September 2006 - Fractint - mailman.xmission.com

FOTD 24-09-06 (Forever Rectangular [Not Rated])
by Jim Muth 24 Sep '06

24 Sep '06

FOTD -- September 24, 2006 (Not Rated) Fractal visionaries and enthusiasts: There are six mutually perpendicular planes through every point of the four-dimensional Z^(2.003)+C Julibrot. The strange rectangle that has appeared in the recent FOTD's apparently exists only in the Julia plane, but I wondered how the rectan- gle, or the area in which it lies, would appears in the other five planes. Today's image is a slice through the vicinity of the rectangle in a direction rotated 10 degrees from the Oblate orientation toward the Rectangular orientation. Surprisingly, the rectangle still appears quite clearly at the center of the image. The rectangle is obvious, but its surroundings have undergone a dramatic change. Instead of the converging tree-like features, we have near total chaos -- an image that cannot be described and must be seen to be appreciated. I named today's image "Forever Rectangle". It appears that the rectangle will remain visible regardless of the direction from which it is viewed. I gave the picture no rating. If I had rated it, a score of 6 would have been appropriate. The render time of under 11 minutes is slightly slow. But when the image is viewed on the FOTD web site, rendering is not an issue. The web site may be accessed at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Early morning rain gave way to a partly cloudy and warm after- noon, with a high temperature of 77F 25C. The fractal cats paid no notice. They were too busy chasing each other all around the place. They did not settle down until treat time arrived in the evening. My day was average; tomorrow looks to be a repeat. The next FOTD will appear in 24 hours, when I'll see what other havoc I can wreak on that Z^2.003 rectangle. Until then, take care, and be of sound mind and body, but don't be too strong on the sound. You would not want to disturb the neighborhood. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= ForeverRectangular { ; time=0:10:51.64--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=1 center-mag=-0.00016211607850631/+0.000876409345622\ 04/1359.729/0.01759/-90/79.5200240071283986 params=10/90/0/90/-1.7435/0/0.00019/0.07388/2.003/\ 0 float=y maxiter=15000 inside=0 periodicity=10 colors=000O8tP1yM1vJ1sG1pD1mA1j71g41d11b83_E4XL5VR\ 6SY7Pc8Nj9KpAIlDGiFFfIEbKD_NCXPBTSAQU9NW7JZ6G`5Dc4\ 9e36h23j10l03j15h17g1Ae1Cd1Eb1G`1J_2LY2NX2PV2ST2US\ 2WQ2YP2ZS4ZV6_Y7_`9`cB`fCaiEalGboHbrJcuLcwMZpJVjHQ\ cFMYDISADL89F65948B8BCBDDEGFIIGLLHONISQKVSLYVMaXNd\ _PgaQkdRnfSqkUrpWstYts_rsaprcnrdlqfjqhhpjfpkdomboo\ `nqZnrXknUhjSfgQccO``MZXKWTHTQFRMDOJBLF9JC7HE9GGBF\ ICEJECLFBNHAOI9QK8SM6UN5VP4XQ3ZS2_T7aXBb_GdcKefPgj\ ThmYjqaktbjrbiqbhpbgnbfmbelbdkcdicchcbgcafc`dc_ccZ\ bcZaZH`U0`_EWeSRkeMpsIlqKioMfnNclP`jQYiSVgTSeVPdWM\ bYJaZOcVTdSYeObfLggIlhEqiBuj8tg7se6rc5ra4q_3pY2oW1\ oU0nT3mT5mT7lT9lSBkSDkSFjSHjRJiRLiRNhRPhRRlMSoHTpR\ GpAOrCUsDZtEduFivGowHtxIyuJyrKyoLylMyiNygOyfLteIpd\ FlcChc2cc9dcFecLfHjkNTe76oSC`gNGiKJkHMmFPoCSqAVk9U\ e8U`8UV7UP6TK6TE5T30P95TEAWJFZPKaUPd_VjZUgZTdYSaYR\ ZALnMOeDpMFhSHaYJUcKNhMFn } 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: Fractint Digest, Vol 43, Issue 12
by jackoftradez＠comcast.net 24 Sep '06

24 Sep '06

I am making an animation from these: 6CARPT92 { ; ; t= 0:04:00.90 on a P4 2Gh at ; 1600x1200 Image Copyright 2006 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 4 reset=1960 type=formula formulafile=fractint.frm formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00329066420895892/-0.00013311712830545/\ 277.0445/1/25.0000000000000426/-5.05012698326368081e-\ 014 params=92/92/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=0000Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>\ 8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_\ <3>zb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2\ >I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8x\ u7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq\ 0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>\ F9LAAG7FO4KW } 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=z2.003+c, |z| <= 100 } It's looking awesome - like a comet turning into a flying carpet. Now exactly who gets the credit? Muth? Lane? Skinner? ALL?? JoTz

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FOTD 23-09-06 (Sandstorm Pyramid [Not Rated])
by Jim Muth 23 Sep '06

23 Sep '06

FOTD -- September 23, 2006 (No Rating) Fractal visionaries and enthusiasts: Today's scene is a zoom into the 'bof61' chaos that fills the distorted rectangle in yesterday's image. I was curious to see whether the chaos is as complete as it appears. Surprisingly, I found that some order is hidden in the apparent depths of the chaos. True, most of the chaos inside the rectangle simply goes on forever with no signs of order, but mixed in with the total chaos are tiny areas of order, such as those that prevent today's image from being just another screen full of sandy debris. The pyramid on the left side of the frame is mostly obscured by the chaotic haze, but enough of its triangular shape shows through to make the image worth being declared FOTD for Septem- ber 23. The string of sparkling yellow-orange things curving up the right side adds to the interest. Most of the other apparent order in the chaos is an artifact of limited resolution. To add some width to the pyramid and to straighten it, I stretched the image by a factor of 13.7 in the horizontal direction and skewed it slightly to the right. The resulting shape reminds me of the bent pyramid in Egypt, as it might appear in a sandstorm. (The pyramid had to be bent to prevent it from collapsing.) I named the image accordingly. Since the scene lies inside the workhorse Z^(2.003)+C rectangle, and this is about the 20th FOTD trip to the rectangle, I did not give the picture a rating. If I had rated it, a rating of about 7 would have been appropriate. With a render time of 34 minutes, the image is a rather slow one. But those pangs of impatience may be eliminated by going to the FOTD web site and viewing the finished image there. The web site may be found at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Some sun, some clouds and warmer temperatures in the low 70's, around 22C, made conditions quite pleasant here at New Fractal Central on Friday. The fractal cats paid little attention to the weather however. They found enough excitement indoors to keep them fully occupied. My day was busier than yesterday but still slower than usual. All this means that the next FOTD will appear on schedule in 24 hours. Until then, take care, and what additional surprises could lurk in an innocent rectangle. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Sandstorm_Pyramid { ; time=0:34:01.75--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=1 center-mag=+0.00363659192954869/+0.001741560509220\ 49/22401.94/13.698/87.5/0.446164143791587364 params=90/0/89/0/-1.7435/0/0.00019/0.07388/2.0031/\ 0 float=y maxiter=1500 inside=bof61 periodicity=0 colors=0000K70L80M90NA0OB0OC0PD0QE0RF0SG0SH0aQ0kZ0\ cP0WG0wz0RJ0PL0NM0KO0IP0GR0ES0BU09V07X05Y08_2B`5Da\ 8GcAJdXefXfhXgi`daRcgLZdPSXAP_4KX0FV0AS05Q04P03O03\ N00BNTc0LU0LU0LT0WF0VF0VE0VE0VE0VE0VE0VD0VD0VD0VD0\ UC0UC0UC0UC0UC0UB0UB0UB0UBzh00aR0YM0OG0QB0M60J00G0\ 0D00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E\ 00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00E00\ E00E00E00E00E00E00E00E10E10E10E20E20E20E20F30F30F3\ 0G40G40G40H40H50H50I50I50I60J60J60J70J70J70J70J80J\ 80J80J90J90J90J90JA0JA0JA0JB0JB0JB0JB0KC0KC0KC0KC0\ KD0KD0KD0KE0KE0KE0KE0KF0KF0KF0KG0KG0KG0KG0KH0KH0KH\ 0KI0KI0KI0KI0KJ0KJ0KJ0KJ0KK0KK0KK0KL0KL0KL0KL0KL0K\ M0KM0KN0KN0KN0KN0KO0KO0KO0KP0KP0KP0KP0KQ0KQ0KQ0KQ0\ KR0KR0KR0KS0KS0KS0KS0KT0KT0KT0KU0KU0KU0KU0KV0KV0KV\ 0KW0KW0KW0KW0KX0KX0KX0JY0KX0KX0KX0KX0KW0KW0KW0KW0K\ W0KV0KV0KV0KV0KV0LU0LU0LU } 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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Parm file to calculate near-rectangular shape w embedded fractal tree
by Hal Lane 23 Sep '06

23 Sep '06

############################################################## Below is the parm file for calculating the near-rectangular shape that has the embedded fractal tree I referred to in my Sept 19, '06 post. It is a zoom into Jim Muth's Oct 7, '03 FotD (Original date Jan 6th, 1998, often erroneously given as Jan 1st, 1998.) Here is a description of the fractal from my Sept 19, '06 post: >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. Does anyone else think that it is unusual that a particular fractal formed by a simple substitution process could also be created by a complex formula 'finding' it hidden at a very specific location and rotation in the four-dimensional Julibrot? <---<< You can calculate it at a lower resolution than 1600 x 1200 to keep it from taking 52 minutes -- as it did on my P400. - Hal Lane ######################### # hallane(a)earthlink.net # ######################### START PARAMETER-FORMULA FILE================================ Projective_PlaneC { ; Hal Lane Sep22,06 51:31 P400 1.6Kx1.2K ; Zoom into Jim Muth's Oct 7, '03 FotD, ; the 'rectangle'. Shows a tree-like ; branching pattern a la substitution ; fractals like Koch snowflake. ; reset=1960 type=formula formulafile=pastengo.par formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00020758063848563/-0.00003926828671266/90\ 6.3389 params=88/88/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 sound=off colors=000QVZ<2>PXZPYZP_Z<3>PfZPgZPiZPjZPlZPnZRt_<3>PnZ\ PmZPkZ<3>NaZN_ZNYZMVZMTZ<9>KGZJEZJDZ<2>I9ZI8ZJ6a<14>I8S\ I8RI8Q<2>I8OI8NH9KH9IH9HH9IH9IH9HH9FH9FH9H<6>HACHACHAB<\ 2>HA9HA9JCB<2>OIGQJHRMJ<3>YXP__RabSbdUdgVejW<3>lmbnncoo\ eqnf<3>wshxuixwjyylyzm<3>zxjzwizvhzug<3>zshzshyrg<4>uod\ tocsnb<3>ol_mkZkjY<3>chVagV_gUYfTWfS<3>S`PRZOQXNPYN<3>L\ WKKVJJVIIUHHTGGUG<3>I_IJ`IJ`I<32>ZpQ_qR_qR<3>asSXrT<14>\ mtQntQptQ<2>stPttPvvJvuM<3>oqWmpZmqZ<3>moZnoZopZskZwzZz\ wZzwZ } 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: 268.12.7/454 - Release Date: 9/21/06

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Re: Fractint Digest, Vol 43, Issue 9
by Vortex Swirling 22 Sep '06

22 Sep '06

>Someone named Vortex Swirling (what is this guy a freakin' tornado >or something?) Think of me as a fractal spiral. A wisp in the wind. No... less.

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Re: Fractint Digest, Vol 43, Issue 11
by Vortex Swirling 22 Sep '06

22 Sep '06

At 10:27 AM 9/21/2006, you wrote: >When you say "page" I assume you mean a webpage on the hosting site for >Jim Muth's FOTDs ?? If so, try the following URL: > > http://home.att.net/~Fractals_1/FotD_98-04-01.html > > >Later, >P.N.L. Thanks, Paul. I was on that page before but the entry for the 1st wasn't there. Hm... I noticed a lot of entries are missing. For instance there are none for Feb 98, but in the collections they exist. If you are providing these on an as needed basis, do not consider this a request. Observation only. Roger

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FOTD 22-09-06 (Virtually Virtual [Not Rated])
by Jim Muth 22 Sep '06

22 Sep '06

FOTD -- September 22, 2006 (Not Rated) Fractal visionaries and enthusiasts: The day started normally enough on Thursday here at F.C. When I checked my e-mail, I found that I had won three lotteries that I did not buy tickets for, and I also needed to verify my identi- ty for three internet banking accounts that I do not have. One would doubt that anyone would actually fall for these scams, but from the way they keep proliferating, it is hard to believe that they totally fail to catch a few suckers. Maybe I should start selling certified authentic Mandelbrot sets. Today's striking image consists almost entirely of 'inside' stuff made visible by the 'bof61' fill. It is another variation of the strange rectangle in one of the Julia sets of the Z^(2.003)+C Mandeloid. The orientation is rotated only one degree toward the Elliptic plane, but the result is a very unusual variation. The rectangle is not really there. When the inside is set to the normal flat black, there is no sign of the rectangle. It has become a virtual rectangle. But the rectangle was virtual from the start, so now it has become virtually virtual, which is what I named it. The 'bof61' inside fill is not the only one that works with today's image. The 'fmod' fill also works quite well, and the 'zmag' fill works reasonably well also. The other inside fills simply color the inside areas a flat color. I did not rate the image, but if I had, it would probably have earned a rating of 8 or 9. The passes=b option not only works fastest with the image, it is by far the most interesting one to watch in action. The render time of 9-1/2 minutes will be irrel- evant if the image is viewed on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies and a brisk high temperature of 68F 20C made things reasonably pleasant for the fractal cats, who spent the day indoors, unconcerned with the outside conditions. The light work load made my day pleasant also. The next FOTD will appear in 24 hours. Until then, take care, and if someone offends a fractal, expect no violent protest. Fractals are very peaceful. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Virtually_Virtual { ; time=0:09:24.40--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=b center-mag=-0.00368788/0/42.12754 params=90/0/89/0\ /-1.7435/0/0.00019/0.07388/2.0031/0 float=y maxiter=1500 inside=bof61 periodicity=0 colors=000wwwzzzzzzzzzpvxfnsjdrP_kHTf8Lc1FZ09X08V4\ 7U88S00CE7PH5PL4OP4NV4N00Bf4Mk5Nf5Nc6N`6O60BU7NR7N\ M7MK7OJ9O3A`FBPDCPBBR7BR5CR1C`0CS0CS0BV0BX0BY0Ae0A\ b0Ac0Af09h09i08m09n18p18x17u28w26r37z38x27r27u27s1\ 7n27p28p18k17m18k17i17h18h07b07e08cM8b07`07`77R55S\ 74OU2V91GB0DD0AG08J05`0MP01R02M12S23U54g5GV85V95SA\ 5XC5YE5hM5ZH7`J7YK6bN7bO7hS8cS8eV9bW8fY9fZ9kXAhbAi\ cAidCkfCkgCmaDiiDikDimFinFipFpeFisHiuHhwIhxIizJvbH\ frKemLeiNdfNcbOicQcZRcXTcWUcWWbXYg__ZXYYYYYYYZYZ`_\ bkZc`_e`ah_`i_`mZanY`rWasVbwUbxUbzGae7hP0iB0n00c44\ VAAMFo`ILDPT6Ya0ej0mf2heccbG_`OYYXXXXWZeUZnRYxOYzN\ YzOZsQYmRYeTWZTUUUVUVVOUXJWXDXY8ZY3`xpzunzrlxpkumi\ rjgnigkedhccebbbZZZXXXUUURRROOOOOOMMMJLJGLHFJGCIDA\ IA8H85G54G33H42I51J61L71M80M90OA0PB0RC0SD0UE0UG0VG\ 0XI0YJ0ZK0ZL3nZDzm4rZ0eL0`N0YO0VQ0SQ0PU1NV2KY3JZ3G\ b5Ec7Df7BhBGkFJmJNnOSrQVs } 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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Rough Explorations of rectangle parameters
by Lee H. Skinner 21 Sep '06

21 Sep '06

I zoomed out a bit from Jim Muth's Projective Plane image of Jan. 1, 1998, and did a sequence of 7 images (parameters from 80/80/ to 92/92), with different colors: 6CARPT80 { ; ; t= 0:19:07.43 on a P4 2Gh at ; 1600x1200 Image Copyright 2006 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 4 reset=1960 type=formula formulafile=fractint.frm formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00329066420895892/-0.00013311712830545/\ 277.0445/1/25.0000000000000426/-5.05012698326368081e-\ 014 params=80/80/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=0000Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>\ 8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_\ <3>zb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2\ >I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8x\ u7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq\ 0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>\ F9LAAG7FO4KW } 6CARPT82 { ; ; t= 0:15:05.34 on a P4 2Gh at ; 1600x1200 Image Copyright 2006 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 4 reset=1960 type=formula formulafile=fractint.frm formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00329066420895892/-0.00013311712830545/\ 277.0445/1/25.0000000000000426/-5.05012698326368081e-\ 014 params=82/82/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=0000Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>\ 8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_\ <3>zb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2\ >I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8x\ u7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq\ 0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>\ F9LAAG7FO4KW } 6CARPT84 { ; ; t= 0:13:34.87 on a P4 2Gh at ; 1600x1200 Image Copyright 2006 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 4 reset=1960 type=formula formulafile=fractint.frm formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00329066420895892/-0.00013311712830545/\ 277.0445/1/25.0000000000000426/-5.05012698326368081e-\ 014 params=84/84/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=0000Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>\ 8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_\ <3>zb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2\ >I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8x\ u7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq\ 0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>\ F9LAAG7FO4KW } 6CARPT86 { ; Flying Carpet ; t= 0:06:36.07 on a P4 2Gh at ; 1600x1200 Image Copyright 2006 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 4 reset=1960 type=formula formulafile=fractint.frm formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00329066420895892/-0.00013311712830545/\ 277.0445/1/25.0000000000000426/-5.05012698326368081e-\ 014 params=86/86/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=0000Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>\ 8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_\ <3>zb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2\ >I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8x\ u7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq\ 0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>\ F9LAAG7FO4KW } 6CARPT88 { ; ; t= 0:04:38.97 on a P4 2Gh at ; 1600x1200 Image Copyright 2006 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 4 reset=1960 type=formula formulafile=fractint.frm formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00329066420895892/-0.00013311712830545/\ 277.0445/1/25.0000000000000426/-5.05012698326368081e-\ 014 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=0000Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>\ 8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_\ <3>zb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2\ >I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8x\ u7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq\ 0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>\ F9LAAG7FO4KW } 6CARPT90 { ; ; t= 0:06:21.23 on a P4 2Gh at ; 1600x1200 Image Copyright 2006 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 4 reset=1960 type=formula formulafile=fractint.frm formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00329066420895892/-0.00013311712830545/\ 277.0445/1/25.0000000000000426/-5.05012698326368081e-\ 014 params=90/90/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=0000Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>\ 8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_\ <3>zb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2\ >I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8x\ u7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq\ 0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>\ F9LAAG7FO4KW } 6CARPT92 { ; ; t= 0:04:00.90 on a P4 2Gh at ; 1600x1200 Image Copyright 2006 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 4 reset=1960 type=formula formulafile=fractint.frm formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00329066420895892/-0.00013311712830545/\ 277.0445/1/25.0000000000000426/-5.05012698326368081e-\ 014 params=92/92/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=0000Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>\ 8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_\ <3>zb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2\ >I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8x\ u7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq\ 0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>\ F9LAAG7FO4KW } 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=z2.003+c, |z| <= 100 }

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Re: 4th dimension rotations
by jackoftradez＠comcast.net 21 Sep '06

21 Sep '06

Along with a currently ongoing discussion here, a bunch of PARS were recently posted of this type: 6CARPT80 { ; ; t= 0:19:07.43 on a P4 2Gh at ; 1600x1200 Image Copyright 2006 ; by Lee H. Skinner ver=2004 ; Fractint Version 2004 Patchlevel 4 reset=1960 type=formula formulafile=fractint.frm formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00329066420895892/-0.00013311712830545/\ 277.0445/1/25.0000000000000426/-5.05012698326368081e-\ 014 params=80/80/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 colors=0000Qc<3>5Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<\ 3>civflvinvlqvotvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>\ 8JP8FL8CI<4>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW\ `BYcC<3>hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_\ <3>zb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8KJ8<2\ >I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriAtm9vq8x\ u7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px8Rx7S<3>z5\ _<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0BO0G<3>g0Ul0Xq\ 0`v0d<2>y0fz0gy0h<3>u1mt1ns1or2q<2>v2u<3>c5eZ6`U6X<2>\ F9LAAG7FO4KW } with variations of the 80/80 parameters. The problem is this: formulaname=multi20031 It isn't there (or maybe I just missed it), and I need it to checkout these images. Can someone post (repost) it please? Thanx JoTz

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FOTD 21-09-06 (Starring a Rectangle [NO])
by Jim Muth 21 Sep '06

21 Sep '06

FOTD -- September 21, 2006 (Not Rated) Fractal visionaries and enthusiasts: Since September is a month with no minibrots, I have decided to spend a few days manipulating the mysterious rectangle in the Z^(2.003)+C Julia set. To see the rectangle in its pure form, bring up the julzpower formula, set the value of C to -1.7435,0 and the exponent of Z to 2.003. Then go to the F6 screen and set the center point to 0.00019,0.07388, set the magnitude to 125 and strike the 'enter' key twice. A few minutes later a most unusual fractal will fill the screen. This empty rectangle and its incredible variations will be the subject of the next few FOTD's. Don't be deceived by the emptiness inside the rectangle. The empty area is paper thin and lies exactly in the Julia orienta- tion. Even the slightest variation of the imaginary part of C totally destroys the perfect rectangular shape and fills the empty area with detail. In today's image I have added a tiny imaginary part to the exponent of Z rather than to initial C. This tiny change has not only broken up the rectangle and filled it with intricate detail, it has rotated the rectangle. I named today's image "Starring a Rectangle", and why not? The rectangle certainly is the star of the show. I have featured this same fractal object so many times that I could not give today's version a rating, but the image certainly is worth the 2-1/2 minutes required to render the scene from the included parameter file. Rendering can be a nuisance on over-qualified machines. Those with such units may view the rendered and dismembered rectangle on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Mostly cloudy skies, gusty northwest winds, and a temperature of 66F 19C here at New Fractal Central on Wednesday made conditions a bit brisk for the fractal cats -- not that it worried them. They spent the afternoon inside, getting into trouble. The mischief peaked when Cassie tried to climb the living room curtains to catch a fly on the ceiling and ended up on the floor with the drapes on top of her. Oh well, it's a cat's duty to get into trouble. In my department, the work remained on the slow side, which means the fractals were on the fast side. More of the same is expected tomorrow, so I can see no reason the FOTD will not appear on schedule. Until then, take care, and who knows what might come next? Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Starring_Rectangle { ; time=0:02:29.46--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=SliceJulibrot4 passes=1 center-mag=+0.00020125342561368/-0.000100679231968\ 01/92.98646 params=90/90/90/90/-1.7435/0/0.00019/\ 0.07388/2.003/3e-005 float=y maxiter=1500 inside=0 logmap=51 periodicity=10 colors=0002Qk2Qj2Qi2Qh2Qg2Pf2Oe2Nd2Mc2Lb2Ka2J`2I_2\ HZ2GY2GX2GX2FW2FW2FV2EV2EU2DU2DT2DT2CS1CS1BR1BR1BQ\ 1AQ1AP1AP1AO1AO1AN1AN1AM1AM1AL1AL1AK1AK1AJ1AJ1AI1A\ I1AH1AH1AG1AG1AF1AF1AE1AE0AD0AD0AC09C09B08B08A08A0\ 79079078068067057056056045045034034033023022012000\ 000000000000000000000000000000000000000000c`Ab_9cZ\ 9cZ9cY9cY9cX9cX9cW8cW8cV8cV8cU8cU8cT8cT7cS7cS7rR7r\ R7rQ7rQ7rP6rP6rO6rO6rN6rN6rM6rM6rL5rL5rK5wK5zJ5zJ5\ zI5zc4zc4zc4zc4zc4zc4zc4zc3zc3zc3zc3zc3zc3zc3zc3zc\ 2zc2zc2zc2zc2zc2zc2zc1zc1zc1zc1zc1zc1z41z30z30z20z\ 20z10z10z00zF4zE3zE3zE3zE3zE3zE3zD3zD3HmzHmzGmzGmz\ GmzGmzGmzFmzFmzFmzFmzFmzEmzEmzEmzEmzEmzDmzDmzDmzDm\ zDmzCmzCzzCzzCzzCzzCzzBzzBzzBzzBzzBzzAzzAzzAzzAzzA\ zz9zz9zz9zz9zz9zz8zz8zz8zz8zz8zz7zz7zz7zz7zz7zz7zz\ 6zz6zz6zz6zz6zz5zz5zz5zz5zz5zz4zz4zz4zz4zz4zz3zz3z\ z3zz3zz3zz3zz2zz2zz2zz2zz } 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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