August 2003 - Fractint - mailman.xmission.com

Re: [Fractint] Sucess
by nick.grasso＠hrads.com 04 Aug '03

04 Aug '03

Andrew Coppin wrote: >>>For several months I have been utterly unable to sent messages to this list... I have now discovered the cause of this devistating problem: I typed the address wrong in my address book. (Even that is not beyond doubt - there was a single letter missing. It may simply be that I have a malfunctioning keyboard!)<<< Welcome back Andrew, but you (or your keyboard) also dropped a single letter from 'success' ;o) Sorry, I couldn't resist that. Nick

1 0

FOTD 04-08-03 (Cosine-Square [6])
by Jim Muth 04 Aug '03

04 Aug '03

FOTD -- August 04, 2003 (Rating 6) Fractal visionaries and enthusiasts: A number of years ago, a local auto dealer ran a series of ads proclaiming that nobody has better cars and nobody sells them for less. The ads worked great until a second auto dealer started calling himself Mr. Nobody. and took advantage of the first dealer's advertising. The clever second dealer won the day by making something of nothing. Today's image, which was created by the Mystic2 formula, consists entirely of blank inside space, which in traditional fractal rendering is nothing. But that nothing has been turned into something by the bof61 inside fill. Like that clever auto dealer, (and true mystics), I have turned nothing into something. I named the image "Cosine-Square" simply because those two functions are used in its creation. It is an unusually complex image for one that consists only of inside stuff. The 4-way symmetry almost gives the impression that a Mandelbrot midget lies at the center. But don't bother looking. At a slightly deeper level, the apparent 4-8-16-way symmetry breaks down into an awkward figure with 13 lobes, and then the entire image goes flat blank. Considering the image's assets and faults, I decided that a rating of 6 would be best for it. Its chief asset is the render time, which is only a bit over one minute. One of its faults is the color palette, which uses only a few of the 256 available GIF colors, and gives a rather muddy overall effect. As always, those who choose not to render may pick up the finished GIF image at 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> Sunday turned questionable in a hurry. The temperature reached only 83F 28C, but just after noon a series of thunder-showers moved in. The rain was not unusually heavy, but it persisted until sunset, and was enough to keep the fractal cats confined to the indoors, sulking about their confinement and skittish about the prolonged rumbling. The evening treat of tuna eased their nerves and disappointment. Today is starting even worse than Sunday. It's raining already. As a result, I expect another sulky cat day. Between showers, I'll accomplish a few other tasks and find a few fractals, one of which will appear as the next FOTD. Until 24 hours from now, take care, and don't get caught in a square cosine. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Cosine-Square { ; time=0:01:20.53--SF5 on a p200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=cos passes=1 center-mag=0/0/8.226655 params=-6.3/9.2/-3.4/-1.4\ /-7.1/6.2 float=y maxiter=95 inside=bof61 logmap=yes periodicity=10 colors=000UoroMGgaZ7F5HSLRU`iAzfLwdWuafrzzzXcmcmkw\ clcpzcvBJNBSbW7KXHWcAAjChrKkqSnpMX_Tgh_3icrGbqQaqZ\ `qgSlZVndYpjIvfooUgpeklmeooVSvXZtYdsZkq84iSvJVtVYr\ eLYjTgmsY8ldNeka3Lir`2meFhiScmd8kSMnda`AfsHMULTe`m\ WhfflwBmqMnkXoegpr4PhTbv0ZcknOPRUccdkZangFhcadJQ8z\ VVu5nNLpaPguTksXnq60sEErLRqTdpXUmZeo7Iaus8mrNfqapa\ LkeTgi`cmhx6NqIVkUaeeiU0zXRuXZ9YeOZkbl_KfdQciZamgY\ m7ZoU7ZwHetRkrvnIpoRjp_dqhB5eKMiSamDuILsUTreXmSZod\ IGPOTZUegO4fRHiUTkXenmRRfdcUYMXgahRIYMoZUpZap_ipq`\ vTq7hd459488XMVf_wk_tnSW6WfUTUuOmDRnNUoXXpfNWgRajU\ flXlnV9xXLvYWtZfr7_FFdPMhYTmgG_3NeKUk`oAiiPldcnmlC\ DWJJP2FREBTQ8VaDcfIlkei8SbFEXMOZRX_Wfa`oberUitMmvE\ q_VcDjQJmTPpVVsY_u_t8Yz_wsdulhsemqFBcQXjhADIJYNSbR\ `gWilawD`tXohtikrdnqje6ghIdkUanesV0aOE`bYG38LGKQTV\ VeeNdWRhaUkfXnk_yD_vR_scnq`iqfdqkzrMs_bndfihidmmYE\ rZSq_dpm9ZhOdcbj9hyGkvNmt } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

1 0

Sucess
by Andrew Coppin 03 Aug '03

03 Aug '03

Hi folks. For several months I have been utterly unable to sent messages to this list... I have now discovered the cause of this devistating problem: I typed the address wrong in my address book. (Even that is not beyond doubt - there was a single letter missing. It may simply be that I have a malfunctioning keyboard!) But anyway... I'm back! Yay!! I've just been doing some stuff with the good old cubic function f(z) = z^3 - 3(a^2)z + b. This formula has (IIRC) several critical points, but all bar 2 of them are always within the basin of attraction to infinity. (Corrections, anyone?) The two that (sometimes) aren't are +A and -A. (If I'm not mistaken, 0 is NOT critical for this mapping...) Now, the cubic Mandelbrot is defined as being the set of points (A, B) for which for orbits of Z[0] = +A *and* Z[0] = -A remain bounded. (Compare the classic quadratic Mandelbrot: this is the set of all C such that Z[0] = 0 remains bounded.) Thus, the set M+ is defined as the set of (A, B) for which Z[0] = +A remains bounded, and M- is defined as the set of (A, B) for which Z[0] = -A remains bounded. (I have a feeling the two sets are mirror images or something... not entirely sure.) Then the M set itself is simply the intersection of M- and M+. (Try telling that to fractint!!!) I've got a number of formulas that attempt to draw the cubic M, but none of them seem to work entirely properly. They do, however, draw some rather fabulouse images! Of course, having to navigate a 4-dimensional M set that is really the intersection of the mirror-image M+ and M- sets (which, therefore, are also 4-D) is somewhat confusing to say the least! But the results are well worth it... Out of interest, I would rather like to know 1) if the statements I've made thus far are actually correct, 2) what the "generalised form" for a 4th order polynomial looks like... Hey - keep fractalling ;-) Thanks. Andrew. PS. I've heard it said that z^3 - 3(a^2)z + b is more complex than needed, and z^3 + az + b will work. My reason for using the former is that it draws a much nicer image. (Oh, and finding the critical points is easier ;-)

1 0

FOTD 03-08-03 (Fractal Explosion [7])
by Jim Muth 03 Aug '03

03 Aug '03

FOTD -- August 03, 2003 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal image comes on with a bang. Or at least it appears to. It is another of those 'anything can happen' images produced by my little-used 'Mystic2' formula. Curiously enough, in today's image, the function that produces the best picture is the function with an error in it -- the 'cosxx' function. Since the image consists entirely of 'inside' material, an active inside fill is needed to reveal the details. Today's image uses the 'bof61' inside fill, though several other fills work almost as well. When I saw the explosive nature of the image, I immediately named it "Fractal Explosion". I rather like the image, so I rated it a 7. The render time of 4 minutes 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> But when downloading, be cautious. I have seen a report that the version of Fractint that Scott is using might draw incorrect images with the 'Mystic2' formula, which creates images that consist entirely of inside fill. If so, this is an unusual situation. Scott's images are almost always correct. Saturday was warm and muggy enough. The temperature reached 86F 30C, but it did not rain, and the cats had an enjoyable several hours in the yard. Today is starting exactly the same, so there is no reason to expect anything other than happy cats. For me, it's a lazy day. I think I'll simply read some thought- provoking articles in the magazines piled on the shelf, and see if I can provoke some thoughts. Later, I'll turn to fractals. Until next time, which will be in 24 hours, take care, and think deep thoughts. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Explosion { ; time=0:04:27.60--SF5 on a P200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=cosxx passes=1 center-mag=+0.00401393777775/-0.9968332050329/347.\ 2512 params=1.1/3.6/2.6/-3.1/-0.6/-0.4 float=y maxiter=100 inside=bof61 logmap=yes periodicity=10 colors=000DEABC8000NqTMnRLlQKjPJhOJeNR7MVRLQMJGXIF\ VHETGDRFDOECMDBKBAIAAF99D88B7796ObuSZtWVq`RndNkhJh\ lFeWouXqpYrkZse_t``uVavQekPi`OlQOaZNSgMIpMJqRKqVLq\ ZMrcNrgOrkOroQpmSnlUlkVmgWmcXm_YmWZmS_mOWjSThVQfZN\ daKadH_hEYkBWnAgbAsRAzGIuIPkJWaLbSM`QVZOcXMlVKuUIu\ zwurvqjvkcueWuZOtTHtNLnTOiZSdcVZiZUnaPtdKuaZd_lLYi\ KWfJUcIS`HQZFOWEMTDKQCINBGLAEI9CF87FIAC7896zTmxQhq\ OcjLZcJUYGPREKKBFD9ApuudhhUWWIJIDu9Cn8Bh8Aa7AW79Q6\ 8J67D5RlsOfkL`dIVYFPQCJJ9DCsugnocij_deW_`SVWOQRKLM\ GGHCBC8veirben_bjX_fVXbSUZPRVNNRKKNHHJFEFCBB98GeVE\ _QDUMBOIAID8C9jaSg_QeYPcWOaVMZTLXRKVPJTOHRMGOKFMJD\ KHCIFBFDADC8BA7986V_rUYoTXmSWkRViQTgPSeORcNQaMP_LN\ YKMWJLUIKRHJPGHNFGLEFJDEHCDFBBDAAB999887z`uyZqvXnr\ VkoThkSehQbdO_aMXYLTVJQRHNOFKKEHHCEDABA88Vq9Pe8JU7\ DI6VzHRpFNgDJZBFP9BG7nwgkteiqcgoael_cjYagW_eVYbTW`\ RUYPRWNPTLNRJLOIJMGHJEFHC } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

2 1

Re: Correction! etc.
by JackOTradez 03 Aug '03

03 Aug '03

Whomever may be affected: In last post I mentioned Russ Walsmith was making an error in his PAR file posts. Wrong! The error is mine! Russ - there is nothing wrong. Don't change anything! I confused a couple things myself and typed before I thought about it. Sorry ... <sg> As for Golden Ratio - anyone who has downloaded / used any of my programs (like the Fractint Animators) might notice that they open up in a window with the Golden Ratio. Actually, noone has noticed it yet. It is the ratio of adjacent Fibonacci numbers as the sequence is taken to infinity. Or, as the Ancients knew, it simply looks cool. The rectangle is not "too fat" or "too long" etc., it looks "Just Right". The Nautibrot4 animation is posted on my web site now (shortened version); the full viddie is over 400 MEG! The Cornucopia animation is almost done - it is way cool, the best of them yet. JoTz

1 0

Re: [Fractint] Re: L'Escargot
by Russell Walsmith 02 Aug '03

02 Aug '03

-- --------- Original Message --------- DATE: Thu, 31 Jul 2003 14:07:21 From: "JackOTradez" <JackOTradez(a)email.msn.com> To: <fractint(a)mailman.xmission.com> Cc: > >BTW, I have just animated the L'Escargot (Nautibrot4) over 3000 frames at >1024x768, set to the tune "Green Onions", by Booker-T & MG's (anyone >remember that one?). In-f'n-credible! Yeah, that's a cool tune. Green Onions and L'Escargot... sounds savory, I gotta check it out. Let me know what I can do to expedite acquiring a copy. Thanx. > >Russ - you are not posting your files correctly. Those (like me) who know >the rite way can fix it, but others may have a problem, and will not see >your fantastic images. > >In the PAR, there is a line like "formulafile=next.frm". It is wrong. >Instead of "next" you should have the name of the specific formula, in this >case "Nautibrot4". Ok, I'll try it, but I think it's maybe more complicated than that. E.g., the guys who post a lot of pars (J.M., L.S., A.N. ...) use all sorts of filename assignments, and I gathered from that that it's arbitrary. What might have gone wrong is that I changed the assignment AFTER saving the par; as I now recall from earlier experience, that's a no-no. > >These images are incredible - how do you find these things??? Hey, I'm glad you like them. These formulas are so rich that finding compelling images is no problem. In fact, it's probably more difficult to find parameter values that DON'T make nice graphics. For example, consider the par below (which I will also repost as per your suggestion); ---------------------------StartParfile--------------------------- La_Tropicana { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls4.frm formulaname=Nautibrot6 function=ident passes=3 center-mag=0.0996911/0.234681/1.103753 params=1.618033989/1.618033989/1/0 float=y maxiter=200 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } -----------------------------EndParfile--------------------------- This is about as basic as it gets, save that p1 is complex with the phi constant in both the real and imag values... So there's lots of bang for the buck in this par, and it takes off from there. Since at this point it's all new, images essentially find themselves in this context. The larger question then is, "How do I find the formulas?" Well, they find themselves too. It all started years ago when I was trying to figure out to play 5-string banjo... I was pretty agressive sometimes in pestering the accomplished pickers for the logic behind the long cascades of notes that seemed to spill effortlessly from their instruments. Musicians, btw, were a subset of a greater artistic community that included writers, painters, sculptors and etc., and hell, I wasn't proud; I'd pick anyone's brain if I thought it would afford me some insights into the creative process. And it was all very maddening, because the more accomplished the artist, the more likely they were to tell me, "Logic? I don't need no stinkin' logic, man..." It took me a while to recognize the limits of logical processes, but once I did, I was able to also perceive the value of balancing the mind with the intuition. Ever since, Virtually everything becomes progressively easier as I attend to that focus, and I expect that even posting par files will be a piece of cake pretty soon... > >I will now try to animate Cornucopia; me and ((( 5^(1/2)) + 1) / 2 ) >"Golden Ratio" go back a long way . . .. ... ..... ........ I'd like to hear sometime about the contexts in which you've explored the GR. As for Cornucopia, that looks like a tough'n to animate, but good luck! I'm not now as infatuated with that image as I was a few days ago... I've just discovered a new one, and I think I'm in love... ---------------------------StartParfile--------------------------- Las_Conchitas { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=dcls4.frm formulaname=Nautibroid function=conj/cabs passes=3 center-mag=-0.899316/0.230079/0.4862158 params=5/1/3/1/-1/0 float=y maxiter=1000 colors=653xwulHICXNwuIDCTjCRATl653xwulHICXNwuIDCTjCRATlccc<238>c\ cc } -----------------------------EndParfile--------------------------- Isn't she pretty? I am enthralled with the graceful lines of this image and the exquisite necklace of shells from whence is taken the name. The formula 'Nautibroid' incorporates the 'Dynamic Coefficients' concept into nautibrot6. (This idea is explored more extensively at http://fibonacci-arrays.com) ---------------------------StartFrmfile--------------------------- frm:Nautibroid {; by Russ Walsmith z = 0, c = pixel, k=1, j=p3: j=p3*j k=p1*fn1(k)*j z = z^k + c j=p3*j k=p2*fn2(k)*j z = z^k + c z < 1000 } frm:Nautibrot6 {; by Russ Walsmith z = 0, c = pixel, k=1, j=p2: j=p2*j k=p1*fn1(k)*j z = z^k + c z < 1000 } -----------------------------EndFrmfile--------------------------- Still Amazed, Russell Alternate parfile versions: ---------------------------StartParfile--------------------------- La_Tropicana { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=Nautibrot6.frm formulaname=Nautibrot6 function=ident passes=3 center-mag=0.0996911/0.234681/1.103753 params=1.618033989/1.618033989/1/0 float=y maxiter=200 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } Las_Conchitas { ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=Nautibroid.frm formulaname=Nautibroid function=conj/cabs passes=3 center-mag=-0.899316/0.230079/0.4862158 params=5/1/3/1/-1/0 float=y maxiter=1000 colors=653xwulHICXNwuIDCTjCRATl653xwulHICXNwuIDCTjCRATlccc<238>c\ cc } -----------------------------EndParfile---------------------------

1 0

Re: FOTD 02-08-03 (Neo-Fractal [5])
by Paul N. Lee 02 Aug '03

02 Aug '03

Lee H. Skinner wrote: > > The FOTD pictured on S.D. Boyd's website > today is very different from the image > generated by Jim's par! > Yes, I noticed that as well. I do not remember this happening since the first few weeks when Scott first started hosting Jim's FOTD. Do not recall what caused the problem then, and how it was resolved, but maybe I can look back on some old postings to see if there was an explanation. Sincerely, P.N.L. ------------------------------------------------- http://home.att.net/~Paul.N.Lee/PNL_Fractals.html http://www.Nahee.com/Fractals/

2 1

Shear Amazement
by Russell Walsmith 02 Aug '03

02 Aug '03

In a recent perusal of Bradley Beacham's "AN INTRODUCTION TO THE FRACTINT FORMULA PARSER" (the FRMTUTOR.TXT file in Fractint) I came across the 'fibo-A' formula. This .frm introduces Fibonacci-type recursions to the Mset formula, and it inspired me to investigate this idea further. I thus came up with the 'Fibrot' formula, presented (in a generalized version) below: ------------------------------parfile----------------------------- Nautiloid { ; July 23, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Fibrot1 passes=3 center-mag=-6.42033/2.44459/0.04984424 params=-5/-1/1/0 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } ------------------------------frmfile----------------------------- frm:Fibrot1 { z = 0, c = pixel, j=0, k=1: a = p2*j + p1*k j = k k = a z = z^k + c z < 1000 } -------------------------------endpar----------------------------- Soon thereafter, Jack O'TradeZ used this .frm to render the 'Mosaic' viddie now playing at: http://www.sonic.net/~jot/ufvp.html Both the 'stills' and the video demonstrate that complex parameter values in 'Fibrot' induce a shear factor along the real axis that warps circular shapes into nautiloids. It occurred to me that a variant formula might give more insight into this effect, and this led to a series of 'Nautibrot' formulas, some of which are presented below: ------------------------------parfile----------------------------- Nautilii { ; July 23, '03 ; Version 2002 Patchlevel 5 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Nautibrot2 passes=3 center-mag=-6.84262/0/0.04783259 params=5/1 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } ------------------------------frmfile----------------------------- frm:Nautibrot2 { z = 0, c = pixel, k=1, j=-1: j=j*(-1) k=p1*k*j z = z^k + c z < 1000 } -------------------------------endpar----------------------------- Another variant introduces i-axis shear: ------------------------------parfile----------------------------- ShearMadness { ; July 23, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Nautibrot3 passes=3 center-mag=0/0/0.6666667 params=-1/1 float=y maxiter=300 colors=00000j0j0jj0j00j0j0jjkkkkrkdmwW000W0WW000WW0W0WWFNF<4>rNF\ zNFFVF<4>rVFzVFFbF<4>rbFzbFFjF<4>rjFzjFFrF<4>rrFzrFFzF<4>rzFzzFF\ FN<4>rFNzFNFNN<4>rNNzNNFVN<4>rVNzVNFbN<4>rbNzbNFjN<4>rjNzjNFrN<4\ >rrNzrNFzN<4>rzNzzNFFV<4>rFVzFVFNV<4>rNVzNVFVV<4>rVVzVVFbV<4>rbV\ zbVFjV<4>rjVzjVFrV<4>rrVzrVFzV<4>rzVzzVFFb<4>rFbzFbFNb<4>rNbzNbF\ Vb<4>rVbzVbFbb<4>rbbzbbFjb<4>rjbzjbFrb<4>rrbzrbFzb<4>rzbzzbFFj<4\ >rFjzFjFNj<4>rNjzNjFVj<4>rVjzVjFbj<4>rbjzbjFjj<4>rjjzjjFrj<4>rrj\ zywccdWWWz000z0zz000zz0z0zzzzz } ------------------------------frmfile----------------------------- frm:Nautibrot3 { z = 0, c = pixel, k=1: k=p1*conj(k) z = z^k + c z < 1000 } -------------------------------endpar----------------------------- Finally, in these "Not-a-Brot" calculations, 2 + 3 = 4: ------------------------------parfile----------------------------- L'escagot { ; July 23, '03 ; Version 2002 Patchlevel 5 reset=2002 type=formula formulafile=next.frm formulaname=Nautibrot4 passes=3 center-mag=-0.58651/0.281617/0.6666667 params=4/1 float=y maxiter=300 colors=000z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0\ zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc\ 00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000zk0kW0Wc00z00zW0zj00W000\ zk0kW0W } ------------------------------frmfile----------------------------- frm:Nautibrot4 { z = 0, c = pixel, k=1, j=-1: j=j*(-1) k=p1*conj(k)*j z = z^k + c z < 1000 } -------------------------------endpar----------------------------- A generalized nautibrot is: ------------------------------frmfile----------------------------- Nautibrot5 { z = 0, c = pixel, k=p2: k=p1*fn1(k) z = z^k + c z < 1000 } -------------------------------endpar----------------------------- That's about the gist of it... I suspect that these efforts haven't been all for 'naut', for there are perhaps many other patterns that will emerge in this context. I hope that list members will find something of interest here, but hey, it got me all in a state of sheer amazement and that's the bottom line... Ciao, Russell (PS: I think I have this .par file thing down, but if they fail to render correctly,lemme know.)

2 1

FOTD 02-08-03 (Neo-Fractal [5])
by Jim Muth 02 Aug '03

02 Aug '03

FOTD -- August 02, 2003 (Rating 5) Fractal visionaries and enthusiasts: This discussion will have to be brief. We have unexpected work waiting to be done here at F.C. and a customer who wants his job before he brings in the material. Some fractals simply defy logic. Today's image, which was created by the 'Mystic2' formula, is one of these. It has more themes than a Mexican TV-novella, any one of which could have served as the basis for a fractal. (Any theme, that is. I don't think I've ever seen a fractal based on a soap-opera.) There is so much that could be discussed in today's image that discussion is nearly useless. The only thing to do is to study the image, sit back and mutter, "Oh my!". The image is so mixed up in fact that it almost appears to have been constructed by hand from many different fractals. The image certainly is something new, which is why I named it "Neo-Fractal". I think that the mixture of unrelated themes actually goes too far, and this holds the rating to an average 5. The render time of 4 minutes can be avoided by downloading the finished image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> Friday was cloudy and exceptionally humid here at Fractal Central. The temperature of 81F 27C was fair enough, but a two-hour period of light rain in the afternoon spoiled the cats' day in the yard. A treat of tuna was needed to restore their good moods. Today promises to be more of the same. I expect the same response from the dynamic duo. In 24 hours I shall return with the next fractal. Until then, take care, and when searching for truth, be sure you recognize it when you find it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Neo-Fractal { ; time=0:04:20.02--SF5 on a P200 reset=2002 type=formula formulafile=jim.frm formulaname=Mystic2 function=cos passes=1 center-mag=-0.001194479/-0.968563902/222.9189/1/22\ .5/8.944234242e-014 params=4.18/3.94/3.99/-4.27/2.\ 37/-2.66 float=y maxiter=95 inside=bof61 logmap=yes periodicity=0 colors=000mNWoSTqWPs_LudIwhEylBpeAhZ\ AXRuSKAKGALIAYUASPAVSAXVAWYEW_IWbMWdQVgUViXVk`VndU\ phUslUupUwsVrtVmtWhtWctXZtXVtXQuYLuYGuZBuZ6uZ2uY7s\ YCqXHoXMnXRlWVjW_hWdgVieVncVrbZq_apYdoWgoTjnRnmPqm\ MtlKwkIzkGwfHtbHqYHnUIkPIhLIeGJbCJ_8J`8Ib8Hc8He8Gf\ 8Fg8FdBHbDJ`FLZIMXKOVMQTPSRRTPTVNWXLYZJ__HbaFdcDfe\ BhfAdcA``AYZAUWAQT9NR9JO9FL9CJ98G95E88H7BK7DN6GP6J\ S5LV5OX4Q_3Tb3Wd2Yg2`j1cl1eo0hr0jt1kq1kn1ll1li2mf2\ md2na2n_3oX3oU3pS3pP4qM4qK4rH4rF6nH7jI9fJAbKC_LDWM\ FSNGOOIKPJHQLDRM9SO5TP2ULJQHZMM_JQ`GRZGSYGTXGTVGUU\ GVTGWRGWQGXPGYNGZMGZLG_JG`IGaHGaGGbHHcHIdIJdIKeJLf\ JMfKNgKOhKPhLQiLRjMSjMTkNUlNVlNWhQYeS_aUaZXbWZdS`f\ PbgMeiIgkFimCln8np5pr2rs3no3kl3hi3ef3bc3Z`3WY3TV3Q\ S3NP3JM3GJ3DG3AD37A347768A89D99GBAJDANEBQGBTHCWJDZ\ LDbMEeOEhQFkRFnTGqUGmVIjVJgVKcVL`VMYVNVVORVPOVQLVR\ IVSNTVSQYXO`aLceJfQA_B1TI7UODVUIV_OWkJ_ } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END 20.0 PAR-FORMULA FILE==================================

1 0

Re: L'Escargot
by JackOTradez 02 Aug '03

02 Aug '03

Yea - I figured the typo. It does look like a snail. Those weird people across the pond actually eat the disgusting things - raw! BTW, I have just animated the L'Escargot (Nautibrot4) over 3000 frames at 1024x768, set to the tune "Green Onions", by Booker-T & MG's (anyone remember that one?). In-f'n-credible! Russ - you are not posting your files correctly. Those (like me) who know the rite way can fix it, but others may have a problem, and will not see your fantastic images. In the PAR, there is a line like "formulafile=next.frm". It is wrong. Instead of "next" you should have the name of the specific formula, in this case "Nautibrot4". These images are incredible - how do you find these things??? I will now try to animate Cornucopia; me and ((( 5^(1/2)) + 1) / 2 ) "Golden Ratio" go back a long way . . .. ... ..... ........ Stay Amazed, JoTz

2 1