October 2003 - Fractint - mailman.xmission.com

Classic FOTD 01-01-98 (Projective Plane)
by Jim Muth 07 Oct '03

07 Oct '03

Classic F.O.T.D., January 01, 1998 (Projective Plane) Fractal visionaries: The world of higher dimensions is filled with objects which are impossible in our three-space, and can be represented here in only a distorted way. The Klein Bottle is one such object. In three dimensions it appears as a closed figure which intersects itself and joins itself in such a manner that despite having no breaks it has only one side. The inside is also the outside. But this is a distortion of the true object, which can exist only in spaces of four or more dimensions. In four dimensions, the Klein Bottle is constructed by taking a rubber sheet, curling it and connecting one pair of edges so that a tube results, then bending the tube and joining the open ends into a doughnut shaped object. But before joining the edges, and with no cutting, the tube is given a half-twist and turned inside- out, so that without self-intersection, the resulting doughnut- shaped object has only one side. Its inside is also its outside. The Klein Bottle is difficult enough to visualize, but the Projective Plane is even more difficult. In fact it is difficult to even describe. In this case, the sheet of rubber is given a half-twist into a kind of Moebius Strip tube before being curled and given a second twist before the open ends are joined to each other, forming the Projective Plane. In this case, even a distorted model is nearly impossible in three-space. Well, if an accurate model of a Projective Plane is impossible in three dimensions, one could never hope to illustrate the monster on a two-dimensional screen. I named today's fractal "Projective Plane" only because that's what I thought of when I saw the image. Actually, it is a picture of a curious feature that appears at Z=0.00019,0.07388 C=-1.7435,0.0 in the Z^2.003 Julibrot figure. This object is extremely thin and exists only very near the Julia orientation, where it appears as a near- perfect rectangle. To create today's image, I gave the object a 2-degree double rotation from the Julia orientation, which distorted the rectangle into the curved shape in the picture. A little playing with the colors produced the effect of a flying sheet of rubber. The flying plane has landed at Paul's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow, I'll have another interesting FOTD. At this time I have no idea what it will be, but something will turn up -- as it always does. Until then, take care, and keep finding those fractal gems. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER-FORMULA FILE================================ Projective_Plane { ; 3-1/2 min on a P200 at SF5 reset=1960 type=formula formulafile=multirot.frm formulaname=multi20031 function=flip/ident/ident\ /flip passes=1 center-mag=-0.00037327503160875/\ +0.00003799627771399/514.8005/1/25 params=88/88/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=000QVZ<2>PXZ\ PYZP_Z<7>PlZPnZRt_<4>PmZPkZOhZ<6>MTZMRZMQZ<12>I9\ ZI8ZJ6a<19>I8OI8NH9KH9IH9HH9IH9IH9HH9FH9FH9H<11>\ HA9HA9JCB<2>OIGQJHRMJ<7>dgVejWgkY<3>nncooeqnf<3>\ wshxuixwjyylyzm<4>zwizvhzugzugztgzthzshzsh<10>pl\ `ol_mkZ<7>YfTWfSVdR<3>RZOQXNPYN<6>IUHHTGGUG<3>I_\ IJ`IJ`I<38>asSXrT<19>stPttPvvJvuM<3>oqWmpZmqZ<3>\ moZnoZopZskZwzZzwZzwZ } frm:multi20031 {; Jim Muth, best=ifif, fiif, fifi, iffi a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*fn3(real(pixel))+cos(a)*fn4(imag(pixel))+p3: z=z^2.003+c, |z| <= 100 } END PARAMETER-FORMULA FILE==================================

2 1

Classic FOTD 22-11-97 (Budrise)
by Jim Muth 06 Oct '03

06 Oct '03

F.O.T.D., November 22, 1997 (Budrise) Fractal visionaries: How can I describe today's fractal? Well, to begin, I'll let my imagination run wild. (It won't be difficult; that's my usual mental state.) :^) Picture yourself alone at night on an alien beach, standing under a sky filled with strange constellations. In the darkness you can hear the alien surf washing gently up the sands and swishing back out. Out on the methane ocean, strange lights are gently blinking on and off. You have no idea what they are -- this world is supposed to be uninhabited. In the distance to your right, a barely discernible glow like that of a city below the horizon reveals where methane ends and sky begins. Perhaps this planet is not deserted. But as you watch and wonder, the glow increases and spreads, until at last, in its undiminished splendor, its radiance piercing the high clouds, accompanied by the opening of "Thus Spake Zarathustra" the great cosmic bud rises into the sky. Day has come and you are still alone, but those dots that were lights blinking in the night still mar the horizon. . . . OK, so I exaggerated a little! Perhaps today's fractal isn't quite that spectacular, but it's still a striking one, and I feel it's good enough to make it as the FOTD for 22-11. When I saw this image, a sunrise, or budrise in this case, was my first and only impression. The image is a scene in the Z^24-(1.1*Z) figure, sliced halfway between the Mandelbrot and Oblate directions. It is another example of an order-2 object where none should appear. I had intended to post a different formula today, but this particular fractal so struck me that I felt it must be shown at once. And so here it is -- my FOTD for 22-11 -- not my best, but not my worst either. The finished image, which takes 6 minutes on an 80486-DX4 at 100mhz, is posted to Paul's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow, if I find no more irresistable images in the M-O rotation, I'll post an image from the M-R rotation. Until then, take care and put your best fractal forward. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE================================== budrise { ; 55 seconds on a P200--SF5 reset=1960 type=formula formulafile=minusrot.frm formulaname=M-O-rotation passes=t center-mag=1.26462/-3.33067e-016/4.372549/1.454/-90 params=24/44.5/0/0/0/0 float=y maxiter=1200 bailout=100 inside=253 logmap=yes periodicity=10 colors=000A00PF0UF0XG0aE0aI0`H0RG67CL7CN8DN<2>7C\ R6CP<2>8BKEBHKBFJACJ9AJ87H64J75K75H85<2>LC5MD5MD\ 5LE5<2>NE5NF5MF5<25>vL6<29>lbhkcjlckmdloel<6>tao\ paor`o<36>rJzrJzrKx<13>rWjqXiqYhpZgo_f<13>ekTelS\ dmRdmQenP<3>frLfsKgrK<28>et9gz2<4>cmIbzMbzPayS`v\ V_vX<8>deZdcZccX<12>hadzwP7V`7U` } frm:M-O-rotation {; Jim Muth ; real(p1)=power of Z, imag(p1)=rotation angle ; p2=parallel planes, p3=rotation point a=real(p1), b=imag(p1)+.0000000000001, z=sin(b*.01745329251994)*real(pixel)+p2, c=cos(b*.01745329251994)*real(pixel)\ +flip(imag(pixel))+p3: z=z^a-(1.1*z)+c, |z| <=25 } END PARAMETER FILE====================================

1 0

Re: Fractint and IEEE
by Raymond Filiatreault 06 Oct '03

06 Oct '03

>Intel(-type) Processors IIRC use 80 bit FP numbers for internal >calculations and do a conversion back to 64 bit when saving the results >to registers. If by registers, you mean the regular (non-FPU registers) this is correct. However the FPU register stack maintains values in 80 bit form exclusively, and these values CAN be copied to memory intact as 80 bit values. Parts of both statements may be right or wrong. The FPU internal computing registers are 80-bits but it also has a few 16-bit registers for various functions. One of them is the Control Word register in which 2 of the 16 bits are used for Precision Control and define how the results will be rounded after an instruction is performed. The choices are 32-bit, 64-bit or 80-bit. Depending on your OS, those bits may be set initially to 64-bit mode when a program first starts (such as under Windows). If those bits are not reset to get 80-bit precision, all results get rounded to the 64-bit precision when "saving the results to registers" although all computations are performed with 80 bits. The FPU cannot save any data directly to the regular non-FPU registers (and they're still only 32-bit registers in most computers). But, yes the FPU can copy 80-bit values to memory intact as long as the Precision Control has been set accordingly. However, if you store intermediate results as 64-bit values, you immediately waste the higher precision of the 80-bit computations. Raymond _________________________________________________________________ Help STOP SPAM with the new MSN 8 and get 2 months FREE* http://join.msn.com/?page=features/junkmail

1 0

Re: Fractint Hack
by JackOTradez 05 Oct '03

05 Oct '03

Tim - you mentioned: "Once I did a huge hack of fractint for Lee Skinner in which I changed nearly all "double" types to "long double" so Lee could squeeze out another couple of orders of magnitude of precision for a very deep zoom (but not quite arbitrary precision) image he was working on. " Can I get a copy of that? JoTz

2 1

Re: Floating Point, 64 bit, 80 bit and beyond
by Jim White 05 Oct '03

05 Oct '03

I've done a lot of fractal programming in Visual Basic, and have built an engine which runs Fractint-compatible formulae in Windows. The speed of modern PC's makes the slightly slower calculation times less inconvenient, and I don't have to worry about video drivers. Using VB's "Double" data type gave me the standard 64-bit FP calculation mode. When I learned that most FPU's today can do 80-bit mode, I was disappointed that VB doesn't support this type. I converted my engine to PowerBasic, a VB-like 3rd-party compiler that offers a data type called "Ext", which is the 80-bit extended FP. PowerBasic also lets you create DLL's which you can't do in VB, so I was able to easily replace the VB engine with the PB version, retaining my VB front-end. Of course, 80-bit is only a marginal improvement over 64-bit, with just a few extra digits of accuracy. Of the extra 16 bits, it seems that only 10 are given to the mantissa, the other 6 being given to extending the exponent (as far as I can tell). I've been looking at arbitrary-precision options over the last few months. I'm very interested in the public domain library GMP (Gnu Multiple Precision) which can be built in optimised form for specific CPU's, e.g. Pentium2, Pentium4, i386 etc ... The "primitives" (fundamental operations like add, multiply) can be performed very fast, much faster than generic/portable libraries. Deploying GMP to use with fractals under Windows has proved to be tricky, as GMP is mostly used in Unix environments, but I've managed to overcome these problems and now have a GMP DLL I can use. Soon I hope to be able to do some comparative time tests to see how GMP performs "in the field" - ie. with a deep-zoom fractal calculation. Regards Jim White ________________________________________________________________________ Want to chat instantly with your online friends? Get the FREE Yahoo! Messenger http://mail.messenger.yahoo.co.uk

1 0

Classic FOTD 19-06-97 (Prophet)
by Jim Muth 05 Oct '03

05 Oct '03

Fractal of the Day, June 19, 1997 Fractal visionaries: Every once in a while there comes a fractal picture that fairly shouts its name. Today's image is one of those. Despite the abysmal initial coloring, the moment I saw the image, with its stylized figure standing on a mountain top, showering blessings, I knew it could be named nothing but "prophet". It took only a carefully selected palette to bring the prophet to life. The formula is one of my failed efforts. But though the formula doesn't give me exactly what I was after, it does draw some very interesting images, which have earned it a place in my permanent formula file. Probably half the formulas in my collection were failures when I first tried them. But success can sometimes come from failure, and unless a formula draws nothing but a blank screen, I almost never give up on it until I have tried a wide variety of parameters. My current effort to draw all the oblique and skew planes in the julibrot figure is producing an unusually rich variety of formulas and images. For tomorrow's fractal, I'm going to wing it. Maybe I'll post another of my lucky accident fractals; maybe one of my older gems. But whatever it turns out to be, it will be interesting. Today's image has been solemnly posted to Paul's web site at: <> for the convenience of those who can't tie up their machines. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START COMBINED FILE FOR 19.6================================ prophet { ; 22 seconds at 200mhz, 640x480 reset=1960 type=formula formulafile=jim.frm formulaname=Test1XY passes=1 center-mag=2.66454e-0\ 15/-1.31262/0.2554581 params=0/0.5/0.5/0/-2/0 float=y maxiter=1000 bailout=100 inside=bof60 logmap=yes symmetry=yaxis periodicity=10 colors=00000000BFBDFFEGLGIQHKRJLSKNTMOUNQVPRXQTYSU\ ZTW_VX`WZaY`bZcc`fdbieclfeogfqhhtiiwjkzklzmlzmlzll\ zllzlmzkmzkmzzzzyyzxxywwxvvwuuvttusstrrsqqrpppoonn\ nlmnjlnhknfjndinchncgobfoaeo`do_coZboZaoYaoYaoX`oX\ `oW_oW_oV_oVZoUZoUZpTYpTYpSXpSYpRYpRXpQXpPXpOXpOXp\ OXpPXpPWpPWpPWpPWpPWpQWpQVpQVpQVpQVpRVpRVpRVpRUpRU\ pRUpSUpSUpSUpSUpSTpTTpTTpTTpTTpTTpTSpUSpUSpUSpUSpU\ SpVSpVRpVRpVRpVRpVRpWRpWQpWQpWQpWQpXQpXQpXQpXPpXPp\ XPpYPpYPpYPpYPpYOpZOpZOpZOpZOpZOpZNp_Np_Np_Np_NpZM\ pZMpYLpYLpYKoXKoXJoXJoWIoWIoWHoVHnVGnVGnUFnUFnUEnT\ EnTDmTDmSCmSCmSBmSAmR9mR7mR5mQ3mQ1mQ0mP0mP0lO0lO0k\ O0kN0jN0jN0iM0iM0hM0hL0gL0gL0fK0fL0eK0eJ0dI0dH0cG0\ bF0aE0`D0_C0ZB0YA0X80W60V40U20T00S00R00Q00P00O00N0\ 0M00L00K00J00I00H00G00F00E00D00C00B00A009008007006\ 00500400300200100000000000000000000000000000000000\ 0000000000000000000000000 } frm:Test1XY { z=real(pixel)+(p1*(imag(pixel)))+flip(real(p2)), c=imag(pixel)+(p1*(real(pixel)))+flip(imag(p2)): z=z^p3+c, |z| <= 16 } END COMBINED FILE===========================================

1 0

Fractint and IEEE
by Tim Wegner 04 Oct '03

04 Oct '03

One little addendum to an earlier message. It may actually be false that Fractint uses IEEE math. In some modes, fractint uses 80 bit "IEEE-like" numbers. I'm not an IEEE math expert, but I'm not entirely sure that 80 bit numbers as used in an Intel Floating Point Unit are legal "IEEE" (though they are very "IEEE-like"). Fractal types in fractint that are implemented 100% in assembler use pure 80 bit floating point math. In other modes implemented primarily in C, Fractint does an odd mixture - the 64 bit double precision numbers used to implement double types are IEEE, but these are converted to 80 bits briefly when passed to the math coprocessor. In my workplace (NASA) this mixed precision behavior on the Intel platform has caused some problems we don't get on machines that use pure IEEE 64 bit doubles consistently. None of this affects my negative critique of the statement that minbrots are an artifact of IEEE math. That claim is pure unadulterated hogwash. Tim

2 2

On vacation
by Scott D. Boyd 04 Oct '03

04 Oct '03

List members and FOTD enthusiasts: I will be out of town Monday - Wednesday, Oct. 6th - Oct. 8th, so I will not be posting Jim Muth's FOTD's during that time. They will be posted when i return on Thursday the 9th. Scott ------- sdboyd56(a)swbell.net http://sdboyd.dyndns.org/~sdboyd/ ------------------------------------------------------------ No Microsoft or other proprietary products were used in the creation of this email.

1 0

Classic FOTD September 28, 1997 (Pollock)
by Jim Muth 04 Oct '03

04 Oct '03

F.O.T.D., September 28, 1997 (Pollock) Fractal visionaries: Today's prize-winner fractal is named in honor of that not quite so famous American abstract artist, J. Pollock. The resemblance to the paint drippings which made him almost famous is apparent. I achieved such an effect by taking a nondescript Rectangular plane fractal and redoing it with the inside fill set to epsilon cross. I'm not sure how this option achieves its effects. I think it colors the image according to whether the points' orbits come closest to the real or imag axis. Until recently I had never used this option, considering such a fancy fill method artificial, but I have now had second thoughts about fractals. There is no such thing as a "natural" or "pure" fractal other than the bare formula. And since a natural frac- tal doesn't exist, it makes no sense to try to maintain fractal purity. And since I no longer must try to keep my fractals pure, I will be able to use the entire range of Fractint's coloring options without compunction. For best effect, today's fractal should be drawn at a minimum resolution of 1024x768, to prevent the streaks of paint from breaking up. The finished image is available at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Until tomorrow then, may your fractals be infinitely beautiful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 FILE============================================= pollock { ; 17 seconds on a P200--SF5 reset=1960 type=formula formulafile=jim.frm formulaname=Rectangular passes=1 center-mag=-7.\ 77156e-016/-2.05391e-015/1.369962/0.6701 params=0.42/0.33 float=y maxiter=500 bailout=100 inside=epsiloncross logmap=yes symmetry=origin periodicity=10 colors=000Wgq00ZTal<4>LN_000HHVGETEBQzsfz0dD8O\ <6>ObZm``db_Xd_KhZ<6>q`dg9z<3>rVhu_dve_vjWgEJnRM\ ucPvoSenU3yL<9>gYkHRiOSjYFK<12>BQiGBN<4>9Up8Yv4r\ N5l`6fn7`zHdvRhqQ_A`np<5>`hd`gb`fa`e`<12>`ZTUZE\ <8>mZugrnkhtklzmgznbz<2>rQusLsv8y<7>nd_Dyz<9>Spf\ <9>OfiOeiPbe<2>NgqMhuNmzMkz<5>LaoL`mLZj<5>KPZCQW\ <10>XKYTDl<6>aQNcOH<12>Xa`XbaWed<4>UrqBkzFmz<4>Y\ vraxpgzqfzp<3>bwoavnatn<4>XolZrm<7>Tbl`pyZmvXjs } frm:Rectangular {; Jim Muth z=flip(real(pixel))+real(p1), c=flip(imag(pixel))+imag(p1): z=sqr(z)+c, |z| <= 36 } END 19.6 FILE===============================================

1 0

Classic FOTD 11-08-99 (Zodiac)
by Jim Muth 03 Oct '03

03 Oct '03

FOTD August 11, 1999 (Zodiac) Fractal enthusiasts and visionaries: I named today's fractal picture "Zodiac" not because of its appearance, but rather because I was wishing that I could be somewhere along the path of the solar eclipse. But the eclipse is in Europe and Asia, and I'm stuck here on the East coast of North America. Curiously enough though, if the path of totality were extended beyond the sunrise line, it would cross Maryland. As it is, we will see 20 percent of the sun obscured at sunrise. But alas, we will not even see that tiny event, for it will be overcast at sunrise. While I'm bemoaning our bad luck, I'll remind the fractal fans of the world that today's fractal is not a bad one. The midget is part of the fractal that results when a large amount of Z is subtracted from a little Z^100 and the difference multiplied by a factor of 0.0103. The parameter file is slow, so downloading the image file is strongly recommended. The image file can be found posted to: <alt.binaries.pictures.fractals> and to: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The always unimportant weather was partly cloudy and quite a bit warmer. The midday temperature of 88F (31C) was perfect for fractals of all ages, both liberal and conservative. And don't ask what a liberal fractal is. If you're not totally confused by this time, check here again next time, which will be in 24 hours plus or minus 1-1/2 hours. You'll be totally and absolutely confused if you do. Until then, take care of your pet fractal, and if you have no pet fractal, get one immediately. They work wonders for high blood pressure. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 19.6 PAR-FORMULA FILE================================ Zodiac { ; t=0:13:12.57 on a p233, 640x480 reset=1960 type=formula formulafile=critical.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+1.664072112263802/+0.3928892632790632/2.\ 145788e+007/1/-5 params=0.01/100/-100/1/-0.9897/0 float=y maxiter=12000 bailout=25 inside=0 logmap=267 symmetry=none periodicity=10 colors=000DGNCHKBIK<6>6IS6IT7IU<10>CHdCHeDHeDHe<16>K\ Fa<5>mkw<28>6Fg<10>`Ztm`u<3>zgyzkzzgrwfkrecmeX<6>EaN\ <13>SW4<18>2ju<8>oajn`io_hp_hqZg<3>ubevcewcdwcc<13>w\ cXwcWwcWwcW<78>wcU } 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 19.6 PAR-FORMULA FILE==================================

1 0