From: owner-fractint-digest@lists.xmission.com (fractint-digest) To: fractint-digest@lists.xmission.com Subject: fractint-digest V1 #580 Reply-To: fractint-digest Sender: owner-fractint-digest@lists.xmission.com Errors-To: owner-fractint-digest@lists.xmission.com Precedence: bulk fractint-digest Thursday, July 5 2001 Volume 01 : Number 580 ---------------------------------------------------------------------- Date: Sun, 1 Jul 2001 10:22:46 -0400 (EDT) From: Jim Muth Subject: (fractint) C-FOTD 01-07-01 (Pac-Man Strikes Again [6]) Classic FOTD -- July 01, 2001 (Rating 6) Fractal visionaries and enthusiasts: Who can forget Pac-Man? It was one of the first computer games. In the game, a yellow ball with a big mouth ran through a maze, gobbling up energy pills and avoiding ghosts, except when the ghosts became vulnerable. I assumed I'd seen the last of the yellow fellow a few years ago, but what should show up on my screen today but a Pac-Man. Well, actually it's not a Pac-Man but rather a mis-shapen midget in the Z^(sqrt2)+C fractal. If the midget were black, I might have seen Marvin the Martian when I studied it, but it is yellow, so "Pac-Man" it is. Yes, I realize that Pac-Man's mouth is too small, and he actually seems to be drowning, but it is Pac-Man at the center of today's image. There is no doubt of that I named the picture "Pac-Man Strikes Again". Just when we assumed the little gobbler was gone for good, he shows up to annoy us again. With the outside set to the normal , the image is all right, but just average. The setting of makes the image just striking enough to qualify as the first FOTD for the month of July. The image has been rated at a 6 -- slightly above average. But this rating is true for the 640x480 resolution. At a higher resolution the bands become better defined, and the rating jumps to a 7. The render time of the parameter file is a relatively slow 29 minutes and 14 seconds on a 200mhz Pentium at 640x480. As is always the case, the GIF image will soon be available on the internet at: and at: The fractal weather today was hazy, hot and humid, with a temperature of 96F (35.5C) and a noisy thunder-storm with heavy rain in the evening. The cats took it easy in the yard all afternoon and hid themselves when the storm came up. It's now time to enjoy (if possible) a relaxing Sunday. But I'll return at the usual time with another fractal to awe and inspire. Until then, take care, and fractals are more fun than a barrel of Pac-Men. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ PacManStrikesAgain { ; time=0:29:12.18--SF5 on a P200 reset=2001 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.28719980382691/-0.683275948032916/71\ 42.408/1/-37.5 params=1.414213562373/0/-4/0 float=y maxiter=12000 inside=255 outside=tdis periodicity=9 colors=000GnYFmaEleEkhDjlCipBhsAgwAgzFfvJesNepRdmV\ cjZcg`_bbWZdSVfPQhLMjHIkEEiHDhKCgNBfQAeT9dW9bZ8aa7\ `d6_g5Zj4Ym4Ue5RY6NQ7KJ8MKANLCOLDPMFQNHRNISOKTOMUP\ NVQPWQRYRSZRU_SW`TXaTZbU`cUadVceWefWfgXhhXigWggWeg\ WdgWbgWagW_gWZgWXgWWgWUgWTgWRgWQfTTeQVeNXdLZdI`cFb\ cDd`BYY9SV7LS5FQ49S6AU8AW9AYBA_CBaEBcFBeHBgICiKCkL\ CmNCoODqQDsRDuTDwUDxXGx_IybKyeMyhPzkRznTzqVfe`NVf3\ KlEOcOSVYWNg_Eqb6n`Ak_EiZIfYMcWQaVUZUYWTaUReRQiOPm\ MOqTNg_MZfLQmKHsK8mMBgNDaOFWQHQRJKSLFTNFSMGSMGSLHR\ LHRKIRJIQJJQIJQIKPHKPHLPGLOGMOFNSCMOFLKHKGJHANKDLN\ FJQHHUP9TJGSENR8UJTAR3`P8cNCeLGhKKjIOmGSoFWrD_tBcw\ AgyCevEdtGbrIapK`nMZkOYiQXgSVeTUcVT`XRZZQX`PVbNTdM\ QfLOhJMjIKkHI97gA8fB9fCAeDBeECdFDdGEdHFcIGcJHbKIbJ\ FdLIbNK`PMZROYTQWVSUXUSZWR_YPa_NcaMecKgeIigGkiFmkD\ omBvt8poAkkBefC`bDWZEQUFLQGEKHGMHHNHJOHKPHLQHNRHOS\ HPTHRUHSVHTWHJrKJqNIpRzr0 } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z| Subject: (fractint) C-FOTD 03-07-01 (The Smallest Midget [7]) Classic FOTD -- July 03, 2001 (Rating 7) Fractal visionaries and enthusiasts: The FOTD for July 2, which, due to a power failure, was finished too late to be the FOTD for July 2, now appears as the FOTD for July 3. I named the picture "The Smallest Midget", not to be confused with "The Littlest Angel". The 'smallest' in the name refers not to the size of the midget, but to the exponent of Z in the formula that drew the midget. With an exponent of only 1.15, the function of today's fractal is perilously close to being linear, and linear functions do not produce fractals. But thanks to the 'Branch Cut' formula, we can go as far out the logarithmic spiral as necessary to find an interesting section of the infinite fractal, which seems to expand and become ever more detailed the farther out we travel. In today's case, we travel out 320 turns, to where the parent fractal resembles nothing as much as an egg with just about the longest tail ever seen. Today's midget lies about halfway out that mammoth tail, and finding it was no easy task. The shape of the midget quite accurately reflects the shape of the parent fractal, humungous tail and all. The excessive maxiter is necessary to fully define the midget, which at a lower maxiter has sections where the surrounding chaos appears to blend smoothly into the midget rather than form a well- defined sharp edge. I colored the inside of the midget a brilliant white instead of the normal black. This way the midget reminds me of the candles that kept Fractal Central illuminated last night when the entire area was blacked out. The stream of chaos trailing from the midget could almost be taken for the column of heat rising from a candle flame. I rated the picture at a 7. The picture is worth it considering the extra attention I gave to its coloring. And with a render time of 11 minutes, running the parameter file does not try one's patience beyond endurance. Of course, the GIF image will soon be available on the internet at: and: But give Paul and Scott a chance to post the image before visiting. The fractal weather today was as good as it gets around here, with the bluest skies and a temperature of 72F (22C). These conditions made the fractal cats happy, much in contrast to yesterday, when a violent thunder-storm struck in the evening, with winds of near 120kph, torrential rain, continuous lightning and even a scattering of hailstones. When the wind and thunder finally died down, the cats didn't show themselves for over an hour. Luckily, it was a Sunday, with little computer work to be done when the power failed. It's now Monday evening however -- time to give the cats their end-of-day snack and shut down the fractal place until tomorrow. Until then, take care, and weather is supposed to be chaotic and even fractal in nature, but I saw no fractal midgets in yesterday's storm. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ TheSmallest_Midget { ; time=0:11:01.14--SF5 on a P200 reset=2001 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=-12.88324182229829000/-10.9467020423215\ 4000/4045361/1/150 params=1.15/0/320/800 float=y maxiter=75000 inside=255 logmap=94 periodicity=10 colors=000K0AK0AK0AK0AK0AK0AK0AK0AK0AK4AK7AKBAKEAL\ IAOLARPAUSAXVA_ZAbaAeeAhhAklAnoAqrApm9pi8pd8p`7pX7\ pS6pO5pJ5pF4pB4lC8iDCfDFbEJ_FMXFQUGTQHXNH_KIcHJfDJ\ jAKm7Lq4LtKOq_RnbUkd_hUdeJjb8g`JfrTlzPqwLqwIqrJccK\ _ULXKLUBKTBJRBIQBHOBGNAFMAEKADJACHABGAAFA9DA58A8CA\ 7AA69AgoCcmB_kBWiBVgBVeBUcBTaBS_BRYBRWBQUBPSBOQBNP\ BNOBMOBLNBKMBKMBJLAIKAHJAGJAGIAFHAEGADGACFACEABDAA\ DA9CA8BA8AA7AA6FA5KATPKSUUSZcR_iRZnQZnQYmQYlPZkP_k\ O`jOaiObhNchNdgMefMfeMgeLhdLicKjbKkaKlaJm`Jm_InZIn\ ZIoYHoXHpWGpWGqVFqUFrTFrTEsSEsRDtQDtQDuPCuOCvNBvMB\ wMBwLAxKAxJ9yJ9yI9zHAzGCzGEzFGzEIzDKzDMzCOzBQzARzO\ SzNTzNUzMVzMWzMXzLYzLZzL_zK`zKazKbzJczJdzJezIfzIgz\ IhzHizHjzHkzGlzGmzGnzFozFpzFqzErzEszEtzDuzDvzDwzCx\ zCyzCzzBzzBzzBzzAzzAzzYzzXzzXzzWzzWzzVzzVzzUzzUzzT\ zzTzzSzzSzzRzzRzzQzzQzzQzzPzzPzzOzzOzzNzzNzzMzzMzz\ LzzLzzKzzRzzYzzdzzkzzlzzz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z| Subject: (fractint) July's FOTD Jim! What happened to this...? - -------- On June 15, 2001 Jim Muth wrote... "I have decided that the month of July will me a midgetless month." - -------- I was kinda looking forward to this. Not that I'm not enjoying what we're getting but... O Bd. - -- _______________________________________________ FREE Personalized E-mail at Mail.com http://www.mail.com/?sr=signup FREE PC-to-Phone calls with Net2Phone http://www.net2phone.com/cgi-bin/link.cgi?121 - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 3 Jul 2001 09:36:52 -0400 (EDT) From: Jim Muth Subject: (fractint) Re: July's FOTD At 07:15 PM 7/3/01 +0800, O Bd wrote: >Jim! > >What happened to this...? > >-------- > >On June 15, 2001 Jim Muth wrote... > >"I have decided that the month of July will me a midgetless month." I meant a month without a *quadratic* midget. >I was kinda looking forward to this. There will be enough FOTD's with no 'midgets' of any kind before the month is finished. >Not that I'm not enjoying what we're getting but... ...you're a bit disappointed? Jim M. - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 03 Jul 2001 16:07:37 -0000 From: "Andrew Coppin" Subject: Re: (fractint) Re: July's FOTD > >On June 15, 2001 Jim Muth wrote... > > > >"I have decided that the month of July will me a midgetless month." > >I meant a month without a *quadratic* midget. Now there's a thought... quadratic midgets occur in all sorts of formulas, but has anyone ever seen, say, a cubic Mandelbrot in any formula other than z^3+C? Thanks. Andrew. _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 3 Jul 2001 10:13:40 -0600 From: dmj@fractalus.com Subject: Re: (fractint) Re: July's FOTD Andrew, You can find cubic midgets in HalleyNova fractals, which are like Nova fractals (derived from Newton fractals) but using Halley's method instead of Newton's method. Newton's method converges quadratically, but Halley's method converges cubically. You can extend the technique to use any-degree approximation and thus produce Newton-like fractals qith any kind of midget you want. - --Damien - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 3 Jul 2001 14:33:06 -0400 From: "Multiple Bogeys" Subject: Re: (fractint) Fractal math - ------=_NextPart_001_0001_01C103CD.138EF700 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable > I did the math and roots in Octave. I hope I haven't made any mistakes= but if I did someone will help. > Respectfully > Doug Stewart I have a text file on my disk with all these up to period 8, and to more = decimal places. :-) From a short C program I wrote that calculates them w= ith Newton's method.
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&g= t; I did the math and roots  in Octave. I hope I haven't made any mi= stakes but if I did someone will help.
> Respectfully
=
> Doug Stewart
 
I have a text file o= n my disk with all these up to period 8, and to more decimal places. :-) = From a short C program I wrote that calculates them with Newton's method.=


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- ------=_NextPart_001_0001_01C103CD.138EF700-- - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 3 Jul 2001 14:39:28 -0400 From: "Multiple Bogeys" Subject: Re: (fractint) C-FOTD 30-06-01 (Head of Zardoz [4]) - ------=_NextPart_001_0002_01C103CD.F6F4C560 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable > This three-way stretching appears quite often around holes when > they are sliced in odd directions. There must be some geometric > feature of the Julibrot causing the effect, which would be quite > apparent if we could visualize four-dimensional forms. The stretching is also a dead giveaway that the image is in an odd slice = and not merely perturbed. It's because the behavior of the iteration with= respect to the screen coordinates is not constrained by the Cauchy-Riema= nn equations, which it is in slices parallel to the c-plane (fixed z_0) o= r the z_0 plane (fixed c).
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> This thre= e-way stretching appears quite often around holes when
> they are s= liced in odd directions.  There must be some geometric
> featu= re of the Julibrot causing the effect, which would be quite
> appar= ent if we could visualize four-dimensional forms.
 
=
The stretching is also a dead giveaway that the image is in an odd = slice and not merely perturbed. It's because the behavior of the iteratio= n with respect to the screen coordinates is not constrained by the Cauchy= - -Riemann equations, which it is in slices parallel to the c-plane (fixed = z_0) or the z_0 plane (fixed c).


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- ------=_NextPart_001_0002_01C103CD.F6F4C560-- - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 3 Jul 2001 14:41:50 -0400 From: "Multiple Bogeys" Subject: Re: (fractint) Fractal math - ------=_NextPart_001_0003_01C103CE.4BB6C4E0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable > But if you just plot all the points in all those infinitesimal bays, > together they will appear like an outline of the Mandelbrot set (a kind > of dust that grows ever denser near the "shoreline"...) I think I mentioned that earlier in the thread, when I said that these po= ints accumulate on the boundary of M.
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> But if you just plot all the points in all those infinitesimal bay= s,
> together they will appear like an outline of the Mandelbrot se= t (a kind
> of dust that grows ever denser near the "shoreline"...)=
 
I think I mentioned that earlier in the thr= ead, when I said that these points accumulate on the boundary of M.
=


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- ------=_NextPart_001_0003_01C103CE.4BB6C4E0-- - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 3 Jul 2001 14:50:32 -0400 From: "Multiple Bogeys" Subject: Re: (fractint) Fractal math - ------=_NextPart_001_0004_01C103CF.82D38B60 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable > But there is only one root per bay so you will see an outline of the > manelbrot set but the shore line will not be defined, only a dot for ea= ch > small bay and there are many small bays on the shore line. The proof is in 3 steps. 1. A point on the boundary of M with rational internal angle in a compone= nt in M is where a cardioid cusps or a bud attaches to a component -- a "root". In images, the bottom of a "valley". In th= is valley, other buds form sequences that shrink toward the root. The centers of these are in the above set and accumul= ate on the root. So these points are in the set. The set of points with rational external angle with odd denominator in= lowest terms thus lies in the closure of these centers. 2. The remaining points of rational external angle (even denominator in l= owest terms) are the Misiurewicz points -- points on filaments, often filament tips or branching points. These are easil= y seen to have sequences of mini Mandelbrots that shrink toward them. The centers of their cardioids accumulate to them,= and the Misiurewicz points lie in the closure of the set of component centers. That takes care of all points with ratio= nal external angle on the boundary of M. 3. Here we assume that M is locally connected, a conjecture with strong e= vidence for it, but to the best of my knowledge not yet proven (or disproven). If this is true, all points with irrati= onal external angle are accumulation points of points with rational external angle, and lie in the closure of the closure of the = set of component centers. But the closure of a closure is the original closure, which puts the whole of the boundary of M in = the component centers' closure.
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> But there is only one root per bay so you will see an outline of t= he
> manelbrot set but the shore line will not be defined, only a d= ot for each
> small bay and there are many small bays on the shore = line.
The proof is in 3 steps.
1. A point = on the boundary of M with rational internal angle in a component in M is = where a cardioid cusps or a bud attaches
   to a com= ponent -- a "root". In images, the bottom of a "valley". In thi= s valley, other buds form sequences that shrink
   t= oward the root. The centers of these are in the above set and accumulate = on the root. So these points are in the set.
   The = set of points with rational external angle with odd denominator in lowest= terms thus lies in the closure of these
   centers.=
2. The remaining points of rational external angle (even deno= minator in lowest terms) are the Misiurewicz points -- points
=    on filaments, often filament tips or branching poi= nts. These are easily seen to have sequences of mini Mandelbrots that
   shrink toward them. The centers of their cardioids a= ccumulate to them, and the Misiurewicz points lie in the closure of
=
   the set of component centers. That takes care of all p= oints with rational external angle on the boundary of M.
3. He= re we assume that M is locally connected, a conjecture with strong eviden= ce for it, but to the best of my knowledge
   not ye= t proven (or disproven). If this is true, all points with irrational exte= rnal angle are accumulation points of points with
  = rational external angle, and lie in the closure of the closure of the se= t of component centers. But the closure of a closure
 &nb= sp; is the original closure, which puts the whole of the boundary of M in= the component centers' closure.


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- ------=_NextPart_001_0004_01C103CF.82D38B60-- - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 3 Jul 2001 14:55:36 -0400 From: "Multiple Bogeys" Subject: Re: (fractint) Re: July's FOTD - ------=_NextPart_001_0005_01C103D0.3779E1E0 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable > I meant a month without a *quadratic* midget. Someone here seems to be a prime candidate for public office... :-)
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> I meant a= month without a *quadratic* midget.
Someone here seems to= be a prime candidate for public office... :-)

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- ------=_NextPart_001_0005_01C103D0.3779E1E0-- - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 3 Jul 2001 14:56:48 -0400 From: "Multiple Bogeys" Subject: Re: (fractint) Re: July's FOTD - ------=_NextPart_001_0006_01C103D0.629FB840 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable > Now there's a thought... quadratic midgets occur in all sorts of formul= as, > but has anyone ever seen, say, a cubic Mandelbrot in any formula other = than > z^3+C? Sure. I constructed a quartic years ago to exhibit one. And I did it deli= berately. And it worked. The only requirement is that the critical point = you use be a zero of the derivative with multiplicity two.
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> Now there= 's a thought... quadratic midgets occur in all sorts of formulas,
>= but has anyone ever seen, say, a cubic Mandelbrot in any formula other t= han
> z^3+C?
Sure. I constructed a quartic years ago= to exhibit one. And I did it deliberately. And it worked. The only requi= rement is that the critical point you use be a zero of the derivativ= e with multiplicity two.


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- ------=_NextPart_001_0006_01C103D0.629FB840-- - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Tue, 03 Jul 2001 21:42:57 -0700 From: Mark Christenson Subject: Re: (fractint) Re: July's FOTD At 04:07 PM 7/3/01 -0000, Andrew wrote: >> >On June 15, 2001 Jim Muth wrote... >> > >> >"I have decided that the month of July will me a midgetless month." >> >>I meant a month without a *quadratic* midget. > >Now there's a thought... quadratic midgets occur in all sorts of formulas, >but has anyone ever seen, say, a cubic Mandelbrot in any formula other than >z^3+C? No cubics, but I have witnessed z^4 midgets in one of my gravibrots. Will advise which if you're interested. I could direct you to Bud's Fractal Pages, but they're temporarily offline... Aloha, Bud - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Wed, 4 Jul 2001 10:04:54 -0400 (EDT) From: Jim Muth Subject: (fractint) C-FOTD 04-07-01 (Mand-Newt Eruption [8]) Classic FOTD -- July 04, 2001 (Rating 8) Fractal visionaries and enthusiasts: Today's FOTD image has no quadratic midget. In fact, it has no midget at all. It is simply a design created by number 13 in my series of 14 MandNewt formulae, which use variations of the famous Ikenaga function to create fractals. Formula numbers 13 and 14 are recent additions to the MandNewt series, which until now has consisted of only 12 formulae. Almost the entire image consists of bof60 inside fill. This fill changes an otherwise flat inside area into a series of overlapping bubbles, which can make interesting images. Today's scene is one of these images. It is a rather stately scene with its left-right symmetry. Some may see a series of hot-air balloons filling with a grainy green-and-pink gas; others may see a scene in some surrealistic outer space. I see a kind of eruption, and have therefore named the picture "Mand-Newt Eruption". I rather like the hazy effect created by the bright blue areas. In my opinion, this plus the overall appearance gives the image an exceptional rating of 8, which may be a bit liberal. The 4-minute render time of the parameter file at a resolution of 640x480 is bearable, but this is one of those images that looks best at the highest resolution possible. The download of the GIF image will soon be available on Paul's web site at: and on Scott's site at: The fractal weather today here at Fractal Central was uneventful, with partly cloudy skies and a temperature of 84F (29C). The cats must have approved, for they spent most of the afternoon lounging in the yard. Today however is Independence Day in the USA, and that means fireworks. The cats don't like noise, so I suppose they'll be skittish most of the day. As for myself, I'm simply going to do as little as possible. Until next time, take care, and fractals are fun; arguing politics is not. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Mand-Newt_Eruption { ; time=0:04:22.60--SF5 on a P200 reset=2001 type=formula formulafile=allinone.frm formulaname=MandNewt13 passes=1 center-mag=8.84911\ /-9.84213e-014/3.120633/1/-90 params=-4.159/-3.693\ /-4.144/-0.685/0.119/-0.783 float=y maxiter=90 inside=bof60 logmap=yes periodicity=0 colors=000I8\ UJAXKC_LEbMGeNIhOKkPMnQOqRPtQPwPOxONxNMyMLzLKyKJxJ\ IwIHuHGsGFqFEoEDmDCkCBiBAgA9e98c87a76_65Y07W06U05S\ 04Q03O02M01K00I00G00E0AC0KW3NX5PZ9R`CSaEWcGXeIZhL`\ jNclPemRgnShpWhuUjrUjpSlnSlmRllRmjPmhPmgNncNnaLp`L\ pZLpXKrWKrUIrSIsPGsNGuLEuKEuICvGCvE0w0CvCLuNUsWare\ jpnrnvymzzmzznzznzznzzpzzpzzpzyrz000<158>000 } frm:MandNewt13 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), e=real(p3), f=imag(p3): h=z^a+(g-b)*z-f j=c*z^d+g z=z-e*h/j, 0.000000000000000000000000000001 <= |h| } END 20.0 PAR-FORMULA FILE================================== - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 05 Jul 2001 12:44:03 -0000 From: "Andrew Coppin" Subject: Re: (fractint) C-FOTD 04-07-01 (Mand-Newt Eruption [8]) >From: Jim Muth Reply-To: fractint@lists.xmission.com To: >fractint@lists.xmission.com CC: philofractal@lists.fractalus.com Subject: >(fractint) C-FOTD 04-07-01 (Mand-Newt Eruption [8]) Date: Wed, 4 Jul 2001 >10:04:54 -0400 (EDT) > > >Classic FOTD -- July 04, 2001 (Rating 8) > >Fractal visionaries and enthusiasts: > >Today's FOTD image has no quadratic midget >I rather like the hazy effect created by the bright blue areas. In my >opinion, this plus the overall appearance gives the image an exceptional >rating of 8, which may be a bit liberal. That is indeed a very cool image! Thanks. Andrew. _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. - -------------------------------------------------------------- Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@lists.xmission.com Get Commands: majordomo@lists.xmission.com "help" Administrator: twegner@fractint.org Unsubscribe: majordomo@lists.xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 5 Jul 2001 10:30:32 -0400 (EDT) From: Jim Muth Subject: (fractint) C-FOTD 05-07-01 (Platform in Space [7]) Classic FOTD -- July 05, 2001 (Rating 7) Fractal visionaries and enthusiasts: Since the FOTD is already late, and it is a slow one, I'll make the discussion short. To begin, in keeping with the theme of a midgetless July, the image has no midget. The iterated formula that drew the image is Z^1.03+C. I named the picture "Platform in Space" because that's what it reminds me of. I rated it at a 7 because I feel it's above average. It's an unusually slow image to render, taking over 2 hours of computer time on a tired old Pentium 200mhz machine. Therefore the best way to view it is to give Paul and Scott a chance to render it and then visit their Web sites at: and: The fractal weather on the Independence Day holiday featured fireworks from nature. A series of heavy thunder-showers in the evening put a damper on the man-made variety. The temperature of 86F (30C) did little to ease the fractal cats' skittishness. And it's now time for an active day doing other things. Until next time, take care, and hope for the best. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Platform_in_Space { ; time=2:01:41.52--SF5 on a P200 reset=2001 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-8.54499/-3.05261/4.14962/1/-29.999 params=1.03/0/-7.53/800 float=y maxiter=12000 inside=0 logmap=57 symmetry=none periodicity=10 colors=000ZN`YMaXLbWKcVJdUIfTIgSHhRGiQFjPEkODlODmC\ 5PE7NF9MGBKIDJJEHKGGMIENKDOLCNNENOFNQGNRINSJNUKNVM\ NXNNYONZQM`RMaSMcUMdVMeWMgYMhZMj_MkaMlbLncLoeLqfLr\ gLsiLujLvkLxmLynLzoQujVpeZl`cgWheTgcSfbRfaRe_QdZPd\ YPcXOcVObUNaTMaRM`QL`PL_OKZMJZLJYKIZIJYJIYJIYJIYJI\ YJHYJHXJHXJHXKGXKGXKGXKGWKFWKFWKFWKFWLEWLEWLEVLEVL\ DVLDVLDVLDVMCUMCUMCUMCUMBUMBUMBTJCUMBVOBWRAXTAYW9Z\ Y9_`8`b8ad8`bB_aE_`HZ_JYYMYXPXWRWVUWUXVSZVRaUQdTPf\ TOiSMlRLnRKqQJtSHuQIvOJvMKvLKvJLwHMwGMwENwCOwAPx9P\ x7Qx5Rx2Sz4Rz6Rz8QzAQzCPzEPzGPzIOzKOzMNzONzQMzSMzU\ MzWLzYLz_KzaKzcKzZMzUOzPQzKSzFUzBVzBUzCTzDRzZKzZLz\ ZLz_Lz_Lz`Mz`Mz`MzaMzaNzaNzbNzbNzbNz`PzZRzXTzVVzTW\ zRYzP_zNazLbzJdzHfzFhzDizEgzFfzGezHdzIczJbzKazL_zM\ ZzNYzOXzPWzQVzRUzSSzTRzUQzVPzWOzXNzYMzdMzkMzrMzqLz\ pLzoLznKzmKzlKzkJzjJziJzhIzgIzfIzeHzdHzcHzbHzaGz`G\ zeTzdTzcSzbRzbQzaPz`Oz_Nz } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z| Subject: Re: (fractint) C-FOTD 04-07-01 (Mand-Newt Eruption [8]) - ------=_NextPart_001_0001_01C1058D.7ED06A00 Content-Type: text/plain; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable > Today however is Independence Day in the USA, and that means > fireworks. If you like fJuly 4 fireworks, then there's a particularly apt choice of = sci-fi movie for the night ...
Get Your Private, Free = E-mail from MSN Hotmail at http://www.= hotmail.com.

- ------=_NextPart_001_0001_01C1058D.7ED06A00 Content-Type: text/html; charset="iso-8859-1" Content-Transfer-Encoding: quoted-printable
> Today how= ever is Independence Day in the USA, and that means
> fireworks.
 
If you like fJuly 4 fireworks, then there's a = particularly apt choice of sci-fi movie for the night ...


Get Your Private, Free E-mail from MSN H= otmail at http://www.hotmail.com.<= br>

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