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Re: [Fractint] Fractal Haircut
by Franktal Gallery 02 Jul '02

02 Jul '02

For a nice fractal hair turbulence example : http://www.geocities.com/franktal2002/fb/Nn06_b.jpg Miguel >>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! > _________________________________________________________________ MSN Photos is the easiest way to share and print your photos: http://photos.msn.com/support/worldwide.aspx

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FOTD 29 June
by John Lewis 30 Jun '02

30 Jun '02

I must say Jim's algae are much better looking than the stuff that grows in my pond! John -- John Lewis, jlewis(a)clara.net on 06/30/2002

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Scienide
by Andrew Coppin 30 Jun '02

30 Jun '02

>From: Jim Muth <jamth(a)mindspring.com> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >CC: philofractal(a)lists.fractalus.com >Subject: [Fractint] FOTD 30-06-02 (Algae [7]) >Date: Sun, 30 Jun 2002 10:45:15 -0400 > >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 >} Question: what does this little critter actually do??? As far as I can tell, it iterates z = k(az^b + bz^f)+c (a strange choice of variable names, but hey...) I notice from the way the formula works that both the coefs and exponents have to be purely real. Then there's just the small matter of z0... I'm not sure, but isn't (-abgh)^j the same as the (f-b)th root of (-ab)/fd? And if so... why?!? I find it hard to belive that it just seemed like a nice expression to initialise the orbit to... Another question: when E is not a positive real integer, Z^E is multivalued. How about if E is an imaginary positive integer? Is it multivalued or single valued? Whimsical observation: Z^0.5 is double-valued; Z^0.25 has 4 values, z^0.1 has 10 values, z^0.01 has 100 values... by induction, z^0 has infinity values ;-) [of course, since the solutions to z^0.5, etc get progressively closer together, at z^0 all the infinity of solutions are THE SAME ONE: "1"] Andrew. "More scienide..." _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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FOTD 30-06-02 (Algae [7])
by Jim Muth 30 Jun '02

30 Jun '02

FOTD -- June 30, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today we rise one step out of the rating-of-six rut that we've been mired in for several weeks, all the way up to a rating of 7. The rating seems fairly accurate, considering the unusual textures created by the reference standard outside coloring method of equal iteration bands. Normally, the powers of Z between 0 and +1 do not make fractals, but by using certain tricks, fractals can be coaxed from these powers. One of my favorite methods of getting fractals where none exist is to take the difference between two non-fractal- producing expressions and multiply it by a factor sufficient to create an image. In today's case, that factor is 13. The iterated formula subtracts 13 parts of Z^0.7 from 13 parts of Z^0.75 then adds C. The resulting parent fractal is quite sensitive to its bailout radius. In fact, changing the bailout has such a great effect on today's image that I suspect the entire image might be an artifact rather than a true fractal. But artifact or not, the image is worth being included in that ever-growing list of FOTD's. Studying the image, I was reminded of something that I could not quite remember. Then it came to me. The texture of the fractal elements mimics the texture of algae growing on rocks in a swift- flowing stream not too far from Fractal Central. The name "Algae" soon followed. If the bailout radius of today's image is raised, the picture goes totally black. The image evaporates as all the points become trapped. But then the image can be restored in a new form by setting the logmap to 0 and the inside fill to something non-flat, such as bof61. The 9-minute render time is somewhat slow, but fast relief for rendering pain is available in the form of a download 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 Saturday here at Fractal Central was not perfect, but compared to how it can be in this part of the world at this time of year, it was good enough. The temperature of 88F 31C, combined with a hot sun, was warm enough for the kiddies to enjoy a splash in their back yard pools, and the humidity was not so high that the more strenuous activities engaged in by adults became unbearable. The cats spent most of the day just being cats and sleeping. As for me, I've got another curious fractal already waiting for the next appearance of the FOTD, which will be on July 2. (Starting in July, I am increasing the frequency of the FOTD to one every even-numbered day.) Until then, I've got the FOTD-CD to work on and a few fun things to do. Until July 2nd, take care, and do the things that need to be done, while ignoring the things that don't need to be done. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Algae { ; time=0:09:33.15--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.74222863652301170/+0.608902701512313\ 80/4.102563e+009/1/-125/-1.60218892474028873e-006 params=1/0.75/-1/0.7/12/1600 float=y maxiter=1500 inside=0 logmap=199 periodicity=20 colors=000f0T_0Mo0za3zQJzF_z3oz0zz0yx0ss4mo7gjCagG\ XcJS_OMVSGSVAO_4Jc0Ff0C`39XC7SJ4OS3I`0Dg09p04u06g0\ 6T66FCCL9GP6LV3PX1Tf0Yi0am0fs0jx0oz0pz0pz0ry0ry0rx\ 0sx0sv0sz0uu0uT0vs0Fg0zr0xr0xp0xp0loC`SPPo`Dom1oz0\ zz7izPyzfxvxzpzzlzzjzzjzyjyxjvxirviouijsifricrg_pg\ XogSmgPmgLfiI_jDSjALl6Fd37z00o00p00p30sCcuL3xV7ycD\ zlIzuMzvOxxOpyOjzOczOXzOQzOJzODxSApX7i_4ac1Vf0Tg3S\ i6Qi9PjAOlDMlGLmJJmLVdPfXTrOYzF`zGYyIXxITvJSuLPsLO\ rMLpMJoOGmPFlPCjQAiS7gS6fT3dT1fX3g_3ia4id4jf4li6ml\ 6mo7or7ps7rv9ry9szAuzAuzAuz7sz6sz4sz3vz0xz0zv0zp0z\ j0zf0z`0zX0z`0ucAlfLdjXXmfPppIsz0Ax0Iu0Os4Vr7`pAfo\ FmmIslLyjOziPziSzgTzgXzgYzf`zfazddzdfzdizcjzcmzaoz\ apzarz_syYuvXvsTvpSxmQyjPziMzfLzcJzdIzgFzjDzmCzpAp\ sF`vIJvM3vP6vT7vX9v_AvaCvfDviFvlGvoIvrSvmavilvdvva\ svdpvfmvgjviivjfxlcym`zoYzpXzrTzsQzuOzvMzxPzvSzuVz\ sYzs_zr_zp_zo_zo_zm_zl_zl } 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] FOTD 27-06-02 (Birth [6])
by Jim Muth 29 Jun '02

29 Jun '02

At 08:00 AM 6/29/02 EDT, Bob Carr wrote: >Are discussions about religious, political and >moral issues really needed on this fractal group >get together? It's getting to be disgusting! I agree. I also accept responsibility for this round of off-topic banter. Being in a rush, I tried to save a minute or two by sending the same letter to the two lists via a C.Copy. I should have taken the time to edit the political stuff from the version that went to the Fractint list. Such blatantly off-topic material will not be posted to this list again. The philofractal list, which thrives on frivolous debate is a different story. Jim M.

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Re: [Fractint] FOTD 27-06-02 (Birth [6])
by Genealogy1＠aol.com 29 Jun '02

29 Jun '02

Are discussions about religious, political and moral issues really needed on this fractal group get together? It's getting to be disgusting! --Bob Carr--(Ocala, FL)

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FOTD 27-06-02 (Birth [6])
by Jim Muth 27 Jun '02

27 Jun '02

FOTD -- June 27, 2002 (Rating 6) Fractal visionaries and enthusiasts: I enjoy human foolishness and today we have a lot of it. The pledge of allegiance to the flag of the U.S.A. has been declared unconstitutional because it mentions God. I suppose the Declaration of Independence and Constitution are also unconstitutional because they also mention God. And our money is also unconstitutional because 'In God We Trust' is written on it. I wonder why Atheists are so intense in their disbelief. I happen to believe in some-something that in some way fits the description of a God. But I do not become offended when Atheists tell me that I am mistaken, or deluded, or clinging to a crying-towel etc. I simply enjoy the debate, satisfied that I am right and they are wrong, while having fun seeing their futile arguments. Why then do Atheists so often become offended when believers tell them and futilely try to convince them that they are mistaken in their disbelief? Actually, as I see it, Atheism is not so much a disbelief in a god as it is a continued belief in and a defense of the philosophy of positivism, a world-view which, IMO, lost credibility about 100 years ago, and except among Atheists has been declining ever since. As to what world-view will prevail to replace it, I have no idea. But one thing is certain -- a new world-view will need to extend beyond the traditional five senses. Most of the universe is invisible to our senses even aided by the best instruments. And we do have a fractal for today. For a change, there is no quadratic midget at the center. In fact, today's image consists of the entire fractal created by the formula -0.2(Z^(-1.25)-0.2(Z^(-0.8)+(1/C). While studying the image, I had the impression of a butterfly emerging from its cocoon. I named the image "Birth". I rated it at a run-of-the-mill 6. The 11-minute render time can be avoided by downloading the completed GIF file 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 Wednesday here at Fractal Central was hot. In fact, it was the hottest day of the young summer. The temperature of 99F 37C and high humidity kept the cats confined to the shade of the porch and the fractalist confined to the coolness of the air-conditioning. Late in the afternoon a shower threatened, but died out before reaching Fractal Central. Today promises to be a repeat of yesterday, and the cats are already in their lazy mode. As for me, I've got work to do. As long as the air cooler keeps working, I'll be fine. Until next time on the 30th, take care, and see you then. Jim Muth jamth(a)mindspring.com START 20.0 PAR-FORMULA FILE================================ Birth { ; time=0:11:53.49--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-53.5822/78.0626/0.003628592/1/-112.5/-\ 3.77822773067748585e-014 params=-0.2/-1.25/-0.2/-0\ .8/0/0 float=y maxiter=12000 inside=0 logmap=yes periodicity=20 colors=000zzzzzxzwxzfvzatzZtzXrzVpz\ TnzRnzPlzNlzLjzJjzHfyFgxDdwBfxBbu9dt9`s7ap7`p7`n5Z\ m5Zj5Zj3Zh3Zh1Zd1Xe1Xb0Xb0XZ0X_0VX0VX0VU0VU0VR0VR0\ TR0TN0TM0TJ0TH0TF0RD0RD0RB0R90R70P70P50P30P10P10P0\ 0N00N00N00N00N00L00L00L00L00L00L00J00J00J00J00J00J\ 00H00H00F00F00F00D00D00D00B00B00B00900900900700700\ 50050050030030030010010010000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00300500900B01F05H09L0BN0FR0HT0LX0NZ0Rb0Vd0Xh0`j0b\ n0fp0ht0lv0pz0rz0vz0xz0zz0zz5tz9jzD`vHTrHVrJVrJXrJ\ XpLXpLZpLZpN`nN`nP`nP_nPYlRWlRUhQScRQZSOUTMPULKVJF\ dB1l50n70p90p90rB0rD1tD3tF5vH9vHBxJDxLHzLJzNLzPNzP\ RzRTzTVzTZzV`zXbzXdzZhz`jz`lzbpzdrzdtzfvzhzzhzzjzz\ lzzlzznzzpzzpzzrzztzzrzztzztzztzztzztzzvzzvzzvzzvz\ zvzzvzzxzzxzzxzzxzzxzzxzzzzzzzzzzzzxzzxzzvzztzztzz\ rzzpzzpzznzzlzzlzzjzzjzzhzzfzzfzzdzzbzzb } 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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Off-topic?
by John Wilson 27 Jun '02

27 Jun '02

Do our fractal lists not have any "off-topic" rule? Who cares about U.S. oaths, other than a few Americans? John W.

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Re: [Fractint] JuhYhgtFFe2
by Mark Christenson 25 Jun '02

25 Jun '02

At 05:00 PM 6/25/02 +1200, MLO wrote: >... >Morgan L. Owens >"And JuhYhgtFFe2 to you to! In fact, FuhhDCekGhgh43p as well! And the horse >you rode in on!" Reminds me of an absolutely hilarious bit Phil HNarFFtmanZ did on Letterman years ago. Egg Latin - including several completely filthy examples, the least offensive of which was "eggassheggole." Ahola, Bud

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Re: [Fractint] JuhYhgtFFe2
by Andrew Coppin 24 Jun '02

24 Jun '02

Ah, Mr. Lee, concise as ever! Andrew. "I read a lot of math litriture, but don't know much about it!" >From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com >Subject: Re: [Fractint] JuhYhgtFFe2 >Date: Mon, 24 Jun 2002 04:39:03 -0500 > >corollary (kôr´e-lèr-ê, kòr´-) noun > plural corollaries > Abbr. corol. > 1. A proposition that follows with little or no proof > required from one already proven. > 2. A deduction or an inference. > 3. A natural consequence or effect; a result. > >lemma (lèm´e) noun > plural lemmas or lemmata (lèm´e-te) > 1. A subsidiary proposition assumed to be valid and used to > demonstrate a principal proposition. > 2. A theme, an argument, or a subject indicated in a title. > 3. A word or phrase treated in a glossary or similar listing. _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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