4so4to4uo4vo4wo4xo4yn5zn6zn7zn8zn9zn9znAznBznCznDz\ nDznEznFznGznHynHxnIwnJvnKunLtnLsnMrnNqoOpoPooPnpQ\ mpRkpSiqTgqUeqUcrVarW_rXYsYWsYUsZTt_Tt`UtaUuaVubVu\ cWvdWveXveXwfYwgYwhZxiZxi_xh_xh`yh`yhayhayhaygbzgb\ zgczgczgdzgdzfdzfezfezffzffzfgzegzegzehzehzeizeizd\ jzdjzdjzdkzdkzdlzclzcmzcmzcmzcnzcnzbozbozbpzbpzbpz\ bozanzamzbmzblzbmzcmzc000 } END PARAMETER FILE=========================================

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FOTD 12-09-07 (A Hairy Situation [10])
by Jim Muth 11 Sep '07

11 Sep '07

FOTD -- September 12, 2007 (Rating 10) Fractal visionaries and enthusiasts: This is unheard of -- two 10-rated FOTD fractal images in a row, and once again from the prolific parent fractal that has been the source of the FOTD images for over a week. Today's image comes from the tip of a half cut-off ring on the northeast shore of the largest bay of the parent fractal. It is another half-evaporated image, with the inside part brought to life by the inside=atan option. For a reason known only to the powers that be, this option creates the blatantly obvious violet blue ring that fills most of the frame. I named today's FOTD "A Hairy Situation". One glance at the image will reveal the reason for the name. Then I rated it at a top-of-the-scale 10. In my opinion, it's as good as yesterday's half-and-half image, which also rated a 10. The calculation time of 33 seconds or 3 minutes is brief enough to hardly be noticed. And even the minor effort of setting up and running the parameter file may be avoided by going to the FOTD web site, where the finished image is posted for viewing. The FOTD web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature was a reasonable 75F 24C here at Fractal Central on Tuesday, but off-and-on rain kept a damper on things. I was busy enough with commercial work to have no time to complain. The fractal cats did complain however. They complained about the lateness of their daily treat. The next FOTD will appear in 24 hours. Until then, take care, and be kind to your iterated fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Hairy_Situation { ; time=0:00:32.90-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+8.694009672137327/-1.671633724707316/\ 1.982862e+011/1/45/-0.004 maxiter=550 params=-5.5/\ -1.4142/-1.1/-4/0/47055000.0/0/0 float=y inside=atan periodicity=10 mathtolerance=0.05/1 colors=000bkVMkmlTYhV`eXcRSSMQSHOSCMR7KR3JR5FP7BN9\ 7LF0JD6IF8HHBHJDGLGFNIFPLERNDTQDVSCXVBZXB`_AbaAXc9\ Re9Lg9Fi89k84l86gA8cBAZDCVEERGGMHIIJ00HM9MO5NP1OO5\ MN8L0H0L0IKJGJNFIRDHVCGZAFc9Em7zr6zzUzw3zz19z0Az2B\ z4Bv5Ct7Cq8DnAEkCEhDFeFFbGG`IH_KHYLIWNIVOHWNHXMHYL\ HZKH_KFZKG_MH_NH`OI`PI`QJaRJaSKbTKbULbVLcWMcXMcYTa\ WZ_UeYTkWRrUPxTOeNxfPvgQugRshSrhTpiVoiWmjXlkYkkZil\ `hlafmbemccndbneag_VaUOWOHQJBOKCMKDKKEJKEHLFFLGELG\ CLHAMI9MI7MJ5MK4MK6ON7PP9QSARUBSXDUZEVaGWcHXfIYhuB\ DlFKcJRVNXMRcDUiCWgCYe000C_cCaaCc_BeYBgWQ12SA9UJFW\ RLY_S_hYapcvlpsVZf2S`9IVG8ZaWavrcQ_hIimBsGXjqbkQfl\ UemZgncio00rlzzqtzuqzrpponollnijlfhkcgjeUzYcgVbfSb\ ePcdMcbJcaGc`Ed_GeXIfUKbRM_OOVLPQIRLFTHCVC9X76Y34l\ f1ne3od5pd7rc8scAtbCvaDwaFx`Hy`IlYF`VCPS9RVATYBV_C\ XbCZdD`gEaiEcdCd`AgS7iN6jJ4lE3mA1n60oA1oD2pG3pJ4pM\ 5qP6qT6rW7rZ8ra9sdAsgBsjB } frm:MandAutoCritInZ {; 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)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 11-09-07 (Inferno and Paradise [10!])
by Jim Muth 10 Sep '07

10 Sep '07

FOTD -- September 11, 2007 (Rating 10!) Fractal visionaries and enthusiasts: Is today's image truly worth the top rating of a 10? Well, I am not fully convinced it is, but what's the use of having a rating of a 10 if nothing ever makes it there. The image is yet another one in the same parent fractal that has supplied so many FOTD fractals over the past couple weeks or so. It's rare that such a harmless looking parent fractal turns out to hold so many unsuspected goodies. Today's half-and-half scene is located in a little cut-off ring- world near a large ring at the southeast extremity of the parent fractal. So far so good. But what makes the image a 50-50 one? The secret is the bailout radius. I have tweaked the bailout until the line that divides the all-there part from the half- evaporated part runs directly through the center of the frame. The left side of the image is normal equal-iteration-band stuff; the right side is half-evaporated, with the inside parts filled in by the 'zmag' option. While studying the image for a name, I noticed the hell-heaven contrast, and decided to name it "Inferno and Paradise". The rating of a 10 is based half on the artistic effect and half on the mathematical interest. I leave it to the individual fractal fan to judge if the image is truly worth the rating of an almost impossible to achieve 10. The calculation time of a brief 1-1/4 minutes on the P4-2000mhz machine will make the trip to the great fractal beyond quite a short one. On a P200mhz unit, the trip will take 7 minutes -- slower but more scenic. Another easy way to make the trip is to go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the completed GIF image there. The heat and humidity fell off a bit here at Fractal Central on Monday, but the 82F 28C was still oppressive, especially for those who must work outdoors. The fractal cats do their work indoors, so they do not worry about weather. With a 10-rated fractal, my day was good enough. Tomorrow will likely be much the same. The next FOTD will appear in 24 hours. In the unlikely event that it exceeds today's, I will have to expand the rating scale to 11. Until then, take care, and never abandon all hope, even if you find yourself hopping around on the coals of the inferno. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= InfernoAndParadise { ; time=0:01:14.92-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+11.19123687238325/-16.75458653288057/\ 17818.43/1/-147.5/8.86548195966341268e-010 params=-5.5/-1.4142/-1.1/-4/0/32750200000.0/0/0 float=y maxiter=550 inside=zmag periodicity=10 colors=000rzzLCzH7zE3zI7zMAzPEzTHzXLz_OzYRzWUzUXzS\ _zQbzOezMhzKkzImzLizOfzRczU_zXXz_UzbRzdNzgKzjHzmEz\ pAzs7zv4zx1z2AF6AFAAFEAFIAFMAFQAFUAEYAEaAEeADiBDmC\ DpDDqKIrQKwZKtaKuaKzhKzgKviKugKseKscKsaKr`Kr_JrZGq\ YEqXBqW9pV7pU4pT2pS0oV6oYCo_InbOndTngZmidmljmnohjl\ cfiZcfU_cQW`LTYGPVBLS7IP52z95zD7zH9zLCzPEzTGzXIz`L\ zdNzhPzlSzpUztWzwYzvVzuTztRzsPzsNzrKzqIzpGzoEzoCzn\ 9zm7zl5zk3zk1zmAznIzoRzqZzrgzsozqizpczoYznSzmMzlGz\ kAzj5z`6zPMzE`z3oz5kz6gz8cz9_zBWzCSzDPzCYzBezBgzQ1\ zSAzUJzWRzY_zK9zLAzLBzMCzNDzOEzOEzKHzHKzENzBQzDRzE\ RzFRzGRzHRzISzJSzKSzLSzMSzNTzOTzPTzQTzRTzSTzUVzVWz\ WXzXYzYZz`_zb`zd`zfazibzkbzmcz000qdzlbzh`zdZz`XzXV\ zTUzPSzLQzHOzDMz9Kz5Jz8HzAGzDFzFEzHDzKBzMAzO9zR8zT\ 7zV6zT5zS5zQ4zP4zN3zM3zK2zJ2zO8zTEzPDzMCzIBzFAzCAz\ B9zB9zB8zB8zB7zB7zB7zA6zA6zA5zA5zA4zA4zA4zF8zKBzPE\ zUIzZLzcOzhSzmVzrYzWQzSLz } frm:MandAutoCritInZ {; 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)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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IFS, L-Systems in Fractint
by Tony Hanmer 10 Sep '07

10 Sep '07

Hi Richard (regarding L-systems & IFS types in Fractint, & their future development), Sorry it's taken me so long to respond. I've been away from the internet a good deal this summer, in the high Caucasus mountains of the Republic of Georgia... I've discovered a programme which seems to be the LS equivalent of Apophysis in 2d or XenoDream in 3d: Context Free Art http://www.contextfreeart.org/ I describe it thus because it allows LS programming plus a lot more non-LS work, and because its language is at least related to LS. Are you aware of it? As far as IFS goes... one difference between Apohysis IFS and that of Fractint is a great feature of the latter about which I have not found any literature, so I might as well claim credit for discovering it unless someone else can correct me. This is that if you start off with a shape like a square filled *solid* with holons, and then simply alter the numbers in the 7th column - those which deal with probability - you end up with fantastic fractal textures instead of the solid fill. (These probability numbers should still sum to 1.) I have done a huge number of explorations of squares in this manner, some with triangles, and also discovered new textures for the Dragon Curve and TwinDragon. I was waiting for the new Fractint version to reveal this, but now seems a better time to point it out, in the context of a plea not to do away with such a possibility. (It doesn't seem to work in Apophysis, or at least works differently; I haven't tried it in XenoDream yet.) I don't understand all of the details of your letter below about IFS, but am eagerly awaiting a demonstration of what it all means. Tony Hanmer On 8/1/07, Richard <legalize(a)xmission.com> wrote: > > I'd appreciate input on you regarding the L-systems stuff I posted to > the list recently. For L-systems I want the code to ultimately > approach the realistic plant rendering capability of Prusinkiewicz's > code. We're a long way off from that, but that's the target. > > For IFS, right now the code only supports probabilistic 2D/3D IFS. I > want to add more IFS types like language restricted IFS. For > rendering, I want to use OpenGL to give interactive manipulation of > the IFS rendering as well as a design interface that's better than > editing transformations coefficients in a text file. I also want to > use "point sprite" rendering for IFS which will give them more "body" > with fewer iterations and still be interactive. I've also thought > about doing a potential rendering technique where rendered iterations > define a charge in space and the rendering draws the potential > resulting from such a charge. Finally, I want to extend the text file > specifications so that you can specify the transformations in a > transform language rather than as just raw coefficients. That way you > could naturally right s(sqrt(2)/2)*r(180)*t(0.5,0.5) to mean "scale > uniformly by sqrt(2)/2, then rotate by 180 degrees about the Z axis, > then translate by (0.5,0.5)". I've come across a very nice recursive > descent parser framework for C++ -- the spirit module in the boost > library -- that will let me make a number of improvements across the > board in fractint, both for formula types and for IFS and L-system > types. > -- > "The Direct3D Graphics Pipeline" -- DirectX 9 draft available for download > <http://www.xmission.com/~legalize/book/download/index.html> > > Legalize Adulthood! <http://blogs.xmission.com/legalize/> >

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FOTD 10-09-07 (The Biggest Bang [8.5])
by Jim Muth 09 Sep '07

09 Sep '07

FOTD -- September 10, 2007 (Rating 8-1/2) Fractal visionaries and enthusiasts: For today's FOTD I decided to see what I could do with the parent fractal that has been the source of the images for the past several days, some of which have been unexpectedly good. To begin, I partially evaporated the parent fractal by raising the bailout radius to 1,000,000,000. Then I tried the different 'outside' options and found that 'mult' works best on the outside parts. Next I found that inside=bof61 works best on the inside stuff. Finally I colored the image with a rather harsh blue and gold palette. The result reminds me of a supernova, which is well enough. But why settle for half-way? Why not go all the way back to the big bang and make it an even bigger bang? I did just this, then I named the image "The Biggest Bang". And with a calculation time of 9-1/2 seconds, it would be hard indeed to get more bang for your buck. I did not want to rate today's image as high as yesterday's, one of the all-time best, yet I consider it above an 8, so I decided on a rating of 8-1/2. While searching for a name, I thought of the theory of inflation, which is the present explanation for the enexpected smoothness of the visible universe, but decided that a big bang was enough. Besides, I need some headroom if an even better cosmic-origin fractal comes along. Actually, no one was there at the real big bang, so anything we decide to say about it must remain an undemonstrated theory, backed by the mathematics of course. Speaking of numbers, as I watch the way we manipulate them until they prove our theories, I sometimes wonder whether the universe is made of numbers. To see the biggest bang take a few seconds to run the included parameter file, or go to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and view the finished GIFimage there. Summer heat and humidity continued Sunday here at Fractal Central. With weakened sun and a temperature of only 86F 30C, it was not as oppressive as Saturday, but it was sultry enough to keep the fractal cats in lazy mode. My day was once again mostly adequate. The next FOTD will appear in 24 hours. Until then, take care, and make peace with your fractal formulas. They might be the root of the cosmos Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Biggest_Bang { ; time=0:00:09.30-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=-12.0049/6.10011/0.03622717/1/-120/0 params=-5.5/-1.4142/-1.1/-4/0/1000000000.0/0/0 float=y maxiter=800 inside=bof61 outside=mult periodicity=10 sound=off colors=00000K0EZPM_VT_cZahcZkhWrlTvpiztszzzzvqzs_x\ pKzmIqiGjeEeaDZZBWX9TW7RV6PVENUMLUUKZaObdS_gVXjZVm\ bSpeQsiNvlLxkOsjRnjTiiWehY`h`WgbRfeNfgIejDel9Yg7Qb\ 6IY5BU4DW7EX9GYCHZEJ_HK`JMbMNcOPdRQeTSfWTgYShVSiTS\ jRSkOSkMSlKRmHRnFRnDRoARp8Rq6Rq4KiFDaQ6V`AWWEXRHYM\ LZHO_CS`7V`2TcESePRg_QijNhfKgbLf_MeYNdWOcUPbSQaQR`\ OS_MTZJUYHVXFWWDXVBYU9ZT7ZS5UPBQMHMKMIHSEEYACb69h2\ 7m99oFBpLDqSFsYHtcJuiKvkOrmRnnVjpYgqacsd_thWvkTwoP\ yrLzuIytKytLxtMxtOxtPwtQwtSvtTvtUvtWutXutYtt_tt`tt\ attastbstbstcstcstcstdstdrtertertertfrtfrtgqtgqthq\ uhquhquiquipujpujpujpukpukpulpuloumoumoumoun8S_9S`\ 9S`AT`AT`BTaBUaCUaCUbCUbDVbDVcEVcEVcFWdFWdGWdGWdGX\ eHXeHXeIYfIYfJYfJYgKZgKZgKZhLZhL_hM_hM_iN`iN`iO`jO\ `jOajPakPakQakQblRblRblQcmRblRbkSbkSbjSbjTaiTahUah\ UagUagVafV`eW`eW`dW`dX`cX_bY_bY_aY_aZ_`Z___Z__ZZ_Z\ Z`ZY`ZXaYXaYWaYWbYVbYUcYU } frm:MandAutoCritInZ {; 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)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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Re: FOTD 09-09-07 (The Layered Look [9])
by jackoftradez＠comcast.net 09 Sep '07

09 Sep '07

. yeah - way cool. I like layered fractals, like alot of the "mix" formulas posted by russ walsmith and others. but ... yes - work on the colors some more <g> .

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