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FOTD 26-08-02 (The Web of Terror [7])
by Jim Muth 26 Aug '02

26 Aug '02

FOTD -- August 26, 2002 (Rating 7) Fractal visionaries and enthusiasts: The midget at the center of today's image is located on the X-axis of its parent fractal, which has X-axis symmetry. This is demonstrated not only by the coordinates in the parameter file but by the straightness of the arms radiating from the midget. The 180 degree rotation of the image does not change the east-west orientation of the X-axis, so why do 2 out-zooms reveal a north-south oriented axis? The mystery is not very deep, a few more out-zooms reveal the true situation -- the X-axis is not continuous. Actually, only one out-zoom reveals an interesting scene -- a near-perfect array of square figures that almost made it as FOTD. The choice between the squares in the out-zoom and the octagons in today's image was a toss-up. The squares lost only because one of the two images had to lose. The generating formula subtracts 0.2 part of Z^(-3) from Z^(-2) before adding 1/C. If I had added the 0.2 part of Z^(-3) rather than subtract it, the resulting parent fractal would still have had X-axis symmetry, but its overall shape would have been totally different, and of course, today's image would not have existed. (More accurately, it still would have existed but it would never have been found.) I used the MandelbrotMix2 formula to find today's image. This formula works the same as the overworked MandelbrotMix4 formula, except that it includes the capability to change the starting point of Z. This capability is not used in today's image. The name of the image, "The Web of Terror", which sounds like the title of a horror movie, has no connection whatever to the appearance. I might have had a fleeting impression of a spider's web, but if so, I can no longer see the resemblance. The rating of 7 seems fairly accurate, and those who spend the 3 minutes to run the parameter file will not be disappointed. Those who download the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> will not be disappointed either. The Sunday weather here at Fractal Central was perfect for most anything, with blue skies, puffy white clouds, gentle breezes, low humidity, and a temperature of 86F 30C. The fractal duo were happy all day, which is a rare event for them. My happiness however depends on finishing the work I now find before me. If I start now, I can be finished by 3pm. If I wait an hour, I will not finish before 4pm. If I put off some of the work until tomorrow, I can be finished by noon. Most likely, I'll choose the first option. Until next FOTD, which will arrive in all its glory within 48 hours, take care, and beware of fractals lurking in dark corners. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ The_Web_of_Terror { ; time=0:03:13.01--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=recip passes=1 center-mag=+7.662161881652889/0/1.171407e+011/1/180 params=1/-2/-0.2/-3/0/0/0/0 float=y maxiter=500 inside=0 outside=tdis periodicity=10 colors=000z8z89S8AR9AP9BOACMADLADK9CJ9BI8AI89H78G7\ 8G77F66E65E54D53C53CB7EGBFLEHRIIWLJ`PLeSMkWNqZPwbQ\ zeRxcSrbSn`Sk_SgYScXS_VSXUSTSSPRSLPSIOSEMSALS6JS3I\ S4KQ5LP6MO6NM7OL8QK9RI9SHATGBUECWDCXCDYAEZ9F_8F`7I\ b6Kc6Md6Pe6Ug6ch6mi6wj6wl6wm6wn6mo6cjA`fDZbHWZKTUO\ RQROMVMIYKKVILSHMQFONDPLCQIARG8TD7UB5V84W6KdKZlXYj\ YXhYWgYWeYVdYUbYUaYT_YSZYSXYRWYQUYQTYRVXSXVTZUU`SV\ bRWdPXfOYhMZjLZkKWeOT_RQUUNOYKI`ICcJH_KMXKQUJSWJTX\ JVZJW_IX`IZbI_cI`dIbfHcgHdhHfjHgkHhlPilWilcjljjlqj\ leZgUObIDY62TEFPMRL8tF9qKAoOBmSBkWCi_DfdDdhEblF`pF\ ZtH`sIarJcqKdpMeoNgnOhmPilQkkSljTmiUohVpgWqfVpcVpa\ Vo_VoYVoWUnUUnSUnQUmNUmLTlJTlHTlFTkDTkBTk9ShASeARb\ BR`BRYCQVCQTDPQDPNEPLETJDWHD_FCbDCfBBi9Bm7Ap5As3Ap\ 6Cm9DjCFgEGdHHaKJZNKXPL_OIbNFeNDXMrYNsmL5lQAkVEj_J\ idNhiSgnWgq_eoaclcbhe`egZaiYZkWVmVSnWRpXQqYPsZOtZN\ uSWsMdrGmpAvoe1hO4b66X77V } frm:MandelbrotMix2 {; 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)+(p4)), 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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Compiling the sources?
by Marc Schreier 26 Aug '02

26 Aug '02

Hi, did anyone managed to compile the Fractint sources with Visual Studio 6? The Fractint homepage points to a port - work in progress - but still not available. Regards Marc

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FOTD 22-08-02 (Square in Sight [7])
by Jim Muth 25 Aug '02

25 Aug '02

FOTD -- August 22, 2002 (Rating 7) Fractal visionaries and enthusiasts: Checking the fractal gossip lines, I see that a new version of the fractal generating program preferred by the trendy fractal crowd has just been released. I already have the previous version of the program, though I rarely use it, so I may or may not eventually pick up this newest version, for which the program's author is charging a nominal upgrade fee. In any case, I'll wait until a debugged version appears. I have nothing against the performance of this other program, it's a fine fractal generator, but I remember several years ago, when the Fractint list was receiving queries from the author of the other program, asking questions about the operation of the Fractint code. Shortly thereafter, the other program appeared on the scene as a shareware product, and the 'I'm an artist' crowd left the Fractint list to flock to the other program. So far, so good, but I wonder how much of the original Fractint code now resides in slightly modified form in the other program, which is being sold for profit. Something not quite ethical appears to have happened somewhere along the line, but neither I nor apparently anyone else can pin it down. Well, I guess it's time to move on from ethics to today's fractal, which was generated by the old-fashioned Fractint program aided by the MandelbrotMix4 formula. The expression 6Z^(-0.7)-0.12Z^(2.2)+(1/C) was iterated to create the parent fractal, which consists of a large double-lobed Mandeloid with a smaller satellite Mandeloid just to the east. Today's midget lies deep in the main valley on the east side of the large Mandeloid. I named today's image "Square in Sight". No square features actually exist in the image, but the coloring gives the appearance that the midget lies in the center of a square. This illusory square inspired the name. I feel that the rating of 7 is justified in light of the fact that the pattern around the midget is different enough to warrant notice. The render time in the 4-minute range is short enough to make running the parameter file practical and long enough to make it interesting. As always, those who would rather avoid parameter files may download the completed 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 was typical mid-summer fare here at Fractal Central on Wednesday. The high temperature of 88F 31C was just about average; the moderately high humidity and stagnant air were also average for mid-summer. The fractal cat duo had an average day -- one hour outdoors lounging in the shade, 22-3/4 hours indoors lounging on the floor, 1/4 hour eating. With another day's work before me, I'd best get busy without delay. Until the next glorious FOTD appears on August 24, take care, and remain steadfast. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Square_in_Sight { ; time=0:04:16.99--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-0.42420968295669740/-0.001119486396590\ 06/4.82806e+009/1/-70/2.93649964008824149e-006 params=6/-0.7/-0.12/2.2/0/0 float=y maxiter=750 inside=0 logmap=81 periodicity=10 colors=000M0aO0cP0dQ0eS0eT0fV0fX0gY0i_0j`0la1mc3od\ 4pf6rg7jf9cd6Xg4Qj3Lm3Fp19s03vF0yM0zT0rM0jF6cMFVSP\ O`YGif7rp0uy`zz0zz0zz1xy4uv7rsAorDloGilJfiMcfP`d_P\ jiDos1uz0yx0vs3soArjGodOm`TjX_gSffMlcIsaDy_9sYCoiD\ _uFJzAMu7Ol3Qa0ST0YX0cj0_l0Vl0Sm3Om6LmAGoDDoI9oM4p\ P1pT0pX0r`0rc0rf0si0sl0sm0sp0ss3uu4ux7uzAuzCuzDpzD\ mzDizDfzDazD_yFXyFSyFPyFLyFIyFFsIDmJCiLAcO9_P9TQ7P\ S6JV4DX39Y33`10a00c00d00`6AXDMSLXOQgJYrFdzAlz7rzAs\ zDuzGvzJxyLxvOysQzpTzoVzmYyl`xjcuifsgirflofmmdplcs\ iavg`yf_zcYzaYz`0r00m00h30eA0cG0fM0iT0l_0of0rl0ur1\ sm9rjGpgOodVma`l_cgXfcTi_QlVOoQLrMIuKFrPCmUAhZ3cc0\ Zh1Ym4Yr7XvCXvFXvIVuLVuPVuSTsVTsYTsaSudSvgSxjPyiOz\ gLzgJzfGzfFzdCzdAzc7zc6za4zaazmzzxzzpzzjzzczzYzzQz\ zLzzDzz7zz1zz7zzCzzGzzLzzPzzTzz_zzczzgzzlyzpxzuvzy\ xzzxzzyzzyzzzzzzzzzzzzzXzz0zz0vz4lzAczGTzMLzQPzOSz\ LXzI_zFXzDVzCTzCSzAuzszzx } 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 24-08-02 (Sliced Melons [7])
by Jim Muth 24 Aug '02

24 Aug '02

FOTD -- August 24, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's image is named "Sliced Melons". If the first three letters of the second word are reversed, the title becomes "Sliced Lemons". But there is nothing sour about the image, which uses the < tdis > outside coloring option. In fact, after careful consideration, I rated the image at a 7. The parent fractal combines portions of Z^2 and Z^3. The whole- number exponents result in a fractal that has no branch-cut discontinuities when calculated with the outside set to display the standard equal-iteration bands, but the < tdis > outside- coloring algorithm used in today's image introduces the disconti- nuities that are visible in the image. The parent fractal is a distorted Mandelbrot set rotated 180 degrees, with lots of interesting activity on its negative (in this case, positive) stem. East (in this case, West) valley of the parent fractal is also decorated with interesting spurious activity, though I did not explore this area. With a render time of 6 minutes on my humble fractal machine, today's fractal is a bit slow, making a download of the completed image the marginally better choice. The download is available on the W.W.W. at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Friday here at Fractal Central was overcast and very humid -- wet enough to swim in. The temperature of 86F 30C was about average. A few drops of rain fell in the after- noon, which is too bad, since we're in a rather severe drought. The fractal cats finished their outdoor activity before the raindrops appeared, so, unlike the local farmers, they were not displeased. With thunder-showers prowling the area this morning (Saturday), and some real rain hopefully soon to occur, I'd best wrap up this edition of the FOTD and see whether I can console the dynamic duo. Until next FOTD on Monday the 26th, take care, and be serendipitous. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Sliced_Melons { ; time=0:06:12.34--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix2 function=ident passes=1 center-mag=+2.943452875421294/+0.00522078768874016\ /1.530056e+012/1.0002/177.5/0.00916304379004028585 params=1/2/-0.2/3/-0.25/0/0/0 float=y maxiter=1000 inside=0 outside=tdis symmetry=none periodicity=10 colors=000RmRUmUXnX`n`cocgofjpjnpmqqptqsrnpqknpiln\ fimdglaejZciX`hUZfSXePVdMSbKQaHO`FMZINYLOXOPWQPVTQ\ TWRSYRR`SQcTPeTNbSM_SLXSJVSISSHPSGMSEKRDHRCERBBR99\ R86R73R61R7GM8UH9gCAu7IkEQaKYSQdIWUOVKTUAZT0cS4fW7\ h_BkcEmgHojHniHngImfImdIlcJlaJk`Jk_Ml`Pl`Sm`UmaXna\ _naaobdobgobipclpcoqcqqdtrdwrdyrdldX`RPbVMcYKd`Iec\ GffEgiBhl9io7jr5ku3lx1jy2hy3fy3dy4by4`y5Zy5Yy6Wy6U\ y7Sy7Qy8cz8Zt9Qp9VjJV_TKKKcElg3uf8sfCreGpeKoeOmdTl\ dXjc`icdgchfdj`ekWflQgmLhoGipAjq5jr0kp3ln5ll7mj9mh\ BnfDndFobHp`KpZMqXOqVQrTSrRUsPWsNYpMZmLZjKZhK_eJ_b\ I__H_YH`VG`SF`QF`NDRKBHH98RKK_UWicgrmsolklldjlXglQ\ elJdgEccAb_6bW2_Y6YZAW_DTaHRbLPcOMeSKfWIgZFibDjfBk\ iAjj9ij8hj8gj7fj6ej6dk5ck4bk4ak3`k2_k2_k7blBdlGflK\ hmPjmTlmQciOWfLOcJG`KFZLEXMDVNCTPBRUAPZ9Oc8Mh7Km6I\ r5Gm4Eh3Cc2BZ1HU1MJ1SF1XB1b81g72d72a72Z62W62T62Q52\ N52L52I42F42C429326323321 } frm:MandelbrotMix2 {; 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)+(p4)), 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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Recent Newton_elliptic formulae.
by Morgan L. Owens 24 Aug '02

24 Aug '02

So I spent ten minutes just looking. SkeinedSpire { ; Colours by Mark "Bud" Christenson ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=newton_e.frm formulaname=newton_elliptics_3 center-mag=-0.558014/0.500417/12.69162 params=0.1/0.5/-1/0 float=y maxiter=1023 inside=255 periodicity=0 colors=FMUGLUILUKKU<5>NL`OMaPMc<2>RNfSOhSOh<9>ZUo_Up_Vp<2>bXscYtc_t<3>fd\ wffwggxgixhjy<3>nqzprzrtz<3>zzz<27>C__AZZ8YY<3>0UU<10>M_NO_MQ`MS`LUaK<4>\ abFbbEdaC<3>ja8k`6m`5<2>q`2s_0s_0<24>xt0xu0yv0<2>yy0zz0xy0<15>HW0EU0BS0<\ 2>3M00K00L0<36>0u00v00w0<2>0z00z00y0<7>0q00p00o0<2>0l00k00j2<7>0ZI0XK0VM\ <2>0RS0PU1PU<7>DNU } SmallInfinities { ; A Mandelprobe disrupted by a nearby singularity ; SkeinedSpire Closeup ; Colours by Mark "Bud" Christenson ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=newton_e.frm formulaname=newton_elliptics_3 center-mag=-0.58718581135681620/+0.45507375059740630/147.577 params=0.1/0.5/-1/0 float=y maxiter=1023 inside=255 periodicity=0 colors=FMUGLUILUKKU<5>NL`OMaPMc<2>RNfSOhSOh<9>ZUo_Up_Vp<2>bXscYtc_t<3>fd\ wffwggxgixhjy<3>nqzprzrtz<3>zzz<27>C__AZZ8YY<3>0UU<10>M_NO_MQ`MS`LUaK<4>\ abFbbEdaC<3>ja8k`6m`5<2>q`2s_0s_0<24>xt0xu0yv0<2>yy0zz0xy0<15>HW0EU0BS0<\ 2>3M00K00L0<36>0u00v00w0<2>0z00z00y0<7>0q00p00o0<2>0l00k00j2<7>0ZI0XK0VM\ <2>0RS0PU1PU<7>DNU } JuliaImpactFeature { ; When it hit the ground, it hit the ground hard. ; Another SkeinedSpire Closeup with a colour scheme ; from the ever reliable selection by Sylvie Gallet ; Version 2001 Patchlevel 8 reset=2001 type=formula formulafile=newton_e.frm formulaname=newton_elliptics_3 center-mag=-0.58741182340086060/+0.45145680389088130/6416.391 params=0.1/0.5/-1/0 float=y maxiter=1023 inside=255 periodicity=0 colors=000UUZ<15>jjlkkmllm<6>rrssstttu<2>wwwxxxxxv<3>xvmxukxthxtfxsdyra<\ 9>ylLykJyjH<2>yhCxgAxgA<11>nW2mV2lU1<4>fQ0eP0dO0bN0aM0`M0<3>VI0UH0TG0<10\ >B60950740<2>210001112<8>5AE6BF6CH7DI7EJ8FL<10>BJSBJTBJU<3>DLWEMXGNY<6>T\ YfV_hX`i<2>aemcgocgo<9>lmpmnpnopooppppqqq<4>llnkkmjjliikhhjggj<39>55E44D\ 33C<2>00A00A11B<28>TTZ } frm:newton_elliptics_3{ x=real(p1) y=imag(p1) A=real(pixel) B=imag(pixel) phi=tan(real(p2)) t=imag(p2) z=x+flip(y) : oz=z x=real(z) y=imag(z) d=2*y*phi-(3*sqr(x)+A) f=(sqr(x)+A)*x+B-sqr(y) g=phi*x+t-y nx=x-f+2*y*g ny=y-phi*f+(3*sqr(x)+A)*g z=nx+flip(ny) |z-oz|>0.0001 }

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Re: [Fractint] FOTD 22-08-02 (Square in Sight [7])
by Rupert Millard 23 Aug '02

23 Aug '02

Hi Jim, >So far, so good, but I wonder how much of the original Fractint >code now resides in slightly modified form in the other program, >which is being sold for profit. Something not quite ethical >appears to have happened somewhere along the line, but neither I >nor apparently anyone else can pin it down. It's an intersting question but my answer is "probably none." Ultra Fractal is written in Delphi and Fractint in C. The Fractint compatibility formulae are written in Ultra-Fractal's formula language. The source of these is available and IMHO it is indiscernable from the fractint code. Plenty of other programs implement the same forumlae as fractint and many of these are hard-coded in C - I think these are more questionable. btw: can someone give me a link to the old fractint archives from the majordomo days? From, Rupert _________________________________________________________________ Join the worlds largest e-mail service with MSN Hotmail. http://www.hotmail.com

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Re: [Fractint] Extended Fermat's Last Theorem - Slightly Off-topic
by Andrew Coppin 22 Aug '02

22 Aug '02

IIRC, a pair of Japanise (?) students proposed that all elliptic curves are also modular forms. Someone else pointed out that, assuming Fermat was wrong, his equation x^n + y^n = z^n would be an elliptic equation, and the corresponding modular form is decidedly weird. Yet ANOTHER mathematition later proved that this modular form is in fact too weird to actually exist. In other words, assuming that EVERY elliptic curve REALLY IS a modular form, Fermat's Last Theorum MUST be true. Andrew Wiles proved that elliptic curves ARE modular, and as a side effect proved Fermat right. Andrew. PS. I've read the book. And I'm kinda bored today... >From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com, fractint(a)mailman.xmission.com >Subject: Re: [Fractint] Extended Fermat's Last Theorem - Slightly >Off-topic >Date: Mon, 19 Aug 2002 13:43:43 +1200 > >At 01:09 19/08/2002, dirving(a)box.net.au wrote: >>"Ricardo M. Forno" wrote: >> > >> > Does someone in the list know if the following conjecture, that >>includes as >> > a particular case Fermat's Last Theorem, has ever been posed, and >>proved >> > false or true? >> > x[1]^p + x[2]^p + ... x[n]^p = z^p, for x[i] > 0 and 1 < n < p, has no >> > integer solutions. >> > TIA. >> > >> > _______________________________________________ >> > Fractint mailing list >> > Fractint(a)mailman.xmission.com >> > http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint >> >>I would conjecture ... no. > >Reasonable: a proof of this extended conjecture would in turn provide an >alternatve proof of FLT as a special case. > >So if there has been a proof, it has been found more recently than (and >probably develops the ideas of) Wiles' tour de force. > > >Morgan L. Owens >"Yes, Andrew; a corollary :-)" > > >_______________________________________________ >Fractint mailing list >Fractint(a)mailman.xmission.com >http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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Re: [Fractint] Extended Fermat's Last Theorem - Slightly Off-topic
by Franktal Gallery 22 Aug '02

22 Aug '02

Morgan, thanks for the explanation and the link ! Regards, Miguel >From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> >Reply-To: fractint(a)mailman.xmission.com >To: fractint(a)mailman.xmission.com, fractint(a)mailman.xmission.com >Subject: Re: [Fractint] Extended Fermat's Last Theorem - Slightly >Off-topic >Date: Fri, 23 Aug 2002 00:48:14 +1200 > >At 23:46 22/08/2002, Franktal Gallery wrote: >>Could you please explain the "semistable" concept ? > >Oof. Where to start (and where to finish?) > >See http://mathworld.wolfram.com/Semistable - following is a paraphrase. >[snip] >[snip] >[snip] _________________________________________________________________ Chat with friends online, try MSN Messenger: http://messenger.msn.com

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Re: [Fractint] Extended Fermat's Last Theorem - Slightly Off-topic
by Franktal Gallery 22 Aug '02

22 Aug '02

Could you please explain the "semistable" concept ? Thanks, Miguel >From: "Morgan L. Owens" <packrat(a)nznet.gen.nz> > >[snip] > >The two theorems run: >If FLT is false, then y^2=x(x-z^n)(x+y^n) is semistable, but not modular. >(Conjectured in 1982 by Gerhard Frey; proven in 1986 by Ken Ribet via >Jean-Pierre Serre). > >and > >All semistable elliptic curves are modular. (Conjectured by Yutaka Taniyama >in 1955, later generalised by Goro Shimura and Andre Weil by dropping the >"semistable" bit; proven in 1994 by Andrew Wiles). > _________________________________________________________________ Send and receive Hotmail on your mobile device: http://mobile.msn.com

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FOTD 20-08-02 (Fractal Kernels [7])
by Jim Muth 20 Aug '02

20 Aug '02

FOTD -- August 20, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's fractal image is corny. This does not mean that it is trite and old-fashioned, it means that it is filled with corn kernels. The corn in the image appears in neat rows, almost the way corn kernels grow on the corncob. This corniness inspired the name "Fractal Kernels". The effect of corn kernels is produced by iterating the formula Z^(-2)-0.01(Z^2)+(1/C), and doing the calculation with the bailout radius set to 99.999, (which is critical), and the outside set to < fmod >. The small range of colors in the image was not intentional. It exists because the image uses only a small part of the 256-color palette. Unwilling to have yet another consecutive 6-rated FOTD, I rated today's image at a rather liberal 7. Perhaps a 6-1/2 would have been more appropriate, but my rating scale does not have half- step increments. The 4-minute render time is acceptable, but downloading the completed GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> is more acceptable. The fractal weather Monday here at Fractal Central was hot and humid enough to keep the fractal cat duo housebound. The high temperature reached 97F 36C at 4pm, and as is usually the case these days, the promised cooling showers once again failed to appear. One thing that had better appear however is the work that's due, and the only way to finish the work is to start it. So without further fanfare, I'd best get started. Until next time, on the 22nd, take care, and watch your bailout. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START 20.0 PAR-FORMULA FILE================================ Fractal_Kernels { ; time=0:04:00.35--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=recip passes=1 center-mag=-4.43910986029936400/-5.965792592977377\ 00/1.175254e+008/1/-42.4999968823281691/-4.8222949\ 2321933906e-006 params=1/-2/-0.01/2/0/-0.001 float=y maxiter=1000 inside=0 proximity=0.5 outside=fmod logmap=yes periodicity=10 colors=000vtzvtztszqrzqqzopznoznozlnzilzgkzeizegzd\ gzafz_dz_czYazXazV_zTZzTXzQVxOTvMTqMQoKOnIOlHMgFKe\ FKdDIaBHY9FX9FV7DT5BO3BM29K27I07F05D03B03905H27S39\ Z5Bc7Df9FiBHkDIzFKzHMzIOzKQzKQzKQzKQzKTzKTzKTzKTzK\ VzKVxMVvMVqMXoMXnMXiMXgMYeMYaMY_MYYKX_KX_IXaIXaHXd\ HXdFXeFXeFXgDXgDXiBXiBXl9Xl9Xn9Xn7Xo7Xo5Xq5Xq3Xt3X\ t3Xt5Yq7Yo7Yn9YlB_iB_gD_gF_eF_dHaaIa_IaYKaXKaXMdVO\ dTOdQQdOTeMTeKVeKXeIXeHYgFYgD_gBagBag9di7ei5ei3gi2\ il0il0ll0ll0nl0on0on0qn0tn0tn0vo0xo0xo0zo0zo0zv0zz\ 0zz0zz0zz3zz7zzBzzDzzDzzFzvFzoHtiHndHgXIaQIXKKQDKK\ 7MF2M90MH3KM9KTFKYMIdTIiYIoeHvlHzqHzzFzzFzzFzz7zz0\ zz0zz0nz0vz_zzazxdzxdzzatzaaz_Kz_5z_IqQVgIeX9tM2zB\ 0z20z00zT3zO5zM7zK9zI9zHBxFDqDFlBFTIDBQB0X93_IDaTM\ d_VeidgqnizvlzzIzz0zz0zv0zzIzzVzzezzqzxzzqzqlziezd\ dviaIoqD_z7Kz37z7FzBMzFVvI_oMgiQodVx_YzOizDtz2zz0z\ z0zz0zz0zo3ze5zV9zKBzBxtz } 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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