August 2003 - Fractint - mailman.xmission.com

FOTD on 3-day Vacation
by JimMuth＠aol.com 18 Aug '03

18 Aug '03

Fractal fans: An unexpected lull in the work has given me a chance to take an unscheduled 3-day vacation. I don't know where I'm going, but wherever it is, I'll be back late Wednesday. The next FOTD will appear on Thursday August 21. Jim M.

1 0

FOTD 17-08-03 (The Supreme Mystery [7])
by JimMuth＠aol.com 17 Aug '03

17 Aug '03

FOTD -- August 17, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us to number 4 in my series if 12 MandNewt formulae, all of which are based very loosely on the Ikenaga function. Like most images produced by these formulae, today's consists largely of inside stuff, which in today's case, has been brought to life by the 'zmag' inside fill. I named the image, which resembles a scene on an alien world, "The Supreme Mystery". When I gave it the name, I had no parti- cular mystery in mind, so the viewers may take the image to mean anything they choose. The coloring is about as smooth as is possible to achieve with fractals using the measly 256 colors of the GIF format. It raises the normally 6-rated image to a rating of 7. The bottom 1/4 of the image is almost total black, so be careful not to save the image before it has finished generating. The render time of 8 minutes is acceptable, though stretching things a bit. The most efficient way to view the mystery is to download the completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Saturday started threatening here at Fractal Central, and grew more threatening as the day progressed. The temperature reached 88F 31C, then, just after 3pm, the first thunder-shower struck, with a sudden burst of wind and rain that thoroughly soaked the grass and put a quick end to the fractal cats' day in the yard. Another storm, even heavier than the first, arrived after dark, but by then the cats' moods were already sullen, and the rain made little difference. They ended the day sulking and eating tuna. My day was pleasant enough. I enjoy storms. . . . and fractals. Today is starting much better. There may be hope for happy cats. Until next FOTD, take care, and ponder the unspeakable mysteries of life. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_SupremeMystery { ; time=0:07:46.15--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandNewt04 passes=1 center-mag=0.26686\ 1/0.010155/17.31184/1/-80/-3.77822773067748585e-014 params=7.25463423566393/-5.527127903073214/2.36711\ 935789056/-2.570262764366588/-6.781682790612506/-5\ .718723105563524 float=y maxiter=250 inside=zmag logmap=yes periodicity=0 colors=000PTnQTnRToSUoTUoUVoVVoWVoXWoYWpZWp_Xp`Xpa\ XpaYpbYpbYqcZqcZqdZqd_qe_qe`qf`rf`rgargarharhbricr\ icsjcsjcskcskcslcslcskcrjbqiaph`og_nfZmeYmdXmcWmbV\ maUm`Tm_SmZRmYQmXPmWOmVNmUMmTLmSKmRJmQImPHmOGmNGmM\ GmLGmKGmKGmKGmKGmKGmKGmKGmKGmKGmKGmKGmKGmKGmKGmJae\ JbfJbfJcfJdgJdgJegJfhJfhKghKhiKhiKiiKjjKjjKkjKlkKl\ kKmkKnlKolKolKpmKqmKqmKrnLsnLsnLtoLuoLuoLvpLwpLwpL\ xqLyqLyqLzrLzrLzrLzsLzsLzsOSnPSnQSnFFFWVKVUIVQFWPF\ WPFWPFXPGXPGXPGYOGYOGYOGZOHZOHZOH_NH_NH_NH_NH`NI`M\ I`MIaMIaMIaMIbMJbLJbLJcLJcLJcLJdLKdKKdKKeKKeKKeKKe\ KKbLN`MPZNSXNUWMVWMVWMWWMWWMWVMXVMXVMYVMYVLYULZULZ\ ULZUL_UL_TL`TL`TL`TKaTKaTKaSKbSKbSKcSKcSKcRKdRJdRJ\ dRJeRJeQJfQJfQJfQJgQJgQJgRKhRKhRLhRLhRMhRMhRNhRNhR\ OhROhRPhSPiSQiSQiSRiSRiSSiSSiSTiSTiSUiSUiTVjTVjTWj\ TWjTXjTXjTXjTYjTYjTZjTZjU_kU_kU`kU`kUakUakUbkUbkUc\ kUckUdkVdlVelVelVflVflWf` } frm:MandNewt04 {; Jim Muth z=c=pixel: a=z^3+(c-1)*z-c b=p1*z^2+c-1 z=z-p2*a/b p3 <= |a| } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 16-08-03 (Ikenaga Tree [5])
by Jim Muth 16 Aug '03

16 Aug '03

FOTD -- August 16, 2003 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us back to the mysterious Ikenaga function, which was apparently created for the purpose of generating Fractint fractals, and then forgotten by its author, who, as far has I know, has never been definitely determined. Well, it's not exactly the Ikenaga function, since I have made numerous changes and additions to it, but whatever it is, it was inspired by the IkeNewtMand formula that appears in fractint.frm and was written by Ron Barnett, who states in the formula comments that it is based on the Ikenaga function. Several years ago I wrote a series of 12 formulae that I called 'MandNewt**.' These formulae are based on this mysterious 'Ike' function. Today's image was created with number 6 of the series. This series of formulae creates totally unpredictable images that consist largely of 'inside' parts, and therefore must be rendered with an active inside fill. Today's image uses the bof61 fill. The resemblance to some kind of fantastic tree is striking, and inspired the descriptive name, "Ikenaga Tree". The color palette, which uses only a few of the 256 registers, is a model of getting much from little. The rating of an exceptional 8 is fully justified. The frugal render time of 3 minutes is fast enough for all but the busiest fractalists. Of course, the completed GIF image is available as always on the internet at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Another hot, dry, sunny day on Friday here at Fractal Central gave the dynamic cats ample time in the yard. The temperature reached 93F 34C, but cats are native to northern africa, and can easily endure such mild heat. Their day was quite happy. No treat was needed. Today is promising to be a let-down, with clouds and showers possible. But with any luck at all, the duo will have another satisfactory day. As for me, most of my days are satisfactory, which may be because it takes so little to satisfy me. The next fractal will be along in 24 hours. Until then, take care, and good fractal luck. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Ikenaga_Tree { ; time=0:03:28.39--SF5 on a p200 reset=2002 type=formula formulafile=mandnewt.frm formulaname=MandNewt06 passes=1 center-mag=37.3298\ /-49.3884/0.03536232/1/-30/-2.5056345887009e-014 params=-6.47/-5.23/-1.59/-0.59/1.25/2.08 float=y maxiter=100 inside=bof61 logmap=yes periodicity=0 colors=B00c`d`cgYeiVhlSkoOmpZkZghIog0re2sd4vc7wa8z\ `CzZDzYHzWIzWKwaUaMzYSzTWzOezLczJazJ`zJYwJWpJTkIQh\ IOdILZIIVFHQEDNB00NO`OUeQ`oSexTkzVozYsz`uzcxzizzqz\ zwzzzzzzzzzzyizwVlwJYxBIxFKtIKqLKmOLkSLgVLdYL`aMYd\ MUgMRiMMlOKoOFrOCuO8rY4qe0nm0lu0sk7x`MzP`zDmz0zzDt\ zPmu`hnkaguW`zPVzK`zLdzLizLnzLswLwsLzoMzkMzgMzcMzZ\ MzVMzZIdaDvIKz0Oz8SzIWzR`xZduhhqpllxpizskzqkypkwok\ tmkplkmlkkkkhildhlaglZglWelSdlPclMalKakP`iUZiYZhaY\ ggWgkWeoVesVdxUczSczSazRazRczPczOdzMdxLetKepIgmIgi\ HheFhaDiYCiUAkP8kM8eVAaaCYhDToDYmCcmAgl8kl8ok7si5w\ i4zh2zh2zg0zg0ze0ze0zg0zg2zg4zg7zh8zhAzhDzhFxiHviK\ siLqiMniPkkRhkSekVckW`lYYl`VlaSlcOldLghIalFWpBRtBL\ xBFzB8zB2zB7zBAyBFuFIpJMlNPhQScTWZYZV`cRceLehHilCl\ o5os0ru0ux0vu0vt0vs0vp0vo4vm5vl8wiAwhDwgFwdIwcKwaM\ w`Ox`Px`Rx`Rx`Sz`Sz`Uz`Uz`Vz`Vz`Wz`Wz`Yz`Yz`Zz`Zz`\ `z``z`az`az`cz`czZ`hVZeYa } frm:MandNewt06 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=p3*z^2+c-1 z=z-1*a/b 0.000000000000000000000000000001 <= |a| } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 15-08-03 (Dual Pentagons [5])
by JimMuth＠aol.com 15 Aug '03

15 Aug '03

FOTD -- August 15, 2003 (Rating 5) Fractal visionaries and enthusiasts: The world of fractals holds many mysteries that will never be discovered, much less solved. But the mystery of today's image is one that has been discovered and, if I decide it is worth the effort, will be solved. At risk of being considered repetitive, today's image shows what happens to yesterday's image when the angle of the slice is double-rotated merely 0.0000685 of one degree from the Julia orientation. (Double rotation is a motion that can happen only in spaces of four or more dimensions.) When I began the rotation, I expected the octagon that appeared at the center of yesterday's image to become distorted. I did not expect it to break apart into two separate symmetrical holes shaped like near-perfect pentagons. But this is what happened. Now the question arises, which of the two pentagonal holes is a slice of the original rectangle that appears in the Mandelbrot aspect of the scene? And also, what happens to the other hole as we turn toward the Mandel direction? My intuition is that these questions are irrelevant, for there is only a single hole in the four-dimensional Julibrot figure, but this hole is shaped so irregularly that it can be intersec- ted in more than one place by certain slices, such as today's slice. Switching the functions in today's formula shows a very distorted aspect of the hole that would seem to prove this. I named the image "Dual Pentagons". I was ready to rate it at another 8, but then I realized that it is basically the third identical image in a row, and decided that a rating of 5 is more appropriate. Those who enjoy the art side of fractals rather than the math side might be growing a bit bored. Those who are feeling the beginnings of boredom, as well as those who lack the time, may escape the 15-minute wait of rendering the image from the parameter file by downloading the completed GIF image from one of 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> A really unusual thing happened Thursday here at Fractal Central -- for the first time in almost 4 weeks, it did not rain. True, a few showers were in the vicinity, but none reached F.C. The fractal cats, who have made up after yesterday's quarrel, were quite happy, and despite an oppressive temperature of 91F 33C, enjoyed several hours in the yard. Today is due to be a repeat, so I expect a repeat of the cats' good moods. Until next FOTD, take care, and it is sometimes easier to see the light when one is in the dark. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Dual_Pentagons { ; time=0:15:53.78--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=-0.00006842222800720/-0.000036\ 15877643450/1535.55/1/-45/3.88578058618804789e-016 params=90.0000685/89.9999315/2.003/0/0/0/-1.743504\ 25848689/6.977862219e-006 float=y maxiter=7200 inside=0 logmap=641 periodicity=10 colors=000voOtmMrkKpiKngJleJicJfaJd_JaYJZWJWTITRIR\ PIOMILKIIIIEFFGGIHHKJIMKIOMJQNKTOKVQLXRMZTN`UNcWOe\ XPgYPi_Qk`RnbSpcSreTtfUvgUxfXwfZve`vebueetdgtdisdk\ sblqalo`lm_llZljYlhWlfVleUlcTlaSm_RmZQmXOmVNmTMmSL\ mQKmOJmMImLKkOMiQOhSQfUSdWUcYWa_Y_a_ZdaXfcVheUjgSl\ iQnkPpmNrnLwoMtlMqiNneNk_NhVNeRMbNL_JLXFKUBJSCLRDO\ RERQFUQGXPH_PIdOJhOKnNLrNJwOLqNMlMOfMPaLQXLSTKTQKU\ NJWJJXGIYDIXGMWJQVMUUPYUSaTVeSYiR`mO`tRbpUdmXej_gg\ bhdejahkYkmVnnSqpPtqMwsJytGulNrdToXZlPdiHjfApdIocP\ nbWnacm`jm_qlZxl`wjawhbwfcvedvcevafv_guZhuXiuVjuTk\ tSltQmtOntNnkcnbslcrkcqjdpidohengemfelefkdfjcgibgh\ aggeaahXWkRQnMLrGFvB9z64s88iAC`CGSEKKFOIOKGWHEcEDk\ BClEClHBlKBlNAlQAlT9lW9lZ8la8ld7lg7lj6lm6lp6ls9kmC\ jhEibHhYJgTKeOLdJMbENa9O`4Rb7UdAWfDZhG`iJckMemPhoS\ kqVmrYpt`rvcuxfwyhuuetqbsn_rjYqgVpcSo_PmXNlTKkQHjM\ EiIChF9gB6f84eC8eFBmjSnjQ } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 14-08-03 (Mandelbrot Octagon [8])
by Jim Muth 14 Aug '03

14 Aug '03

FOTD -- August 14, 2003 (Rating 8) Fractal visionaries and enthusiasts: The joke of the day is an unusual e-mail from Taiwan that I found when I checked my e-mail box this morning. The sender is having a sale on guano and wanted to know how much I need. The letter closed by telling me that if I did not need guano, to delete the message -- which I did without raising a stink. Today's fractal is also quite unusual, and that's no . . . umm . . . stuff. It is the Julia set of one of those rectangles that appear where the arms branch out in yesterday's image. It is obvious that the Julia set of a Mandelbrot rectangle will be another rectangle . . . at least I thought it was obvious until I actually calculated a Julia set. The Julia set of the Mandelbrot rectangle I chose is not another rectangle; it is an octagon. The figure in which yesterday's rectangles are embedded has also changed. Well, it hasn't actually changed, but rather it looks different when sliced in the Julia direction. It has many more arms, in addition to smaller octagons where the arms branch out. No! Wait a minute! Those are not octagons where the arms branch out; they are rectangles. We have a Julia figure with a large octagon at the center, surrounded by smaller rectangles. Actually, I have seen this doubling before. I once checked the Julia set of the center of a 5-pointed star of the Mandelbrot set and found a 10-pointed star. And as I recall, there were also 20-pointed stars in the vicinity. I don't know if any 16-sided holes lie near today's octagon, but I am certainly going to check. And I wonder what will happen to today's image when I rotate the plane of the slice ever so slightly . . . Some of these questions may be answered by the time the next FOTD appears 24 hours or so from now. I named today's image "Mandelbrot Octagon" for obvious reasons. I rated it at an exceptional 8 mostly because of its mathemati- cal interest. The render time of 17 minutes can be avoided by downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Wednesday started pleasant enough here at Fractal Central, with sun and a temperature of 86F 30C, but at 2pm, a heavy thunder- shower moved in, cutting short the dynamic duo's time in the yard and putting them in a bad mood for the rest of the day. They must have been quite cranky while I was not around, because when I gave them their evening treat of tuna, I noticed a new scratch on Tippy's ear, which means they had had a fight. Thomas looked totally innocent of course. Today is starting in a similar manner. Hopefully, the midday shower will not be repeated, and the cats will have a happy day. For me it will be just another in an unending stream of similar days. Until next time, take care, and be alert for polygons with multiplying sides. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Octagon { ; time=0:17:31.33--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=+0/+0/1878.375/1/-45/3.8857805\ 8618804789e-016 params=90/90/2.003/0/0/0/-1.743504\ 25848689/6.977862219e-006 float=y maxiter=7200 inside=0 logmap=641 periodicity=10 colors=000voOtmMrkKpiKngJleJicJfaJd_JaYJZWJWTITRIR\ PIOMILKIIIIEFFGGIHHKJIMKIOMJQNKTOKVQLXRMZTN`UNcWOe\ XPgYPi_Qk`RnbSpcSreTtfUvgUxfXwfZve`vebueetdgtdisdk\ sblqalo`lm_llZljYlhWlfVleUlcTlaSm_RmZQmXOmVNmTMmSL\ mQKmOJmMImLKkOMiQOhSQfUSdWUcYWa_Y_a_ZdaXfcVheUjgSl\ iQnkPpmNrnLwoMtlMqiNneNk_NhVNeRMbNL_JLXFKUBJSCLRDO\ RERQFUQGXPH_PIdOJhOKnNLrNJwOLqNMlMOfMPaLQXLSTKTQKU\ NJWJJXGIYDIXGMWJQVMUUPYUSaTVeSYiR`mO`tRbpUdmXej_gg\ bhdejahkYkmVnnSqpPtqMwsJytGulNrdToXZlPdiHjfApdIocP\ nbWnacm`jm_qlZxl`wjawhbwfcvedvcevafv_guZhuXiuVjuTk\ tSltQmtOntNnkcnbslcrkcqjdpidohengemfelefkdfjcgibgh\ aggeaahXWkRQnMLrGFvB9z64s88iAC`CGSEKKFOIOKGWHEcEDk\ BClEClHBlKBlNAlQAlT9lW9lZ8la8ld7lg7lj6lm6lp6ls9kmC\ jhEibHhYJgTKeOLdJMbENa9O`4Rb7UdAWfDZhG`iJckMemPhoS\ kqVmrYpt`rvcuxfwyhuuetqbsn_rjYqgVpcSo_PmXNlTKkQHjM\ EiIChF9gB6f84eC8eFBmjSnjQ } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

1 0

re: FOTD 13-08-03 (Mandelbrot Object [8])
by Programmer Dude 13 Aug '03

13 Aug '03

Jim Muth: > I find my fractals; Albrecht creates his. Which method is the > better way of working with fractals? Asking such a question is > like asking whether fractals are art. It is up to each > individual to decide. I would have said it was more like asking if it's better to fly in a plane or eat chocolate ice cream.... I.e., an *utterly* meaningless question with no sensible answer. What makes you think the concept of "better" applies? -- |_ CJSonnack <Chris(a)Sonnack.com> _____________| How's my programming? | |_ http://www.Sonnack.com/ ___________________| Call: 1-800-DEV-NULL | |_____________________________________________|_______________________|

1 0

FOTD 13-08-03 (Mandelbrot Object [8])
by Jim Muth 13 Aug '03

13 Aug '03

FOTD -- August 13, 2003 (Rating 8) Fractal visionaries and enthusiasts: While assembling the parameter section of today's FOTD, I noticed my humble MandelbrotN formula. I saw all four lines of it -- about as short and simple a formula that could produce a fractal. Then I brought up Albrecht's latest Multifractal formula -- a work of fractal-programming genius, a mini-program with hundreds of lines that took many days of labor to develop, and still may not be finished. The two formulas illustrate two different approaches to the art of fractaling. I find my fractals; Albrecht creates his. Which method is the better way of working with fractals? Asking such a question is like asking whether fractals are art. It is up to each individual to decide. In my long fractal career I have written thousands of short, simple formulas, most of which took less that 1/2 hour to complete and have long since been filed away and forgotten. I could never imagine myself working weeks or months on a single formula, even if I did have a clear idea of where I was going. But why should I need to, when nearly every fractal created by every formula contains infinite surprises? Today's image rates an 8. One point of this rating is due to the surprising nature of the image. Until I found it, I had assumed that the near-perfect rectangles such as I used to create yesterday's 'Space Station' image exist only in the Julia plane of the Z^2.003+C Mandeloid. I should have known better. Yesterday, while searching the area of the Julia rectangle in the Mandelbrot direction, I found many small figures like the larger Julia figure that holds the rectangle. I found no midgets, but most surprising, I found that the small figures hold near-perfect empty rectangles where the arms branch out. To see some empty rectangles in their natural surroundings, toggle today's image of one of these small figures in and out of color-cycling mode and watch for the areas that blink. Clearly, I have much more exploring to do in this area. To begin, I must find those elusive Mandelbrot midgets. And if the figures with their rectangles are present in both the Julia and Mandelbrot directions, they should be present in the odd and oblique Julibrot directions also. I gave little thought to the naming of the image. "Mandelbrot Object" was as good a name as I could come up with. But the name is a perfect description of the surprising nature of the scene. The render time of 15 minutes is starting to border on the excessive. Relief in the form of the completed GIF image is 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> Tuesday was actually a pleasant day here at Fractal Central. The temperature reached 86F 30C, the humidity was bearable, and the heavy rain storms that broke out in the afternoon stayed well west of us, leaving the F.C. area with a partly cloudy day and happy cats. If tomorrow's FOTD is as surprising as today's, I'll be happy. If it's not, I'll still be happy. Until next time, take care, and life is just a happy procession of fractals. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Object { ; time=0:15:38.35--SF5 on a p200 reset=2002 type=formula formulafile=slices.frm formulaname=MandelbrotN passes=1 center-mag=-1.74350425707497900/+0.000006977798978\ 60/4.029834e+008 params=2.003/0/0/0/0/0 float=y maxiter=7200 inside=0 logmap=644 periodicity=10 colors=000404601700900A00C00D00F00G00I00J01L01M01O\ 13P33Q33S44T44V64X76Y76_96`97aA7cC7dC9fD9dA6gD9iGC\ jJFlMImPJoSMpVPsYSu`TvcXxf_yiazlczofzrizulzxmzzpzz\ szzvzzxzzvxxvprvilvafuVauOXuGQu9Ls1Fs09s04s06o07j4\ 9gAAcFC_LDXQFSXGOYFP`GLcIIdJFgLAiM7lO4mO1jS7iXDf`J\ ddPaiV`m_YrdXvjTzpSzvPzzOzzLzzJzzGxzFrzCmzAiz7cz6_\ z3Vz1Pz0Lz0Gz0Az06z01z00z00z03z06z39z7CzAFyFIvILuM\ OsPQrTToXXm`_lcaigdgjgfojdrmavp`ys_zvXzyVzzTzzSzrV\ zgXzXYzM_z9azC`xF`uG`sJ`pL`mO`lP`iS`fV`cX`a_`_``Xc\ `YiXVd`SadQ_gOXlLSoJPsGMvDJzCGz9Cu77l63c40V30M10D3\ 0I40L61O74Q97TAAXCD_DGaFJdGMgIPjJSmLVpMYsMYtOXuPWr\ QXmQWiTWdYYaa_YddTikPmqLrvIuxDyz9zz4zz0zz0xz0ru0jp\ 3dl4`i7VdAPaCMgFJoIGvJFvMCvO9vQ7vT4vV1vY0v`0va0vd0\ vi0vf0vd0vc0va0v`0vY1gX1TV3FT41S63Q74O96MA6LC7JC9I\ D9GFADGCCICAJD9LF7LF6II7GL9FO9DQACTCAXC9_D7`D4cF3f\ G1iG0lI0oJ0rJ0uL0vL0uJ0sI } frm:MandelbrotN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=z^(b)+c, |z| <= 16 } END 20.0 PAR-FORMULA FILE==================================

1 0

Multifractal_8
by Albrecht.Niekamp＠t-online.de 12 Aug '03

12 Aug '03

Hi, Although Multifractal has become much longer there is hardly any slowdown due to some efficient speedups in the mainloop. The additional inputs p3, p4 and p5 can be used up to the maximum number of digits if only fractional values are concerned. If the total number is exceeded, the last digits are truncated. Three important changes this time. It now is possible to control the coloring using an alternative bailout which can be applied to one or two channels, imag(P2), last two digits of first input. Just type the number of the channel(s). The first alt-bailout is applied to the first choice, the second one is applied to the second choice. A high value - real(p3) or real(p3) 2nd input, digits 6-11 - compresses, a value lower then bailout expands the coloring of the concerned channel. Another way is to use iter-reset, which causes the iterationcounter to start from zero and so increases the number of iterations for the concerned channel, - coloring is modified in a more subtle way. This of course increases the calculation time, also the warp effect of the following channels is concerned. The second news is the real(p2) input, as now only the number of the frm is needed, no more double choices. This means if you call the "z" screen you can see at one glance which frms are used. The two reset commands and the warpeffect switch are combined in the real(p2) second input, last five digits, 1 digit for each channel. Scroll the text for explanation. (3) I have spend some efforts to get rid of distorted structures, so now I can reintroduce them, but on a controlled basis. This means the 3 inside channels (3-5) now can use bordervalues if wanted. The first digit, 2nd input, image(p4), real(p5), image (p5) controls use of maxiter or border values. The bordervalues can be used bothways, "in" or "out". "In" means that the concerned channel is switched on, if the border value is higher then the input and vv. If the selection is "7" or "8" both, maxiter and border-(both options) are used at the same time. This possibly will cause chaos, if the same part of the image is affected, but maybe thats ok in some cases. Testing this frm I again experienced some difficulties with that infamous fractint-bug (misreadings of the inputs under certain conditions). "Debugflag=322" is activated, but itïs not on my office computer, it does not make any difference. Btw against all rumours fractint runs perfectly under WindowsNT (Gforce2 videocard). Concerned is real(p2), first(!) input, where channel 2 (outside) was not read correctly if zeros follow. I fixed it adding"1" to the last digit and so avoid zero divisions. The second concerned input is real(p2) second input, last 5 digits. I already added 11111 to the input in multifractal_7, but I noticed that the last digit still was misread sometimes, so I used the "round" function for this digit. After many tests all inputs are executed correctly. The images : "House of the Helmets" is a four generations mandel and very beautiful, rather slow though as the "secant" frm used inorder to get rid of the tdis-sausages is very slow and I used iter reset to get the wanted coloring for the helmets. The part of the sausages to be eaten by secant is controlled by "image(p3)" 2nd input (outside border-in), a lower value eats more. "Mandel in the clouds" is an impressive zoom into this one, the new coloring expansion is used to generate the clouds. "Borderwatch" is another one, really extraordinary and worth waiting for. As this was generated under Winnt I cannot tell the actual time needed. "Ganymed" and "Islands" use the new inside border values, option1 (border-out). Btw Ganymed is the biggest Jupiter planet. "Ikebana" is a japanese ornamental floral arrangement. The many different shapes of the flowers are produced by the warp effect. Same goes for the "Jellyfish armada". Fractal Greetings, Al ---------------------------------------start-frm-------------------------- FRM:Multifractal_8 { ; Albrecht Niekamp 090803 ;p1 (spider)julia-seed ;real(p2) 5digits : (1)shape (2)outside (3)inside1 (4)inside2 (5)inside3 ; 0_off 1_secant 2_mand 3_bees 4_jul 5_m_mods 6_phoen 7_newt 8_spider ; input2 : 2digits_many-mods 2digits_phoenix 2digits_spider ; 5digits_reset : 0_no 1_z-reset 2_iter-reset 3_both +5_warp ;imag(p2)(-) 2-4digits : newton input (max 2000) ; 2digits : channel_alt-bailout1 channel_alt-bailout2 ; input2 : 4digits(-)_mand/jul 2digits_secant 4digits_bees ;real(p3) alt-bailout1, 5digits_bailout 6digits alt-bailout2 ;imag(p3) shape : factor (fn1), outside : border-in (5digits+fract.) ;real(p4) outside: factor (fn2), outside : border-out (5digits+fract.) ;imag(p4) inside1: maxit1, 1digit_use:1_maxit 2_bord-in 3_bord-out +5_both ; 5digits_factor1 (fn2) 4digits+fract_border1 ;real(p5) inside2: maxit2, 1digit_use:1_maxit 2_bord-in 3_bord-out +5_both ; 5digits_factor2 (fn3) 4digits+fract_border2 ;imag(p5) inside3: maxit3, 1digit_use:1_maxit 2_bord-in 3_bord-out +5_both ; 5digits_factor3 (fn4) 4digits+fract_border3 ;fn(1) shared by many-mods+bees ; da=real(p2) dd=trunc(da) da=round((da-dd)*100000000000)+11111 dd=dd+1 d=trunc(dd/10000) dd=dd-d*10000 d3=(d==3)+(d==4)+(d==7)+(d==8) d4=(d3==0) vb=d>4 ab=(d==2)+(d==4)+(d==6)+(d==8) d=trunc(dd/1000) dd=dd-d*1000 ex1=d>0 v1m=(d==5)+(d==6) v1j=d>6 dd1=(d==3)+(d==4)+v1j ab1=(d==2)+(d==4)+(d==6)+(d==8) d=trunc(dd/100) dd=dd-d*100 ex2=d>0 v2m=(d==5)+(d==6) v2j=d>6 dd2=(d==3)+(d==4)+v2j ab2=(d==2)+(d==4)+(d==6)+(d==8) d=trunc(dd/10) ex3=d>0 v3m=(d==5)+(d==6) v3j=d>6 dd3=(d==3)+(d==4)+v3j ab3=(d==2)+(d==4)+(d==6)+(d==8) d=dd-d*10 ex4=d>1 v4m=(d==6)+(d==7) v4j=d>7 dd4=(d==4)+(d==5)+v4j ab4=(d==3)+(d==5)+(d==7)+(d==9) ; mm=trunc(da/1000000000) da=da-mm*1000000000 ph=trunc(da/10000000)/100 da=da-ph*1000000000 sp=trunc(da/100000)/100 da=da-sp*10000000 d=trunc(da/10000) ex0=d>4 da=da-d*10000 d=d-5*ex0 ir0=(d==3)+(d==4) d=trunc(da/1000) w1=d>4 da=da-d*1000 d=d-5*w1 rs1=(d==2)+(d==4) ir1=(d==3)+(d==4) d=trunc(da/100) w2=d>4 da=da-d*100 d=d-5*w2 rs2=(d==2)+(d==4) ir2=(d==3)+(d==4) d=trunc(da/10) w3=d>4 da=da-d*10 d=d-5*w3 rs3=(d==2)+(d==4) ir3=(d==3)+(d==4) d=round(da) w4=d>4 d=d-5*w4 rs4=(d==2)+(d==4) tt=ex0+ex1+ex2+ex3+ex4 ; d=imag(p2) t=d<0 if (t) d=-d endif dd=trunc(d) d=round((d-dd)*10000000000) pp=trunc(dd/100)/10 dd=dd-1000*pp ba1=trunc(dd/10) ba2=dd-10*ba1 ; p0=trunc(d/100000000)/10 d=d-p0*1000000000 p6=trunc(d/1000000)/10 d=d-p6*10000000 if (t) p6=-p6 endif p7=trunc(d/10000)/10 d=d-p7*100000 p8=trunc(d/100)/100 d=d-p8*10000 p9=d/100 ; d=real(p3) bb1=trunc(d) da=(d-bb1)*10000000000 ba=trunc(da/100000) bb2=da-100000*ba ; d=imag(p3) sfac=trunc(d) b1=(d-sfac)*100000 b0=b1/2 ; d=real(p4) ofac=trunc(d) b2=(d-ofac)*100000 ; d=imag(p4) mi1=trunc(d) da=(d-mi1)*100000000000 d=trunc(da/10000000000) bt1=d>6 da=da-d*10000000000 d=d-5*bt1 dt1=d>1 iv1=(d==3) fac1=trunc(da/100000) da=da-fac1*100000 bo1=(da/100000)/10 ; d=real(p5) mi2=trunc(d) da=(d-mi2)*100000000000 d=trunc(da/10000000000) bt2=d>6 da=da-d*10000000000 d=d-5*bt2 dt2=d>1 iv2=(d==3) fac2=trunc(da/100000) da=da-fac2*100000 bo2=(da/100000)/10 ; d=imag(p5) mi3=trunc(d) da=(d-mi3)*100000000000 d=trunc(da/10000000000) bt3=d>6 da=da-d*10000000000 d=d-5*bt3 dt3=d>1 iv3=(d==3) fac3=trunc(da/100000) da=da-fac3*100000 bo3=(da/100000)/10 ; mo=vb>ab mo1=v1m>ab1 mo2=v2m>ab2 mo3=v3m>ab3 mo4=v4m>ab4 ; sc=((ab+vb)==0) sc1=((ab1+v1m)==0) sc2=((ab2+v2m)==0) sc3=((ab3+v3m)==0) sc4=((ab4+v4m)==0) ; px=((ab+vb)==2) px1=((ab1+v1m)==2) px2=((ab2+v2m)==2) px3=((ab3+v3m)==2) px4=((ab4+v4m)==2) ; mb0=(ba1==1)+(ba2==1) mb1=(ba1==2)+(ba2==2) mb2=(ba1==3)+(ba2==3) mb3=(ba1==4)+(ba2==4) mb4=(ba1==5)+(ba2==5) ; if (d4) z=0 if (vb) if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel z=pixel endif else c=pixel z=pixel*sc endif else c=p1 z=pixel endif t=0 u=d3 bo=z p=pp z0=p7 zold=(0.0,0.0) cb=p9 bx=ba if (mb0) if (ba1==1) ba=bb1 else ba=bb2 endif else ba=bx endif : If (tt) t=t+1 if (ex0) if (bo>b0) u=2*(fn1(t/sfac)) if (d4) z=z*u if (mo) c=0.4*log(sqr(pixel^mm)) else c=pixel endif else z=pixel cb=p9*u c=p1*u p=pp*u endif if (ir0) t=0 endif ex0=0 tt=tt-1 endif elseif ((ex1) && bo>b1) if (b2>bo) d3=dd1 if (w1) u=2*(fn2(t/ofac)) else u=1,0 endif ab=ab1 if (d3) if (rs1) z=pixel cb=p9*u c=p1*u p=pp*u else c=p1 z=z*u cb=p9 endif vb=v1j else if (rs1) c=z*u z=pixel*(sc1+px1) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v1m if (mo1) c=0.4*log(sqr(pixel^mm)) endif endif if (mb1) if (ba1==2) ba=bb1 else ba=bb2 endif else ba=bx endif if (ir1) t=0 endif ex1=0 tt=tt-1 endif elseif (ex2) if (dt1) if (iv1) d=bo>bo1 else d=bo<bo1 endif if (bt1) d=d+(t>mi1) endif else d=t>mi1 endif if (d) if (w2) u=2*(fn2(t/fac1)) else u=1,0 endif ab=ab2 d3=dd2 if (d3) if (rs2) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v2j else if (rs2) c=z*u z=pixel*(sc2+px2) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v2m if (mo2) c=0.4*log(sqr(pixel^mm)) endif endif if (mb2) if (ba1==3) ba=bb1 else ba=bb2 endif else ba=bx endif if (ir2) t=0 endif ex2=0 tt=tt-1 endif elseif (ex3) if (dt2) if (iv2) d=bo>bo2 else d=bo<bo2 endif if (bt2) d=d+(t>mi2) endif else d=t>mi2 endif if (d) if (w3) u=2*(fn3(t/fac2)) else u=1,0 endif ab=ab3 d3=dd3 if (d3) if (rs3) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v3j else if (rs3) c=z*u z=pixel*(sc3+px3) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v3m if (mo3) c=0.4*log(sqr(pixel^mm)) endif endif if (mb3) if (ba1==4) ba=bb1 else ba=bb2 endif else ba=bx endif if (ir3) t=0 endif ex3=0 tt=tt-1 endif elseif (ex4) if (dt3) if (iv3) d=bo>bo3 else d=bo<bo3 endif if (bt3) d=d+(t>mi3) endif else d=t>mi3 endif if (d) if (w4) u=2*(fn4(t/fac3)) else u=1,0 endif if (mb4) if (ba1==5) ba=bb1 else ba=bb2 endif else ba=bx endif ab=ab4 d3=dd4 if (d3) if (rs4) z=pixel cb=p9*u c=p1*u p=pp*u else cb=p9 c=p1 z=z*u endif vb=v4j else if (rs4) c=z*u z=pixel*(sc4+px4) z0=p7*u ph=ph*u else c=z z=z*u endif vb=v4m if (mo4) c=0.4*log(sqr(pixel^mm)) endif endif ex4=0 tt=0 endif endif endif if (vb) if (d3) if (ab) z=z*z+c ;Spiderjul John Horner c=c*sp+z else z1=z^p-1 ;Qusinewton Pusk s Istv n z2=p*z*z z=z-z1/z2 endif elseif (ab) zt=z*z+ph-0.5*zold ;Phoenix Mike Wareman zold=z z=zt else z2=fn1(z)+c ;Many_mods Linda Allison q=cos(z2) z=c*(1-q)/(1+q) endif elseif (d3) if (ab) z2=z*z ;Julia Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z1=fn1(z)-cb ;Bees Ray Girvan z2=z1^p8-1 z3=p8*(z1^(p8-1)) z=z-(z2/z3) endif elseif (ab) z2=z*z ;Mandel Pusk s Istv n z=z2*z2+p6*z2+c-p0 else z3=z ;Secant Mike Wareman z1=z0*z0*z0*z0-1 z2=z*z*z*z-1 z=z-z2*(z-z0)/(z2-z1) z0=z3 endif bo=|z| bo<=ba } ------------------------------------start-par------------------------------- Ganymed { ; Time 1.12.39.12 ; Albrecht Niekamp aug, 03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/cosxx/cos/exp passes=t center-mag=+0.50549305714185240/-0.61811095723667920/704.0072/1/142.4999\ 99999998181/2.79927470092644626e-012 params=-0.02237006744590594/-0.07473982970671712/20685.64575300005/17053\ .0608020602/82048.03072420481/384.0000045/384.00024/128.3007680000451/25\ 6.300768002431/512.2007680082311 float=y maxiter=3072 inside=maxiter outside=tdis logmap=9 periodicity=0 rseed=-2436 colors=200034<23>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3\ >e`LgbMidN<3>qjRslSunT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25\ >C00A00800<3>000<23>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012 } Ikebana { ; Albrecht Niekamp Aug, 03 ; Time 0.49.15.81 ; ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/cosxx/cos/sin passes=t center-mag=+1.01296887343957000/-0.25355247435077240/268.8172/1/104.9999\ 99999999417/4.71109262711877363e-013 params=-0.02237006744590594/-0.07473982970671712/20856.6459530051/5040.0\ 608020602/82048.02048000001/384.0000045/384.00024/128.1007682048001/184.\ 1007682048001/512.1007682048001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=11 periodicity=0 rseed=-2436 colors=2000NU<8>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslSu\ nT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<25>\ iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<15>0OW } Islands { ; Time 0.47.07.67 ; Albrecht Niekamp Aug,03 ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/cosxx/cos/exp passes=t center-mag=+0.14743939138452520/-0.85700696310343770/988.7742/1/-177.500\ 000000000938/8.0188633511113494e-013 params=-0.02237006744590594/-0.07473982970671712/20685.64575300005/17053\ .0608020602/82048.03072420481/384.0000045/384.00024/128.3007680000451/25\ 6.300768002431/512.2007680082311 float=y maxiter=3072 inside=maxiter outside=tdis logmap=9 periodicity=0 rseed=-2436 colors=200222<22>eeegggiiijjjlllnnn<2>sss<25>BBB999777<2>222000012<24>0b\ o0cq0es<3>0kz<25>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslS\ unT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<31>000 } Jellyfish_armada { ; Albrecht Niekamp Aug, 03 ; Time 0.46.44.55 ; ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/cosxx/cos/sin passes=t center-mag=+1.05590865727923400/-0.26726304367583260/537.6344/1/-120.000\ 000000001336/1.0563286356735091e-012 params=-0.02237006744590594/-0.07473982970671712/20854.6459530051/5040.0\ 608020602/82048.02048000001/384.0000045/384.00024/128.1007682048001/184.\ 1007682048001/512.1007682048001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=11 periodicity=0 rseed=-2436 colors=2000NU<8>09C08A068<2>022000211<13>UQFWSGYTH<3>e`LgbMidN<3>qjRslSu\ nT<2>zsX<25>CB7A96875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000<25>\ iiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<15>0OW } Mandel_in_the { ; Clouds ; Albrecht Niekamp Aug, 03 ; Time 2.57.35.27 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/exp/exp/sin passes=t center-mag=0.798692/0.00022867/24.61116/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/5025.05\ 06030602/89094.02048000094/384.0000545/384.00048/256.1007683001/512.1007\ 683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200444<21>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A9\ 6875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000222 } Borderwatch { ; Albrecht Niekamp Aug, 03 ; ; ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/exp/exp/sin passes=t center-mag=+0.76810386176090220/-0.04756578810250790/866.3365/1/90/-1.23\ 373533611470521e-014 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/5025.05\ 06030602/89094.02048000094/384.0000545/384.00048/256.1007683001/512.1007\ 683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200444<21>fffgggiiijjjlll<3>sss<25>BBB999777<2>222000012<24>0bo0c\ q0es<3>0kz<25>09C08A068<2>022000211<21>icNkeOmfP<3>unTwpVxqWzsX<25>CB7A9\ 6875<3>000400<23>o00q00s00<3>z00<25>C00A00800<3>000222 } House_of_the { ; Helmets ; Time 2.31.23.87 ; Albrecht Niekamp Aug,03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=mfr.frm formulaname=multifractal_8 function=sin/exp/exp/sin passes=t center-mag=0.332423/0.00308737/1.230666/1/-90/3.88578058618804789e-016 params=-0.05825983458967864/0.3785210730307932/21222.32595700021/5025.05\ 06030602/89094.02048049094/384.0000545/384.00048/256.1007683001/512.1007\ 683001/768.1007683001 float=y maxiter=3072 inside=maxiter outside=tdis logmap=4 periodicity=0 rseed=-2436 colors=200600<22>o00q00s00<3>z00<25>C00A00800<3>000<25>iiijjjlll<3>sss<2\ 5>BBB999777<2>222000012<24>0bo0cq0es<3>0kz<25>09C08A068<2>022000211<21>i\ cNkeOmfP<3>unTwpVxqWzsX<25>CB7A96875<3>000400 } --------------------------------------end----------------------------------

2 1

FOTD 12-08-03 (Space Station [7])
by Jim Muth 12 Aug '03

12 Aug '03

FOTD -- August 12, 2003 (Rating 7) Fractal visionaries and enthusiasts: I try to convince myself that the public media is a fair and unbiased source of information, but it is becoming very hard to keep up the self-delusion. Every time I turn on the fractal TV, it seems I see dramatic fear-inspiring stories of record- breaking heat, drought, and fires in Europe and the western U.S. The assumption is that global warming has arrived, and we are ready to run out of water and be wiped out by heat exhaustion, wildfires, flooded coastal cities, and mass starvation. But where are the stories about the ongoing record-breaking cool, rainy summer in the Eastern part of the U.S., or the cold wave in Europe this past April, or the current record-cold weather in Australia? And finally, why are most professional meteorologists more concerned about an ice age than global warming? Those living in the Fractal Central area are already more worried about the next ice age than global warming. The local farmers (in addition to the local cats) are actually praying for dry weather. Yesterday was the 22nd consecutive day with at least some rain here at F.C. While I have been searching for an unbiased news source, I have also been searching for fractals. For today's image I returned to my favorite fractal rectangle -- the one in the Z^(2.003)+C Julia set at C=-1.7435,0.0 and Z=0.00019,0.07388. This object is shaped like a rectangle only when sliced in the Julia direction. Any deviation from that direction quickly distorts the rectangle. In today's image, we deviate only one degree toward the Parabolic direction, but even that small deviation turns the rectangle into a kind of table-top sitting on a platform, creating a convenient landing place for a space ship. I have named the image "Space Station". The image needed a little help to reveal its full potential. The surface of the table top, as well as most of the platform consist of inside material made visible by the 'fmod' option. When this was done, the result was an image worthy of a rating of 7. Changing the imag(p1) parameter even slightly totally changes the image. If imag(p1) is reduced to 80, the effect is more of a cut-away view of a volcano. When the parameter is reduced beyond that, the image stretches horizontally until, by the time the Parabolic direction is reached, it becomes little more than a series of horizontal bands. Four minutes is a fast-enough time for the attached parameter file. And as always, the completely finished image is available in good old-fashioned GIF format 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 weather on Monday here at Fractal Central would have been near perfect if a heavy thunder-shower had not arrived and dropped 0.8 inches or 2cm of rain just as the dynamic duo were finishing their near-perfect day in the yard. Had it not been for the rain, the temperature of 81F 27C would have been ideal. The rain did one good thing however -- it hurried the duo indoors without urging from me. When they were safely inside, I gave them a small treat of tuna to assure their continued good moods. Today is scheduled to be a repeat. Things will be all right if the rain holds off until 5pm. I'll be all right if the work goes smoothly and the next fractal is a good one. Until that next fractal arrives, take care, and where is the heat one expects in this part of the world at this time of year? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Space_Station { ; time=0:04:10.07--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=flip/ident passes=1 center-mag=-0.0058071/1.00614e-016/58.884\ 49/1/90/-1.23373533611470521e-014 params=90/89/2.0\ 03/0/0.00019/0.07388/-1.7435/0 float=y maxiter=1200 inside=fmod proximity=0.0333 periodicity=10 colors=000oT8qS8tQA000wNAyLCzKCzICzGDzFDzDDzCFzAFz\ AGz8Fz8Dz7Cz7Cz5Az58z38z37z25y25w03v02v02t00r00q00\ o00m00l00j00i00g00zwzlazzczjKzzmziazzzziazzqziizii\ zA30C50D70D70F80FA0GC0GC0ID0KF0KG0LG0LI0MJ0NK0OL0Q\ M0QO0SQ0SQ0TS0VT0VV0XV0XX0YY0__0__0aa0ab0bd0bd0de0\ eg0ei0gi0gl0io0jr0qt0yw0zz0zz0zz0zz0zz0zy0ww0wt0vr\ 2to2rm3rj5rj5ri7ri7rg8tg8teAteCtdCvdDvbDvbFvaFwaGw\ _Gw_IwYKwYKyXLyXLyVNyVNzTOzTQzSQzSSzQSzQTzOTzOVzQT\ zOVzOVwNXvNXrNYqLYmL_lL_iK_gKadKabIb_IbYIdVGdTGeQG\ eOFeLFgKDgGDiFDiCCjACj7Cl5Al2Al0Am08m08o08o07q07q0\ 5o07q08q0Ar0Cr0Dt0Ft0Gt0Iv0Kv3Kw5Lw7Ny8OyAQyDSzFTz\ GVzIXzKXzIVzIVzGTzGTzFSzFSzDQzDQzCOzCOzDNzDLzDLzDK\ zFIzFIzFGzFFzGFzGDyGCwGCvIArI8qI8oI7mK5jK5iK3gK2e0\ QCK2dLDQNODO_0Oi0Oj0Oj0Ol0Ol0Ol3Om7OmAOoDOoGOoKOqN\ OqQOqTOrYOraOtdOtgOtjOvmOvqOwtOwwOwzOyzOyzOyzSwzTv\ zXtzYrydb5ea5i_7jY7lX7mV8 } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================

1 0

FOTD 11-08-03 (Disconnected Midget [5])
by Jim Muth 11 Aug '03

11 Aug '03

FOTD -- August 11, 2003 (Rating 5) Fractal visionaries and enthusiasts: I spent too much effort being lazy all day Sunday, so the fractal I eventually found rates only a 5. But after all, even an average fractal is worth seeing. Some fractals, such as the well-known Mandelbrot set, are connected. This means that every apparently disconnected midget is actually connected to the main bay by an infinitely thin filament. Other fractals, such as the parent of today's image, are not connected, and contain areas totally cut off from the main body of the fractal. Today's midget lies in one of these areas that is cut off from the main body of the parent fractal, which appears as a slightly distorted M-set. This is why I named it "Disconnected Midget". I rendered the image with the outside set to 'tdis' to emphasize the disconnected nature of the scene. The 'tdis' outside also makes a better picture. The short render time of a nice neat 0:02:02.02 is pleasant enough, though not quite as much fun as downloading the already- completed GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Sunday was an unusually pleasant day here at Fractal Central. The rain held off and the temperature reached 84F 29C, which made the cats happy, and I got through the day without finding work that needed to be done, which made me happy. Hopefully, today will be a repeat, but there is still a bit of work to be finished first. Until next time, take care, and stay connected. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ DisconnectedMidget { ; time=0:02:02.02--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-1.83854548477051500/+0.410334133501795\ 70/4.195225e+007/1/85/-3.35216519486980502e-007 params=1/3/2/-0.5/0/0 float=y maxiter=500 inside=0 outside=tdis periodicity=10 colors=000vPnyOuqSrjWpc_nXblQfiJjgCne5qc4sj3uq3wwA\ nxGeyNXyTOzZFz`JvbNrdQnfUkhYgj`cld_mgXkXWiMWgCWbEV\ ZGUUITQKTMHOIEKEBGB8C758324M8bK9fPAnUAuYJtaRteZtig\ tmotqwtntpkqmhnjekgbhd`faVa_PXYJTWDOU7JS1FQ2IR3LR3\ OR4QR5TS5WS6ZS6`S8_Q9ZOBZMCYKEXIFXGHWEIWCJ`IKdOKiT\ LmZLqck4eT2SA1FH3MN5SU7Y_8cfAilCorDusCotCiuBcvBYwA\ SxANt8Op7Pl5Ph4Qd2Q`1RY0RnTMfXUZ_`RbhKeoNciQacT_YW\ YSZWMaUGdTAiWUmZlnbmnfmojnonnornpshqsbrsXstRttLutF\ ut9lf6dU4XH2P40S30U30X30Z30`30c30e30g30`49V5HP6PI7\ XC8d69l09tmO4gTHaYUWbfRfsSiwSkzXrmayaXuhTrnOotKlz_\ 96`CAaFDbIHcLKdONeRRfUUgWXfYbe_gd`mcbrccwahx`lyZpz\ Ytz_jt``naSigYjlbkqglvllonhipdcraXtYRvVLxRFzOKpJOf\ ESY9VXJYXT`XbcXlfXvhVqiUmkShlRdmQ`8H8FJPMLeSMvc8O`\ IZYSiWatbSpiJlp9hv0dpGbjWaek``kaWkaSkaQjYOjUNiQLiM\ JhIIhEGgAFg7IiDKjJMkPOlVQm`SnfUolWprUomTnhRncQmZPm\ VYUMXOOWIPgYFjWMmUTpT`sRg } 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==================================

1 0