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FOTD 10-07-02 (Midget Squid [6])
by Jim Muth 10 Jul '02

10 Jul '02

FOTD -- July 10, 2002 (Rating 6) Fractal visionaries and enthusiasts: In the depths of the world's oceans lurks the giant squid, so far unseen while alive and known only from dead specimens washed up on beaches or dredged up in fishing nets. In the depths of the world's fractals lurks the midget squid, neither alive nor dead and known only by a whimsical name given in a moment of fancy. For some strange reason, while viewing today's image, I was reminded of a squid. (I thought I saw suckers.) Since the size of the features in the image is in the sub-atomic range, I named the picture "Midget Squid". It's a pretty ordinary formula that generates the image -- 4(Z^(-0.1))+0.4(Z^2)+C -- a formula that generates a moth-eaten parent fractal with more curious nooks and crannies to explore than a fractalist can shake his iterations at. In today's case, I chose the vague 'East Valley' appearing area of the parent to investigate. I got quite far down before the signs of the tiny midget finally appeared. Because of its less-than-expert coloring, the image rates a 5 or a 6. Feeling generous, I rated it a 6. A better way of rating the FOTD images might be to have the viewers decide. I've been thinking about such a system for some time. Perhaps I'll decide about the ratings when the FOTD-CD is ready. The parameter file's render time of 10 minutes is a bit slow for today's busy world. Time can be saved by downloading the finished GIF image from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Tuesday was once again hotter than a far-cracker. But in the early evening the temperature of 99F 37C was knocked down to 72F 22C by a whopper of a thunder-storm, which sent the intrepid duo of house-cats scurrying for cover and kept them hidden until 10pm. Today promises to be less hot, but before I can enjoy the milder conditions, I must finish some work. And before I can finish, I must start. So until the next FOTD on July 12, take care and be ready for anything. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Midget_Squid { ; time=0:10:24.07--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=-3.18686290593923700/-0.012918240803433\ 52/9.031838e+011/1/-110.25/0.31625297457531909 params=4/-0.1/0.4/2/0/0 float=y maxiter=1200 inside=0 logmap=209 periodicity=10 colors=0000Ki0Mh0Og0Qf0Se0Ud0Wc0Yb0_a0a`4c_6eY8gWA\ iUBjSDlQFnTGoWIqZKsaLudNwgPxjQvmRtgRpbTkXXfSWaMWYH\ YUB`P6`E1YE3YE5_E7bE9dEBfEDhEFkEHnEJqELtENvDRvFQtH\ QrIQpKQnMQlNQjPQgRQeSQcUQaWQ_XQYZQW_QZ`Sa`Uc`WfaYh\ a_kaanbcpbesbgubivcdvd`veWvfSvfNwgJwhEwiAwj5wj1c_A\ e`Jg`Ri`Tk`Um`Ti`SdaS_aRVbRQbQLcPGcPBdO6dO8fP9gQAh\ QCiRDjREkSFlTHnTIoUJpUKqVMrWNsWOtXPuXUt_Ytaascesei\ rhmrjqqluqnyqpypkyogyobynZymVymQylMylItjLohOkgQfeT\ acVYbYT`_OZbKYdFWgBViJYhQ_gYafddelfdshdoh`khXghUch\ Q_hMWhJShFOhBKh8Gh4Ch1Ib7OYDUTJ_OOeJUkE_q9dnDakH_i\ LYfPVdTTaXR_`OXdMVgKXcIY`H_YG`UFbREcOCeLBfHAhE9iB8\ j87kB9lEAmHBmKCnNEoQFoTGpWHqZJqaKrdLsgMsjNpiMniOmi\ RliUkhXjc_iZbhUegPhfKkeFndAqc5tb6qc7nc8kc9hc8hc8ic\ 8jc8kc7lc7md7oe7qf6sg6uh6wi6yj6zkGzlPzmQznQzoRzpRz\ qRzrSzsSztTzuTzvTzwVzxWzyXzzXzzYzzZzzZzz_zz`zz`zzY\ zzVzzTzzQzzOzzLzzIzzGzzqz } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 08-07-02 (A Blue Creation [7])
by Jim Muth 08 Jul '02

08 Jul '02

FOTD -- July 08, 2002 (Rating 7) Fractal visionaries and enthusiasts: Fractals are infinite -- which is why they are called fractals. They are infinite in many ways. But what is infinity. At one time I thought that infinity was the largest possible number. Somewhat later, I realized that if infinity were the largest number, that number could be represented by the letter X and increased by any desired amount by adding another number to it as in X+Y=Z. Of course, the new number represented by Z could be given the same treatment, and the process continued forever, demonstrating that no largest number exists. Infinity is not a number, it is a condition -- the condition of being without limit. This condition is quite easy to see in a case such as a toy train track arranged in a circle. The track has no limit, and a toy train running along it will travel a trip without a limit. As a basic concept, infinity is easy to understand. Paradoxes arise however when we begin asking meaningless questions about infinity. The toy train going in a circle is a simple concept, but if we ask how many circuits of the track will the train eventually make if nothing ever stops it and nothing wears out, or how many days will the train continue running before it comes to the end of the line, we find ourselves faced with questions without answers. In our everyday lives we ask such questions, often without realizing it. Questions about the beginning and end of time and space are puzzling for the same reason that questions involving the end of the toy-train line are puzzling -- we are trying to introduce into our intuitive world-view something that does not exist. I admit that it is fun to wonder about what happened 'before' the 'big-bang', (if the bang itself actually happened), but being able to perceive time intuitively only as an infinite straight line with no imaginable beginning or end, I know that I will never find an answer that appears intuitively correct. And speaking of infinity, today's fractal contains infinite detail, an infinitesimal part of which appears in today's image. I named the scene "A Blue Creation", though I have not decided whether I created it when I entered the parameters, or merely discovered it. Regardless of its origin, the image rates a 7, which makes it almost worth the 6 minutes required to render it from the parameter file. As always, the completed image is available on Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and on Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Sunday here at Fractal Central was smoky. Smoke from forest fires in Canada blew in on north winds and gave us a day with a dull grey sky and visibility of less than 1km. The smell of burning timber was quite noticeable, which may be why the dynamic duo remained outdoors only a few minutes. The temperature of 81F 27C was quite pleasant but hard to enjoy with the smoke totally obscuring the sun. If I'm lucky, I'll get done the things that need to be done, and have enough time left over to enjoy part of the afternoon. But before I hope to finish, I must begin. Until next time on July 10, take care, and before we can know the truth we must know the question. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ A_Blue_Creation { ; time=0:06:15.52--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-1.164418403483855/-0.00416714065635447\ /4.784102e+008/1/-7.5/-1.34769670230433514e-005 params=1.75/0.8/0.175/-8/0/0 float=y maxiter=750 inside=0 logmap=111 periodicity=10 colors=0000005E46D38B0990z0zr0nl0hc0`W3ZQ6YJ9YBDY5\ J_4K`4Lb4Oa3Pb3Qc3Rd2Se2Tf2Ug0Vh0Wj0Xl0Ym0Xq0Vt3St\ 5Op9KkBIfEHcKHbKIYKJUQKRTLPWMLZNJaOGdMEfMBiQFjTIkV\ KnZMo`PpcTsfVtiYul_xoayqezthzxjzzlzzozypzvqztszptz\ nuzkvyhxyexxcyx_zvYzuVzuRztPztMzhflYzVTxPPvJKuDGs6\ Bq08p0Bk0Fh3Jd6M_AQWEUTIYPL`KQdGUhDYk8`o4ds0hv0kq3\ jn8ijEheJfaPeZUeUZdQdcMiaIo`Et_Ay_FscKlePhhUajZYlc\ RphMslGuqBxv5zz0zx2xu3tt3oq4ko4fn5ck5Zi6Vh6Qe8Mc8I\ a9E_99YA5WA2`DAdEJiFRlI_qJhuKpyLxsIynEzhBzc8zZ5zYA\ vYFpYKjYPdYTZTVaPWeLYhG_kD`o9aqFWtLQuQKxWEy`8zf2zk\ 0zl3zn8xoDuoIqpMoqRlqWis`ftedtjavk_xkZykYzkWzkVznV\ ypVysVxuVxvVvyVuzVuzVtzVtzVazeLzo4zy3xv2qu0ks0eq0_\ o0Un0Ok0JjfJihGkhFlhEnhDohAqh9sh8th6u`DsVJqPPoJVnD\ `l6fj0li0sh6piIniTkjcijnfjkjaioUjqkqxuyzzxzzxzxxzu\ vzsvzpvznuzjuzhuzetzctz`tzZtzWkzUdzTYzQQzPIzOAzL3z\ K0zJ0zG0zF0zE0zB2zA3z93z8 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Fairly Gratuitous
by Morgan L. Owens 06 Jul '02

06 Jul '02

Okay, I'll confess. I did the par for the sake of using the title. What interest it has is based on watching it render (this is why I recommend a resolution of 1600x1200: at other resolutions the aliasing effects are different and not the ones I tuned the viewing box for). Watching the rendering, one might see (at least, if one is as sick and twisted as I am) the aliasing as something the title might be alluding to. Another allusion is the fact that the formula derives from the classic Liar Paradox (in the form "Statement 1: Statement 2 is true. Statement 2: Statement 1 is false") via Fuzzy Logic and Scientific American. Chuck Ebbert's Liar1 attack on this problem appears in fractint.frm. I had also written the same formula prior to its inclusion in fractint.frm, but to give the user something to do I parameterised the bailout - in effect, allowing a certain amount of inconsistency to remain in the final result. More lies. It was almost inevitable that p1 would be replaced by pixel to produce what's called below "ChaoticDualist1M". But as I suggested, the title came first and then the par to suit. It had been sitting around on my harddrive until today, when I bethought to dig it up, tweak it, and post it. In short (hurray!), I'm using this whole thing as an excuse to reuse the title of a story by Greg Egan that appeared ten years ago this month in Interzone magazine. Otherwise I probably wouldn't have bothered. Morgan L. Owens "Hey, I marked Galileo's tenth anniversary here, and the twentieth of the Mandelbrot Set's discovery..." UnstableOrbits { ; Unstable Orbits in the Space of Lies ; Best viewed at 1600x1200 ; Greg Egan, Interzone #61, July 1992 ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=logic.frm formulaname=chaoticdualist1m passes=d center-mag=0.67703/0.67703/0.589404/1/44.999 float=y maxiter=16 inside=atan outside=255 periodicity=0 colors=000JG2<24>OG2PG2PG2PG2PG2<2>QH4RI5RJ6SK7TK8<46>vusvvtwvu<3>zzz030\ <9>010010000<6>000000000<52>1E01E02F0<87>JG2 } frm:ChaoticDualist1M{ bailout=pixel z=pixel: x=real(z) y=imag(z) z=1-abs(x-y)+flip(1-abs(x+y-1)) |z|<=|bailout|}

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FOTD 06-07-02 (Interesting Midget [6])
by Jim Muth 06 Jul '02

06 Jul '02

FOTD -- July 06, 2002 (Rating 6) Fractal visionaries and enthusiasts: Today's image is named "Interesting Midget". 'Interesting' or 'nice' is what I say about something when I want to say something good but can't find any particular aspect to say something good about. I use the words frequently in my non-fractal life when I must decline customers' suggestions that I know will never work. The midget in today's image, with its vaguely familiar decorations, is 'nice' in a broad, generic sort of way -- In other words, it is interesting. Finding interesting midgets, or interesting fractals of any kind, can sometimes be a real challenge. Though the parent fractals may appear promising, all too often they hold no midgets, or if the midgets are there, they merely exhibit a duplication of features found in various parts of the Mandelbrot set. When I first saw the oversized parent fractal of today's scene, it did not even look promising, but something told me that a FOTD was hiding somewhere down in its depths. And indeed, my intuition turned out to be true. The midget lay very deep indeed, but it was there, waiting to be discovered and revealed to the world, or at least a small part thereof. The route down to the midget was long and quite eventful, and can be traveled in reverse by setting the logmap to zero and outzooming about 10 times. The formula itself, which adds 1/10 part of Z^(-11.1) to Z^(-1.11) then adds (1/C), is unexceptional, but in the world of fractals, unexceptional beginnings sometimes lead to exceptional ends. Undecided whether to rate today's image a 6 or a 7, I finally decided on a 6. It is a bit above average, though if I continue to produce fractals of this same quality, the average will rise, and I'll need to start rating them a 5. The render time of around 8 minutes on a run-down P200 machine is marginal, but the wait can be avoided by letting Paul and Scott render the image and then picking it up from their web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was sunny and still very warm, but the temperature of 92F 33C and drier air was far better than the humid 106F 41C that was registered in the center of the city Thursday. The cats actually spent an entire hour outdoors in the shade of the dogwood tree, watching the starlings fly by. As for me, I'm planning another restful day. There's not too much work to be done, and I might actually get a chance to rest. But regardless, I'll return in two days on Monday, July 8, with another glorious (I hope) fractal to delight and amaze. Until then, take care, and don't let the fractals obstruct your view. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Interesting_Midget { ; time=0:07:51.48--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+49.36527881043839000/+30.4157556183393\ 0000/2.374188e+009/1/50/-9.25530275780669931e-005 params=1/-1.11/0.1/-11.1/0.5/0 float=y maxiter=800 inside=0 logmap=165 periodicity=10 colors=000EV0GY1JY6Nb9OdERgIViNXiQ_iTbiTdiTbiTaiT_\ iTYiTXiTTgTQfTNdTJbTGYTDXQlTLdNNXIJQEGI9BB48214000\ 000000000001204B08I0BO0EV0Ib1Li2Op4Rx6Vz8Yz9az9dzD\ azG_zJYzQXzQVzWRzXQz`OzbNzdLziIxlEqpDks9dw8Yz4Rz1T\ z0iz0zz0zz0zz0zz1zzDizOTtYJniOgtTbzV_zXVzYRz_NzaIz\ bEzd9zf6zg1zg0zd2za6z_BzXEwTJsRNpORkNVgJ_dGb_EgXBi\ T9iO6iL2iI1iD0q90z60zz0qz0iz0Tz0Dw40p90gE0aJ0TO0NT\ 0EY08b01g0Bk0Ln1Tq6bwBkzEtzJzzOzzRzw_zifzXnsJtk6za\ 0zT0zL0s00n00k00f00b01Y06V09Q1EN1II2NE2R94V64_16b0\ 6g08k08p09s09q0Bq0Dq0Eq0Gq0Iq0Jq0Jq0Lq1Nq2Oq6Qq8Rq\ 9TqBTn9Vk8Xg6Xd6Ya4_Y2_V2aR1aO0bL0dI0dE0fB0g80g40i\ 10i00k00l00l00n00n00p00p00p00q01q04q08q0Bs0Ds0Gs0J\ t0Nt0Qt0Rt0Vw0Yw0aw0bw1as1aq1_p1_n1_l2Yk2_i2ag2bf2\ dd2fb4g_4iY4kX4lV4nT6pR6qQ6sO6tN6wL6xJ8zL8zL9zL9zL\ BzLBzLDzLDzNEzNEzNGzNGzNIzNIzNIzNTzGdzBnz6kzbJzT0z\ L0zJOzVJzJEz89z04z08z0Bz0 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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FOTD 04-07-02 (Mandelbrot Network [7])
by Jim Muth 04 Jul '02

04 Jul '02

FOTD -- July 04, 2002 (Rating 7) Fractal visionaries and enthusiasts: Sensible people see a fractal, say ho-hum, and forget about the thing. Others, not quite as sensible, discover fractals and are surprised at their variety, then experiment with them for maybe a month or two, and eventually grow bored and move on to more sensible and productive endeavors. Those like myself, who have gone beyond the need to act with common sense, become obsessed with the endless intricacies and spend years, perhaps a life- time, exploring the limitless varieties of the things numbers do. And like those fractal fans, some fractals make no sense at all. (Maybe all fractals make no sense, but that's another story.) Today's image is an example of a senseless, illogical and thoroughly irrational fractal. For some reason known only to who or whatever is in charge of the things numbers do, the midget in today's image lies exactly on the shoreline of its parent, with its east (bottom) half surrounded by the expected outside material, but its west (top) half existing invisibly in the potential inside material that forms the upper half of the image. Since invisible things are hard to see, I made the invisible visible by coloring the inside with the <fmod> option, with the proximity set to 0.085. The result is one of the more unusual midgets in the FOTD series. The real(p3) parameter is the one that works the mischief. It is critical, and must be set just right to get the half-and-half effect. I named the image "Mandelbrot Network" because of the delicate network-like elements in the top half of the image. Because of the unusual nature of the image, I raised the rating one point from a 6 to a 7. I suppose it's worth the rating. The render time of 2 to 3 minutes is quite reasonable for an image with so much inside area colored with the <fmod> option. And as always, those who would rather not render may find the finished image posted to Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and to Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> For the benefit of those who concern themselves with the weather in far corners of the earth, the fractal weather Wednesday here at Fractal Central, which is located not far from 39,21N 76,32W, was hotter than a firecracker, with blazing sun and a tempera- ture of 104F 40C. In response, the fractal cats spent the day under the air conditioning vent, stretched to near twice their normal length. Today promises to be just as hot if not hotter, but it's the Independence Day holiday here in the USA, the day when fireworks displays are everywhere, (except where they have been banned because of fear of terrorism), and it's supposed to be hot on the Fourth of July, as the day is usually called. I might wander over to the local fireworks display this evening; or I might not. I haven't decided. In either case, I'll have another glorious FOTD in two days on July 6. Until then, take care, and I'll bet there's snow falling in the New Zealand Alps. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Mandelbrot_Network { ; time=0:02:50.60-SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=+0.523994586278288/0/121.9547/1/90/-1.2\ 3373533611470521e-014 params=1/0.35/-1/0.3/32.175/0 float=y maxiter=500 inside=fmod proximity=0.085 logmap=yes periodicity=10 colors=0008PdAPcCPaEOaGO_INZKNXMMWOMURLSTKRVJPXIOZ\ HM`GKbGJdFHfEGiEEkDDmCBoC9qB8sA6uA5v93x81y92y93x93\ xA4wA4wA5vB6vB6uB7uC7tC8tC9sD9sDArDArEBqECqECpFDpF\ DoFEoGFnGFnGGmHGmHHmHIlIIlIJkIJkJKjJLjJLiKMiKMhKNh\ LOgLOgLPfMPfMQeMReNRdNSdNScOTcOUbOUbPVaPVaPWbOVaPW\ aPWaQWaQXaQXaRXaRYaSY`SY`SY`TZ`TZ`UZ`U_`U_`V_`V`_W\ `_W`_W`_Xa_Xa_Ya_Yb_Yb_ZbZZcZ_cZ_cZ_cZ`dZ`dZadZaeZ\ aeYbeYbfYcfYcfYcfYdgYdgYegYehXehXfhXfiXgiXgiXgiXhj\ XhjXijWikWikWjkWjlWklWklWklWlmWlmVmmVmnVmnVnnVnoVo\ oVooVooVppUppUqpUqqUqqUrqUrrUsrUsrTuqUsrVrrWprXosY\ nsZls_kt`itahtbguceudduecvfavg`vhZwiYwjXwkVxlUxmTx\ kUviUuhUtfUreUqcUpbUo`Um_VlYVkXVjVVhUVgSVfQVdPVcNV\ bMWaKW_JWZHWYGWXEWVDWUBWTAWSAWRAWRAWQAWQBWPBWPBXPB\ XOBXOBXNBXNBXMCXMCYMCYLCYLCYKCYKCYJCYJCYJBXIBXIBXI\ BXIBXHBXHBXHAWHAWHAWGAWGAWGAWGAWGBVHCVIBUJAUKAUKAU\ KAUKAUKAUKAUKAUKAUKAUKAUK } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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Re: [Fractint] Fractal Haircut
by Morgan L. Owens 03 Jul '02

03 Jul '02

At 08:42 01/07/2002, David Boddington wrote: >Dear Fractalists: > >Did anyone else on the list take note of Ronaldo's fractal haircut >during the latter stages of WC Korea\Japan 2002? Better yet, >can anyone provide a par formula? Dunno about Ronaldo (he _has_ hair?), but what about Ahn Jung-Hwan's?! Now _that's_ what I call filamentary structure! Morgan L. Owens "Doesn't really do it justice." Ahn_Jung-Hwan { ; ...or at least his hairstyle ; ...kinda (someone improve the colouring?). ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=chby9.frm formulaname=c07-09 function=cos center-mag=-0.146825/0.146825/0.6426667/1/-45 params=0.01/0.002 float=y maxiter=1023 inside=255 logmap=yes colors=777zzz<35>zzzyzzzyzzyyyyyyyyyyz<9>yyyxyyyxyyxxxxxxxxxxy<5>xxxwxxx\ wxxwwwwwwwwwwx<5>wwwvwwwvwwvvvvvvvvvvwvvvvvvuvvvuvvuuuuuuuuuuvuuuuuutuuu\ tuuttttttttttuttttttstttsttsssssssssstssssssrsssrssrrrrrqrrrqsrqqqqqqqqq\ qrqqqqqqpqqqpqqpppppopppoqpooooonooonponnnnnnnnnnonnnnnnmnnnmnnmmmmmlmmm\ lnmlllllklllkmlkkkkkjkkkjlkjjjjjijjjikjiiiiihiiihjihhhhhghhhgihgggggfggg\ fhgfffffefffegfeeeeeceeecfecccccbcccbecbbbbbabbbacbaaaaa_aaa_ba_____Z___\ Za_ZZZZZXZZZX_ZXXXXXVXXXVZXVVVVVUVVVUXVUUUUUSUUUSVUSSSSSQSSSQUSQQQQQPQQQ\ PSQPPPPPNPPPNQPNNNNNLNNNLPNLLLLLKLLLKNLKKKKKIKKKILKIIIIIGIIIGKIGGGGGEGGG\ EIGEEEEECEEECGECCCCCACCCAECAAAAA7AAA7CA77777777777 } frm:C07-09 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = zC06-C05 t=p1, bailout=4, z=pixel: x=real(z), y=imag(z) xx=x*x, yy=y*y Tx=fn1(x*(xx*(xx*(xx-7)+12)-5)) Ty=fn1(y*(yy*(yy*(yy-7)+12)-5)) x=x-t*Ty, y=y+t*Tx z=x+flip(y) |z|<=bailout }

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Another color map for Ahn_Jung-Hwan fractal
by Harold Lane 03 Jul '02

03 Jul '02

>>Did anyone else on the list take note of Ronaldo's fractal haircut >>during the latter stages of WC Korea\Japan 2002? Better yet, >>can anyone provide a par formula? >Dunno about Ronaldo (he _has_ hair?), but what about Ahn Jung-Hwan's?! Now >_that's_ what I call filamentary structure! > >Morgan L. Owens >"Doesn't really do it justice." > >Ahn_Jung-Hwan { ; ...or at least his hairstyle > ; ...kinda (someone improve the colouring?). > ; Version 2001 Patchlevel 8 >reset=2001 type=formula formulafile=chby9.frm formulaname=c07-09 >function=cos center-mag=-0.146825/0.146825/0.6426667/1/-45 >params=0.01/0.002 float=y maxiter=1023 inside=255 logmap=yes >colors=777zzz<35>zzzyzzzyzzyyyyyyyyyyz<9>yyyxyyyxyyxxxxxxxxxxy<5>xxxwxxx\ >wxxwwwwwwwwwwx<5>wwwvwwwvwwvvvvvvvvvvwvvvvvvuvvvuvvuuuuuuuuuuvuuuuuutuuu\ >tuuttttttttttuttttttstttsttsssssssssstssssssrsssrssrrrrrqrrrqsrqqqqqqqqq\ >qrqqqqqqpqqqpqqpppppopppoqpooooonooonponnnnnnnnnnonnnnnnmnnnmnnmmmmmlmmm\ >lnmlllllklllkmlkkkkkjkkkjlkjjjjjijjjikjiiiiihiiihjihhhhhghhhgihgggggfggg\ >fhgfffffefffegfeeeeeceeecfecccccbcccbecbbbbbabbbacbaaaaa_aaa_ba_____Z___\ >Za_ZZZZZXZZZX_ZXXXXXVXXXVZXVVVVVUVVVUXVUUUUUSUUUSVUSSSSSQSSSQUSQQQQQPQQQ\ >PSQPPPPPNPPPNQPNNNNNLNNNLPNLLLLLKLLLKNLKKKKKIKKKILKIIIIIGIIIGKIGGGGGEGGG\ >EIGEEEEECEEECGECCCCCACCCAECAAAAA7AAA7CA77777777777 >} > >frm:C07-09 {; V.1.1 - earlier versions may be discarded > ; Copyright (c)1998,1999 Morgan L. Owens > ; = zC06-C05 > t=p1, bailout=4, z=pixel: > x=real(z), y=imag(z) > xx=x*x, yy=y*y > Tx=fn1(x*(xx*(xx*(xx-7)+12)-5)) > Ty=fn1(y*(yy*(yy*(yy-7)+12)-5)) > x=x-t*Ty, y=y+t*Tx > z=x+flip(y) > |z|<=bailout >} ################################################# Owen, in response to: "someone improve the colouring?" here's a color map I created applied to (a slightly zoomed out version of) your fractal: - Hal Lane ################################################# Ahn_Jung-Hwan2 { ; ...or at least his hairstyle kinda ; Fractal parm file by Morgan L. Owens ; Color map by Hal Lane 7-2-02 ; 7:05 at 1024 x 768 on a PII 400 ; Owen's par file: Version 2001 Patchlevel 8 ; This par file: Version 2002 Patchlevel 3 reset=2001 type=formula formulafile=pastengo.par formulaname=c07-09 function=cos center-mag=-0.00337391/0.00337391/0.4804985/1/-44.9999999999\ 999929/3.88578058618804789e-016 params=0.01/0.002 float=y maxiter=1023 inside=255 logmap=yes sound=off colors=000000yv0<7>qP0pL0oH0<3>k00<43>400<3>000000000<58>00u\ 00v00w<2>00z00z00y<57>005004003002001<60>w00 } frm:C07-09 {; V.1.1 - earlier versions may be discarded ; Copyright (c)1998,1999 Morgan L. Owens ; = zC06-C05 t=p1, bailout=4, z=pixel: x=real(z), y=imag(z) xx=x*x, yy=y*y Tx=fn1(x*(xx*(xx*(xx-7)+12)-5)) Ty=fn1(y*(yy*(yy*(yy-7)+12)-5)) x=x-t*Ty, y=y+t*Tx z=x+flip(y) |z|<=bailout }

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Problems with '3D's after equals signs
by Harold Lane 03 Jul '02

03 Jul '02

Why have all the equals signs in my posts to fractint(a)mailman.xmission.com had the characters '3D' inserted after them? How can I keep this from happening? I note that other posters to fractint(a)mailman.xmission.com do not have this problem. I have not had other people that I correspond with say that they have had trouble with this problem although an equals sign is not often used in correspondence. I use Robin Bussell's excellent freeware "Fractint paste and go utility" to remove the '3D's after equals signs with the single push of a button when I find them in a par file: http://web.ukonline.co.uk/robin.b2/pastengo.htm Robin's small (15k) utility (V1.3) uses the Microsoft visual basic runtime DLL which he also makes available if you do not already have it on your system. Paste N Go makes using parameter and formula files with Fractint extremely easy. I avoided using parameter and formula files with Fractint for a long time. Now that I have discovered Paste N Go I use them quite often. I use Compuserve 4.0.2 under Win98 original version for my email. If anyone knows how to avoid creating '3D's after equals signs during posts I would really like to know. I do not enjoy creating problems for other people. - Hal Lane

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RE: [Fractint] FOTD 27-06-02 (Birth [6])
by nick.grasso＠hrads.com 02 Jul '02

02 Jul '02

Mark A. Freeze wrote: >>>I have just subscribed to this group. In the future, can I expect more fractal-based discussions AND this childish back-and-forth bantering? I hope so! I love it! Fractals, arrogance, ignorance, conspiracy!!! All in one place! How lucky I am to have found you!<<< Welcome Mark. You may also want to subscribe to the Philofractal list (Fractals and Philosophy). That list has freewheeling philosophical discussions vaguely related to fractals, and perhaps some childish back-and-forth bantering also <g>. I don't have the subscription info, but I think it is run by Jim Muth who is also on this list. Nick

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FOTD 02-07-02 (One Froggy Morning [7])
by Jim Muth 02 Jul '02

02 Jul '02

FOTD -- July 02, 2002 (Rating 7) Fractal visionaries and enthusiasts: Fractals of the Mandel-Julia variety are filled with holes, especially when the iterated expression contains more than one power of Z. These holes come in many varieties. There are the obvious Mandelbrot midgets and Julia sets, and then there are the other types of holes that defy description. Today's image features one of these 'other' holes. The area in question was pointed out to me by Lee Skinner in an image he sent privately several days ago. The orange-colored holes near the center are of a type I have seen in images created with the branch-cuts formula when the exponent of Z is in the area of 1.15, but in today's image, several things appear to be happening at the same time. It almost appears that the two different powers of Z are doing things independently of each other. A math expert might be able to tell what is going on in today's image, but not being a math expert, I have no idea. While studying the image, I had the distinct impression of a frog staring back at me. I promptly named the image, "One Froggy Morning". The rating of 7 is justified because the image is a bit -- well -- cute. The render time of over one hour on a P200 machine is not cute however. I advise letting Paul and Scott do the heavy work and downloading the completed image from their one of the web sites. Paul's site is at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Scott's is at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Monday at Fractal Central was typical summer fare for these parts of the world -- HHH -- hazy, hot and humid. The temperature of 92F 33C, combined with the high humidity and foul air, made the outdoors unpleasant for most of the day. The dynamic duo of cats must have agreed, for they stayed on the porch only a few minutes before coming in and asking for their tuna treat. As for me, it's another Tuesday, even hotter than yesterday, and I've got a bit of work to finish before returning to the FOTD CD, which should be ready for distribution by the end of summer. But the end of summer is still over 2-1/2 months away, and before then we'll have many more fractals added to the ever- growing list. The next fractal will appear on July 4. Until then, take care, and digress but don't egress. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ One_Froggy_Morning { ; time=1:09:42.15--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip center-mag=6.57209/0.000937142/22.6787/1/-80/-1.23\ 37353361147052e-014 params=-0.2/-1.25/-0.2/-0.8/0/0 float=y maxiter=160000 inside=0 logmap=19 periodicity=20 colors=000j85Q85h96g96fA6eA7eB7dB7c\ C8bC8aD8`D9_E9ZE9YEAXFAWFAVGBVGBUHBTHCSICRICQJDPJD\ OKDNKEMLELLEKMFKNFKNFLOFLOFLPFLPFMQFMQFMRFMRFMSFNS\ FNTFNTFNUFOUFOVFOVFOWFOWFPXFPXFPYFPYFQZFQZFQ_FR_FR\ `FR`FRaFRaGSaGSbHTbITbJUbJUbKVbLVcLWcMWcNXcNXcOYcP\ YdQZdQZdRZeS_eT_eU`eU`eV_eV_eX`fZ`f_`gaagcageahfah\ hbhjbilbimcjocjqckrcktdlvdlxemzgnzhozjpzlqzmrzoszp\ tzruztvzvwzwxzyyzxxywwxuwwtvvsuurutqtrosqnrpmrolqn\ jqmipkgojfniemhcluckfnmtakhchWahlZZZb`_eb`idamgcni\ goklpmpqpupotonrnlqmkoljnjhligkgfjfeiddhccgaaf``eZ\ _dYZcWXaWW_VUYUTWTRUSPSSOQRMOQLMPJKOIINGGLEEKCCLDC\ NEDOEDQFDRGESHEUHEVIFXJFYKG_KG`LGaMHcNHdNHfOIgPIiQ\ JjRJlSKnTLoULqVMsWNuXOwZPw`QwbRwdRxfSxhTxjUxlUxnVx\ pWyrXytYzvZzx_zz`zw_zuYzrXzoVzmUzjSzgRzePzbOz_MzYL\ zVJzSIzQGzNFzKDzHCzFAzC9yA7y75y54y32z00y00x11yA1zK\ 1zN1zQ2zT2zU2zU3zU3zU3zU4zU4zU4zU4zU0zU0 } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================

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