September 2006 - Fractint - mailman.xmission.com

I rendered the "Farting Monkey equation" as...
by Hal Lane 20 Sep '06

20 Sep '06

Paul, Re: Your "...somebody else might like playing with [the equation]." I rendered the "Farting Monkey equation:" > f[x,c]=c*x*(x^2 - 2*x + 1)/(x^3 - x^2 - 2*x + 1) > Domain:{x,y}={{-2,3},{-2.5,2.5}} as... FartMonk { ; Roger Bagula via Paul N. Lee z2=z*z zt2=z*2 z3=z2*z c=pixel z=pixel: a=c*z*(z2-zt2+1) b=z3-z2-zt2+1 z=a/b |z|<4 } ...and get a humdrum circle with a few minor non-circular areas. Have I missed something? Anyone have any ideas? <---<< >-----Original Message----- >Date: Mon, 18 Sep 2006 12:38:27 -0500 >From: "Paul N. Lee" <Paul.N.Lee(a)Worldnet.att.net> >Subject: [Fractint] [Fwd: I get a strange nearly linear cut off] >On Mon, 18 Sep 2006 at 10:13:40, Roger Bagula wrote: >> I call it the "Farting Monkey equation" after >> a birthday greeting card: >> >> f[x,c]=c*x*(x^2 - 2*x + 1)/(x^3 - x^2 - 2*x + 1) >> Doman:{x,y}={{-2,3},{-2.5,2.5}} >> >> http://www.bullseyesgames.com/cards/birthday/birthday_card_1.shtml - Hal Lane ######################### # hallane(a)earthlink.net # ######################### -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.405 / Virus Database: 268.12.5/450 - Release Date: 9/18/06

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Empty Rectangle
by Vortex Swirling 20 Sep '06

20 Sep '06

Empty_Rectangle { ; Fractal of the day, 01-04-98 ; 12min on a 486-100, 640x480 reset=1821 type=julzpower passes=t center-mag=+0.00019\ 925630486376/+0.07428965755353106/98.87676 params=-1.7434/0/2.003/0 float=y maxiter=800 bailout=25 inside=0 logmap=53 symmetry=none periodicity=10 colors=000N24K34N54N74N94NA4<2>JG5IJ5GK5<3>9S58U56V54W\ 52W5AV9HVDOUH<3>vSXzS_yS`wSasSb<2>kSdhSegSf<10>SSn<7>Y\ ZcY_bZa`Za_<3>bgVciUdiS<3>llNnlMpmLqmJrmI<2>unEvoDwpBx\ qAyr9zr8<47>zu5zz6<12>lzHkzIkzI<2>wz6<22>RzI<19>czacza\ dz`<17>ozW<17>HzT<10>ez4<15>ZzCZz4 } I found this in the archived pars for April 1, 1998. There doesn't seem to be a corresponding page for it, however. Altering the parm 1.7434 even by a little obliterates the rectangle.

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FOTD 20-09-06 (Ghost of a Julia Set [7])
by Jim Muth 20 Sep '06

20 Sep '06

FOTD -- September 20, 2005 (Rating 7) Fractal visionaries and enthusiasts: Today's image, which was created with the julzpower formula of Fractint, takes us very close to the strange rectangle in one of the Julia sets of the Z^2.003+C Mandeloid. It takes us so close in fact, that the ghostly shadow of the rectangle itself appears at the center of the frame, rotated and distorted, and surroun- ded by apparent fractal ice floes. The distortion is caused by the inexact exponent of Z, which is set to 2.00312 rather than 2.003, and also by the value of C, which has an imaginary part of 0.0003 added to the real part of -1.7435. These tiny changes make a major change in the appear- ance of the Julia rectangle, which is rapidly fading from sight, and will soon vanish into the ether. To add to the interest, I calculated the scene with the inside set to 'fmod' and the outside set to 'summ'. The 'fmod' fill gives the inside parts of the image the effect if ice floes floating on a body of water, while the 'summ' merely livens the coloring of the outside parts. I named the image "Ghost of a Julia Set" and rated it at a 7. The render time of over 11 minutes is a bit slow, but the task of rendering may be avoided by viewing the image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A shower in the morning led to a pleasant sunny afternoon here at New Fractal Central on Tuesday, with a comfortable tempera- ture of 77F 25C. The fractal cats were more eager to explore a just-opened closet than to enjoy the sun coming in their window. My day was a bit slow, but that was no problem, since it gave me more time to work on the fractal agenda. The next FOTD will appear in 24 hours. Until then, take care, and where is the real truth hiding? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ghost_of_a_Jul-Set { ; time=0:11:34.37--SF5 on a P200 reset=2004 type=julzpower passes=1 center-mag=-0.00171559/0.0729636/43.51179 params=-1.7435/0.0003/2.00312/0 float=y maxiter=1500 inside=fmod outside=summ periodicity=10 proximity=0.01 colors=000LqFIqDFqADq8Aq57q35q1Bl8HhEMdLS`RYXYbTch\ PjoMomLplLqkLqjLrA0SWKphLseNfaLl`HsZIrYJqgLsfLteLu\ gHxdLuaOsZSqWVnTZlQajXegchegmeekccgaac___ZYWXWSVUO\ USKSQFTOHRMJQKKPIMOGONEPMCRLATK8UJ7WI5YH2_F4`G6aG8\ bHAcHCcIEcIHcJKcJNcKQcKScLUcLVcMWcMXcNYcNccQhcSocV\ tdXze_zfZzgZzhZzhZzhZzhZzfZzdZwbZt`ZqZZnYXkXZhW_eV\ abUb_UcXUeUUfRUlOUiMUgPUeSUcWUaYU_`UXbUVeUTgURjUPp\ UPnUOlUNkUMiULgZKfeJdkIcqHdnIdlJNgbOjaPmaQnaQoaQpa\ Ol_NhZLdXKaWIYUHUTGQSENQDJPBFNABM98LFCOKGRPJUUNX_R\ _dUbiYerbin`hjZgfXgbVfZTfVReRPeNNdJLdFJcEJ`DIbCHcB\ GdAFeAFf9Eg8Dh7Ci7Cj6Bk5Al49m12p49n6Fl9LkBSiEYhGcf\ JjeLpcKzfNvbQrZSnVVkRYgN_cJb_Fa_A`_5dXCgVIjSOmQUpN\ _yEgsLemRchXabb_XhYNsYSnXXiX`eWe`WjWVsVPnSVjQ`diKd\ gLdeMdbNcmzdYPdWQhYEfWKdUQbSW`QaZOgXMmXNsVLrUKqSJp\ RIpPHoOFnMEmLDmKClIBkH9jF8jE7iC6hB5gA4gB8fCBfDEeEH\ eFKeGNdHQdITdJWcKZcLabMdb } END PARAMETER FILE=========================================

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Jim Muth's "...most surprising discovery of all [his] fractal explorations."
by Hal Lane 19 Sep '06

19 Sep '06

############################################################## In Jim Muth's FotD for September 19th, 2006, named "Rectangle variation" he says: >One day quite a few years ago, I stumbled upon this rectangle, >which still remains the most surprising discovery of all my >fractal explorations. The rectangle is impressive even in its >pure form... I agree with Jim. This is a really extraordinary pattern to find -- even in the often strange fractal world. This fractal really struck me when I first saw it in 1998 and I have remembered it ever since. I was very pleased to be reminded of it again by Jim and to be able to recalculate it at much higher resolution on my more recent computer, as well as zoom into the rectangle's pattern. In addition to the object's clearly being a gently-curving rectangle of a single color, it has another really astounding feature. It has an embedded fractal pattern, like a pattern on a rug. The pattern is of a fractal tree composed of narrow triangles branching at right angles to one another. A version of this tree-like shape is included in Mandelbrot's "The Fractal Geometry of Nature." I'm not able to locate my copy right now as I have just moved also, but if memory serves, Mandelbrot's version was created by a substitution process similar to the ones used to create Hilbert curves and Koch snowflakes. I remember being struck at the time by the fact that a particular fractal formed by a simple substitution process could also be created by a complex formula's 'finding' it hidden at a very specific location in the four-dimensional Julibrot. This tree-like shape appears to be one of the 'self avoiding' branching fractal patterns that, no matter how often limbs branch off, always seem to 'know' where other branches are and carefully avoid them. Perhaps someone who has a copy of the book near at hand can locate the image and confirm the reference and give the page number for me. The rectangle in this image also seems to be suspended in space by a delicate 'railroad switching yard' pattern prominent in Jim's September 17th, 2006 FotD. Zooming into the rectangle reveals that each of the narrow triangles that form the tree-like pattern is covered with the 'switching yard' pattern. At the resolution of Jim's original rectangle image this 'railroad track' pattern on the narrow triangles only appears as a dusting of a few random pixels. If you remove both of Jim's two degree rotations by changing params=88/88/ to params=90/90/ the rectangle loses its slight curve and becomes very rectangle-like. However, the rectangle's tree-like pattern disappears and zooming cannot locate it. If you increment both of Jim's two degree rotations by by two more degrees by changing params=88/88/ to params=86/86/ the rectangle becomes a comet complete with tail. The rectangle's/comet's tree-like pattern remains in this version. Below my signature is Jim's October 7th, 2003 FOTD, which is a repeat of the January 1st, 1998 "Classic F.O.T.D." - Hal Lane ######################### # hallane(a)earthlink.net # ######################### -------------------------------------------------------------- Date: Tue, 07 Oct 2003 08:18:17 -0400 From: Jim Muth <jamth(a)mindspring.com> Subject: [Fractint] Classic FOTD 01-01-98 (Projective Plane) To: fractint(a)mailman.xmission.com Cc: philofractal(a)lists.fractalus.com Message-ID: <1.5.4.16.20031007081910.0d5759b0(a)pop.mindspring.com> Content-Type: text/plain; charset="us-ascii" Classic F.O.T.D., January 01, 1998 (Projective Plane) Fractal visionaries: The world of higher dimensions is filled with objects which are impossible in our three-space, and can be represented here in only a distorted way. The Klein Bottle is one such object. In three dimensions it appears as a closed figure which intersects itself and joins itself in such a manner that despite having no breaks it has only one side. The inside is also the outside. But this is a distortion of the true object, which can exist only in spaces of four or more dimensions. In four dimensions, the Klein Bottle is constructed by taking a rubber sheet, curling it and connecting one pair of edges so that a tube results, then bending the tube and joining the open ends into a doughnut shaped object. But before joining the edges, and with no cutting, the tube is given a half-twist and turned inside- out, so that without self-intersection, the resulting doughnut- shaped object has only one side. Its inside is also its outside. The Klein Bottle is difficult enough to visualize, but the Projective Plane is even more difficult. In fact it is difficult to even describe. In this case, the sheet of rubber is given a half-twist into a kind of Moebius Strip tube before being curled and given a second twist before the open ends are joined to each other, forming the Projective Plane. In this case, even a distorted model is nearly impossible in three-space. Well, if an accurate model of a Projective Plane is impossible in three dimensions, one could never hope to illustrate the monster on a two-dimensional screen. I named today's fractal "Projective Plane" only because that's what I thought of when I saw the image. Actually, it is a picture of a curious feature that appears at Z=0.00019,0.07388 C=-1.7435,0.0 in the Z^2.003 Julibrot figure. This object is extremely thin and exists only very near the Julia orientation, where it appears as a near- perfect rectangle. To create today's image, I gave the object a 2-degree double rotation from the Julia orientation, which distorted the rectangle into the curved shape in the picture. A little playing with the colors produced the effect of a flying sheet of rubber. The flying plane has landed at Paul's web site at: http://home.att.net/~Paul.N.Lee/FotD/FotD.html Tomorrow, I'll have another interesting FOTD. At this time I have no idea what it will be, but something will turn up -- as it always does. Until then, take care, and keep finding those fractal gems. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER-FORMULA FILE================================ Projective_Plane { ; 3-1/2 min on a P200 at SF5 reset=1960 type=formula formulafile=multirot.frm formulaname=multi20031 function=flip/ident/ident\ /flip passes=1 center-mag=-0.00037327503160875/\ +0.00003799627771399/514.8005/1/25 params=88/88/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=000QVZ<2>PXZ\ PYZP_Z<7>PlZPnZRt_<4>PmZPkZOhZ<6>MTZMRZMQZ<12>I9\ ZI8ZJ6a<19>I8OI8NH9KH9IH9HH9IH9IH9HH9FH9FH9H<11>\ HA9HA9JCB<2>OIGQJHRMJ<7>dgVejWgkY<3>nncooeqnf<3>\ wshxuixwjyylyzm<4>zwizvhzugzugztgzthzshzsh<10>pl\ `ol_mkZ<7>YfTWfSVdR<3>RZOQXNPYN<6>IUHHTGGUG<3>I_\ IJ`IJ`I<38>asSXrT<19>stPttPvvJvuM<3>oqWmpZmqZ<3>\ moZnoZopZskZwzZzwZzwZ } frm:multi20031 {; Jim Muth, best=ifif, fiif, fifi, iffi a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*fn3(real(pixel))+cos(a)*fn4(imag(pixel))+p3: z=z^2.003+c, |z| <= 100 } END PARAMETER-FORMULA FILE================================== ############################################################## -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.405 / Virus Database: 268.12.5/450 - Release Date: 9/18/06

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Correction to the date used for Jim Muth's (Projective Plane) fractal
by Hal Lane 19 Sep '06

19 Sep '06

Jim Muth in a 7th of Oct. 2003 correction says, "The 'Projective Plane' fractal appeared on Jan. 6, 1998." (not Jan. 1, 1998 as I quoted from the "[Fractint] Classic FOTD 01-01-98 (Projective Plane)" post also from 7th of Oct. 2003.) If I had read down a little further in the list of postings I would have found this exchange: On 7 Oct 03, at 15:29, Jim Muth wrote: > At 11:23 AM 10/7/03 -0500, you wrote: > > Paul Lee wrote: > > >> Classic F.O.T.D., January 01, 1998 (Projective Plane) > > > >Actually, The above date and fractal name did not > >originally get used together many years ago on the > >"Fractal-Art" List. > > > >Though I am sure this was an accidental mistake by Jim, I > >would hate to see this List end up like a couple of > >others I know of, where the participants try to alter > >history whenever they wish. ;-} > > Lee is right; history is safe. I made a mistake -- most > likely the first of many. The 'Projective Plane' fractal > appeared on Jan. 6, 1998. The fractal of 01-01-98 was > named "Snub-Nosed Midget", an image that I considered but > did not use. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.405 / Virus Database: 268.12.5/450 - Release Date: 9/18/06

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Re: Fractint Digest, Vol 43, Issue 9
by jackoftradez＠comcast.net 19 Sep '06

19 Sep '06

Someone named Vortex Swirling (what is this guy a freakin' tornado or something?) wrote: ""Question is, you stayed in the spirals long enough to discover this. Fortunately you did. But what led you to do that? "" I think I mentioned in my post that this was a Muth FOTD recenty posted, it looked cool so I did a zoom-in and made the discovery. Damien - Thanx for the explanation / info. I didn't know that! I always thought all the spirals were infinite. You can spend a lifetime exploring this little Z^2+C thing. Stay Amazed JoTz

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FOTD 19-09-06 (Rectangle Variation [6])
by Jim Muth 19 Sep '06

19 Sep '06

FOTD -- September 19, 2006 (Rating 6) Fractal visionaries and enthusiasts: Today's image is a variation of the curious rectangle in a Julia set of East Valley of the large midget on the infinitely-split negative X-axis of the Z^(2.003)+C Mandeloid. One day quite a few years ago, I stumbled upon this rectangle, which still remains the most surprising discovery of all my fractal explorations. The rectangle is impressive even in its pure form, but to add interest I have given it a slight transla- tion and rotation, reducing it to the shapeless yet interesting mass featured in today's image. I named the image "Rectangle variation", which is what it is. I rated it at a 6, which is what I feel it is worth. The render time of 2 minutes on my tired old machine should try the patience of no one. For convenience the finished image is posted to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> An absolutely perfect day here at New Fractal Central, with full sun and a temperature of 81F 27C, went unappreciated by the fractal cats, who passed the afternoon sleeping and playing. With not too much work to do, I enjoyed the day a bit more than the cats. I hope to enjoy tomorrow as much as today. The next FOTD will appear in 24 hours. Until then, take care, and be careful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= RectangleVariation { ; time=0:02:06.72--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=1 center-mag=0.00876166/0.00777778/26.82512 params=91.81/90.94/91.93/89.48/-1.7435/3e-005/0.00\ 019/0.07388/2.003/0 float=y maxiter=1000 inside=bof61 logmap=51 periodicity=10 colors=000000000000000000100900H00P00Y04g19p6Ex9Kz\ EPzKUzP_zUez_jzbpzjK_r00x01z01z04z14zH6zU6zg9zx9zz\ CzzCzzzj040zP0zg0zz0xz0rz0mz0ez0_z4Uezzbzzbzz_zz_z\ zYzzYzzUzzUzzSzzSzzSzzPzzPzzMzzMxzKuzKrzHrzHpzEmzE\ mzEjzCgzCez9ez9bz6_z6_z4Yz4Uz4Uzxrzzzzzzzzzzzzzzzz\ zzzzzzzzxzxrzupxujrremp_gpUbmSYjMSjHMgCHe9Ce46b01_\ 00_00Y00U00U00S00P00P00M00K00K00M00P00P00S00U00U00\ Y01Y06_0Eb0Kb1Se4Yg9egEjjKpjMxpHzrEzu9zx6zz1zz0zz0\ zz0zx0eu0Hr00p00m00g00b10Y60SC0MH0HM0CS06Y01b00j00\ p00u00z00z00z00z00z00z00zz00z00z00z00z60zK0zY0zj0z\ x0zu0zr0zr0zp0zm0zm0zj0zg0zg0ze0zb0zb0z_0zY0zY0zU0\ zS1zS4zP6zM9zMCzKEzKEzHCzC9z96z44z14z09z0Cz0Eu0Hp0\ Kj0Pe0S_0UU0YP0_K0bE0g90j40m00p00r00u00r10r90rE0pK\ 1pS9pYHmbPmjUmpbmujjzrjzxjzzgzzgzzgzzgzzjzzmzzpzzr\ zzrzzuzzxzzzxzzrzzpxzmxzguzerz_pzYmzSjzPgzMezHbzE_\ z9Yz6Uzz6zz9zzCzzCzzEzzEz } frm:SliceJulibrot4 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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re: FOTD 06_07_31
by Vortex Swirling 18 Sep '06

18 Sep '06

>I have not explored much East ("elephant") valley, thinking it would >be generally lame, as some earlier work suggested a long time ago. >Not true! Among other things, it seems to be the only area of the >MSET where the "infinite" spirals are NOT! They actually eventually >arrive at something, usually a minibrot. And some interesting unique >patterns too. I need to check more into this. This is very cool. I saw both a two way and four way division occur. Question is, you stayed in the spirals long enough to discover this. Fortunately you did. But what led you to do that?

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FOTD 18-09-06 (The Depths of Despair [7])
by Jim Muth 18 Sep '06

18 Sep '06

FOTD -- September 18, 2006 (Rating 7) Fractal visionaries and enthusiasts: I promised that September would be a month without a quadratic Mandelbrot midget. And my promise remains unbroken. Yes, I realize that a hole of sorts must lie at the center of today's image, but it is totally invisible, lying far beyond the range of conventional math, and even if we could reach it, the midget would look nothing like a miniature Mandelbrot set. The scene is located in a twisting and spiraling, cut-off fila- ment of the Z^(1.15)+C Mandeloid as it appears 115 levels up the logarithmic ladder. Midgets are quite difficult to find in Mandeloids of such a low order, and were it not for the 'fmod' inside fill, I would likely have never found the one that lies invisibly at the center of today's image. I named the image "The Depths of Despair". After all, I know of no law that says fractals must always be cheerful. The image is really not all that gloomy however. True, it holds a lot of blue, but the brilliant white highlights add a kind of sparkling vivacity that chases away the blues and brings a ray of hope. The rating of 7 reflects how I feel about the image. The extra effort I put into the coloring raises the otherwise average scene to an above-average one. The render time of 4-3/4 minutes may be eliminated by going to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and viewing the image there. A damp and foggy morning gave way to a brilliantly sunny after- noon here at New Fractal Central on Sunday. The temperature reached 77F 25C, but the fractal cats were more interested in finding mischief than watching the weather. Cassie managed to overturn a waste basket and spread the contents across the floor. And I'm not so sure Nicholas was as innocent as he pretended. My day was pleasantly quiet. Hopefully, more of the same will follow. The next FOTD is near certain to follow in 24 hours. Until then, take care, and be at one with the object of your choice. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= TheDepthsOfDespair { ; time=0:04:45.83--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC2 passes=1 center-mag=-0.78107692488533510/-2.839509333090241\ 00/4.341345e+011/1/7.49828937455790534/0.001459075\ 1429640683 params=1.15/0/115/0 float=y maxiter=1200 inside=0 periodicity=10 mathtolerance=0.05/1 colors=00083i82e92`91X91SA0OzzJuatnWngRh`LbUGXNARG\ 5LCozBdpBVfAKYAAO_fFYcFXaFVZFUXFSVFRSFPQFONFNLFLJF\ KGFIEFHBFF9FE7FC4FB2Fjh3he4fc5d`5bZ6`X7ZU7XS8VQ9TN\ 9RLAPIANGBLECJBCH9DF7ED4EB2F5Iw6Ht6Gr6Fp6En7Dl7Dj7\ Ch7Bf8Ad89b89`88Z87X96V95T94R94PA3NA2LA1JaNDdRGfUI\ hYLk`NmcPogSqjUtmWvqZxt`zwbtwcowdiwddwe_wfUwfPwgKw\ hEwh9wi4wi5qeA1F6kb6e_7_X7UU8OR9IO9CLA6IOE2ND3MC4L\ B5LB5KA6J97I87I88H79G69F5AF5BE4BD3CC2DC2DB1EA0F3ot\ 4io5dk6_g6Vc7Q_8KV8FR9ANA5JUDBQACN8DK6DG4ED2FBDjAB\ fAMhRQvA7YA6NA5RA3OA2LA1IE9cD8_D7WC6SC5PC4NB3MB2MA\ 1KA0Hzzzvwhildcg_YVWSNSMFNG7JOB4NA5M96L87K78J78I69\ H5AG4BF3CE3CD2DC1EB0FmzUPzQmzMFFIupYqkWmgVicTf_SbW\ QZSPWONSKMOGKLzJH8HD4GolQieOcZMYSLSLJMzIG7GcFuaEr`\ DpzznzzlWBjVzhUAfzzdR8bP7`O7ZzzXL5VK5TzzRH3PF2NE2L\ C1JB0HoKxfGnZCeQ8XI4OvwWooTihRc`PYUNSMLMFJG7HeuobJ\ iYGdUD`QAWM8SI5NE2J74s83n } frm:MandelbrotBC2 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*floor(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|<a } END PARAMETER FILE=========================================

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FOTD 17-09-06 (Fractal of Tomorrow [8])
by Jim Muth 17 Sep '06

17 Sep '06

FOTD -- September 17, 2006 (Rating 8) Fractal visionaries and enthusiasts: Today's image takes us to the East Valley area of the large midget on the complex negative X-axis of the Z^2.003 Mandeloid. This is the area that looks like a railroad switching yard and holds the curious Julia rectangle that I have featured so many variations of as the FOTD. We examine one of the holes found there. But today's image is not a Julia set, nor is it a Mandelbrot midget. It is an oblique view of a random hole, seen in one of the countless double rotations half way between the Parabolic and Rectangular directions. Double rotation is necessary to turn from one of these orientations to the other, since, like the Julia and Mandelbrot orientations, their planes intersect in only a single point. I named the image "Fractal of Tomorrow". This does not mean it will appear a second time tomorrow; it means I rather consider such images to be ahead of their time. Then again I have heard it claimed that, since I am still using a DOS fractal program, my fractals are behind the times. Regardless, I admire today's image, and have rated it at an 8 accordingly. The render time of just under two minutes on my 10-year-old computer will be cut to under one minute on the latest DOS-able fireballs. But some current fireballs that choke on DOS will take all eternity to finish the calculation. Those with such uptight machines can still view the image by going to the FOTD web site, where it is posted. They will also find this discus- sion posted there in annotated form. The FOTD web site can be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Slowly clearing skies and a temperature of 75F 24C made condi- tions quite pleasant here at New Fractal Central on Saturday. The new fractal cats were not concerned with the weather. They cornered some invisible critter in the kitchen pantry and kept watch over it for most of the afternoon. The thing that was annoying them must have escaped, for they had totally forgotten it by treat time. My day featured back-to-normal conditions, which I hope will continue indefinitely. The next FOTD image will appear in 24 hours. Until then, take care, and try to help a fractal in need. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= FractalOf_Tomorrow { ; time=0:01:56.11--SF5 on a P200 ; Fractint Version 2004 Patchlevel 1 reset=2004 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000107316850/-0.000000002948506\ 23/1.033237e+007/0.4572/70/3.88578058618804789e-016 params=45/45/2.003/0/-1.74031254055/0.00286902201/\ -1.74031254055/0.00286902201 float=y maxiter=750 inside=0 logmap=73 periodicity=10 colors=000E02H05K18N3BQ5ET7HW9KZBNaEQdHTgKWkNYoQ`s\ TcwWhxZmyarzevzizAAA49D8BHBDLEFOHGSLIWOKZRMbUNfYPi\ `RmcTqfUtcpr`rqZtpWqoUonRlmPilMkkKnjHpiFrhCtgAvfHt\ gNnhTgi_aj`VkaPlWKiWQg`Ved_bie`ijZwnWzqUzqSzpPzpNl\ pLgpJboNZnRUnVQmZLhbHbfDYjKZhRZfYZdddbki`qn_0uR4pT\ 8kUCfWGaXKXYOS_SN`VJaUIbUIcUHdUHeUHfUGgUGhUGiTFjTF\ kTElTEmTEnTDoTDpTDpYEkaFgfGbjGZoHUsIQwIMpJLiJLcJKX\ KKRKJKKJEKJDIICGICEHBCHBAHHCIMEJSGKXILbKMgMNmOOrPP\ sLUtH_uDev9kw5px9nyDlzHjzLizKgzJezJczIazH_zHYzGWzG\ zzLzzMzzMzzNzzNzzNzzKzzHzzFzzCzzAzz9zz8Pz7Lz6HzA8z\ FDzKPzPNzULzZJzcHzhFzmDzrBzv3zz5zz6zz8zz9zzXzzPzzH\ zzqzzvzzezzQzzEzzDzzDzzCzzCzzBzzBzzAzzJzzHzzGzUEzM\ DzDBzM4zJ5zG6zD7zA8z79zTfzHQzEPzCMzBKzAIz8GzzEzzCz\ zizDSzfbz_YzUTzOOzHJzBEzmqzgkzafzX`zRWzLQzGLzAFzON\ zzKzzHzzFzzCzzozzdzzVzzKzzvzNizHYzBMzb2zY3zU4zQ5zM\ 6zH7zD8z99zDNz9GzmUz_WuWW } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END PARAMETER FILE=========================================

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