May 2011 - Fractint - mailman.xmission.com

<Mike> I enjoyed your: Many Happy Buggy image.
by Hal Lane 16 May '11

16 May '11

Mike, I enjoyed your: Many Happy Buggy image. Thanks for posting the link! "I was looking around in Jim Muth's FOTD for May 15, 2011 and I found a lot of interesting stuff. There was one area that looked kind of like an airplane wing. I kept adjusting things until it turned into an insect. The name Many Happy Buggy is a play on Jim's Many Happy Returns. The find was too lucky to only be seen once, so I decided to post it. Here is a link to a web page with an image: http://www.fracton.org/fmlposts/many_happy_buggy.html " - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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FOTD 16-05-11 (Demon of the Dark [8])
by Jim Muth 16 May '11

16 May '11

FOTD -- May 16, 2011 (Rating 8) Fractal visionaries and enthusiasts: The version of today's discussion posted on the FOTD web site contains mature material about things that those with delicate constitutions may prefer to avoid thinking about. In keeping with the theme of grimness, today's image is a dark one indeed, which I named "Demon of the Dark". It features two glowering demonic-green eyes glaring from the surrounding dark- ness, which itself appears to seethe with unimaginable sinister activity. Actually, the two eyes are two different types of order 3.5 minibrots lying in the positive X-axis area of the (-Z)^(3.5)+C Mandeloid. The rating of an 8 might be a bit liberal, but the image went along with my mood of the day so well that I might have exaggera- ted the rating a bit. The calculation time of 2-1/3 minutes borders on slowness. The nuisance of calculation may be avoided however by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Or in hi-def at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The entire library of FOTD's prior to November, 2010 may be accessed at: <http://www.Nahee.com/FOTD/> Heavy clouds with showers of rain and occasional threats of thunder made Sunday less than ideal for outdoor activities here at Fractal Central. The fractal cats, perhaps picking up the overall gloomy feeling, spent most of the day sleeping and the rest of the day confronting a stray tomcat who found shelter on the back porch. I, the fractalist, made the best of things. FL, the gardener, spent the day working her garden, looking for all the world like a mud-nymph. The next FOTD, almost certainly a cheerier one, will be posted in 24 hours. Until then, take care, and when things go wrong, search for the bright side of things. If there is no bright side to be found, start complaining. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Demon_of_the_Dark { ; time=0:02:23.57-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=MandelbrotMiN passes=1 center-mag=+0.8042605183881186/+0.0001065300352297\ /1.099e+007 params=3.5/0/0/0/0/0 float=y maxiter=2200 inside=255 logmap=219 periodicity=6 colors=0002W_3W`3V`3Va3Ub3Uc4Tc4Ud4Te4Tf4Sf5Tg5Sh5\ Si5Ri5Sj5Rk6Rl6Ql6Rm6Qn6Qo7Po7Qp7Pq7Pr7Or8Os8Nt8Nu\ 8Mu8Mv9Lw9Lx9Kx9Ky9Jz9Jz8Ky8Lx8Lw8Mv8Mu8Nt8Ns8Or8O\ q8Qp8Qo7Sn7Sm7Um7Ul7Wk7Wj7Yi7Yh7Zg7Zf7`e6`d6ac6ab6\ ca6c`6d`6e_6eZ6fY6fX6hW5hV5iU5iT5kS5kR5lQ5lP5mO5cO\ 5cN5cM4cL4cK4cJ4cI4cH4cG4cF4cE4cD4cC4cB4cB3cA3rA3p\ A3o93n93l93k93i83h83g80f1ce8cd7cc7ca7c`7cZ6cY6cX6c\ V6cU5z05z05z04z04z04z04z03z03z03z03z02z02zC2zB2z91\ z81m61m51c40c20c10jYfhXdgWccVbcUacT`cT_bSZaRY_QXZP\ WYPVXOUWNTVMSULRTLQRKPQJOPINOHMNHLMGKLFJKEIJDHHCGG\ CFFBEEADD9CC8BB8AA798687576465454343232121016E9497\ 375253121QOWPSnPRmOQlOUkNUjNTiNSiMWhMVgLVfLUeKTdKS\ dKRcJRbJQaIP`IO_ID_HXUHWUGVXGUWFUVFTVFSUERTEQSDQRD\ PQDOQCNPCMOBMNBLMAKLAJKAIK9IJ9HI8GH8FG7FF7EF7DE6CD\ 6BC5BB5AA59A48947837736625524523413312201100000000\ 0000000000000000000000cz0 } frm:MandelbrotMiN {; Jim Muth b=p1, z=p2, c=p3+pixel: z=(-z)^(b)+c, |z| <= 16 } END PARAMETER FILE=========================================

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Many Happy Buggy
by Mike Frazier 15 May '11

15 May '11

I was looking around in Jim Muth's FOTD for May 15, 2011 and I found a lot of interesting stuff. There was one area that looked kind of like an airplane wing. I kept adjusting things until it turned into an insect. The name Many Happy Buggy is a play on Jim's Many Happy Returns. The find was too lucky to only be seen once, so I decided to post it. Here is a link to a web page with an image: http://www.fracton.org/fmlposts/many_happy_buggy.html The parameter file used to make this image is below: Many_Happy_Buggy { ; Exported from Fracton. ; Many_Happy_Buggy by Mike Frazier ; Based on Jim Muth's FOTD for ; 20110515 Many_Happy_Returns reset=2004 type=formula formulafile=fracton.frm formulaname=SliceJulibrot5 passes=1 float=y center-mag=-1.746310973822129/6.542081035442777e-0\ 9/296296.3/1/-90/0 params=0/0/0/0/0/0/0/0/2.0035/0 maxiter=1500 inside=0 logmap=62 periodicity=6 colors=000HEWCAO87G438fGaWCSL8JA490000000000000000\ 000000000000000000FG0AB055IcM9KBixhGXLAME5B7gSg_N_\ TITMEME9E747q25JqSC_I6I9j8hd7bZ6XT5SN4MH3GB2B5150r\ i0g_0XR0MI0B92bR1JDaOIVKFPGCJC9C866436jdWP6LG4A82O\ TLKOIHKFDGCeHKgEGiBCk88fABbBDZCFVDHQEKMFMIGOEHQiUF\ mj5tm8jgBk_ElZGkaIkdJjgLjjMimOipPhsRhvSbuVXtYSs`Ms\ cGrfBqi5pl0poOMvPSrQYnRbjShgTmcUs_UxXTmXTcXTUXTKXT\ AXQQcNejLtpMqqNnrOksOhsPetQbuQ_uSXtUVtWSsYQs_Nr`Lr\ 8X3AZAC_HDaOFbVHdaIehKgoLhvQcvV_vZWvcRvgNvlJvpFvjD\ qeBm`9hW8dQ6`L4WG2SB1O75L48J1BHSCOrDUhAP_8KR6FI4A3\ 10925`jcOVQCFDm3Kc2GU1CK18A041cM0QE0D7xv7pn6hg5a_4\ UT3MM2FE1770nholvM_gGOTBCE5sbmiWd`QXSJPIDG968ApC8g\ A6Z85Q63H4182GwmDneBeZ9YS6PL4HE287gY1h0k`0cU0cM0cF\ 0m70muDmgJm`GmVDmPAmI8mC5m62mhz5_z4Rz3Iz29z1GzVAzK\ 5zAtzRlzNezKZzGSzDLzAEz67z3zzwzzUzzszzkzzczzWzzOzz\ Gzz8zzhzzXzzMzzBzzszzkzzc } frm:SliceJulibrot5 { ; draws all 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),esc=imag(p5)+9, c=p+flip(q)+p3,z=r+flip(s)+p4: z=(-z)^(real(p5))+c, |z|<esc } -- Mike Frazier www.fracton.org

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FOTD 15-05-11 (Many Happy Returns [6])
by Jim Muth 15 May '11

15 May '11

FOTD -- May 15, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's discussion is brief because an antiquing trip did happen on Saturday. The image turned up when I decided to see if any rectangles exist in the (-Z)^(2.003)+C Mandeloid. I found no rectangles but I did find some interesting other stuff. Today's image is a sample of that 'stuff'. Most of the effect is due to the high-contrast color palette. It takes more than sharp colors to create a great fractal however, so I could rate the image no higher than a 6. The name "Many Happy Returns" has nothing to do with the image. In fact, I have no idea why I chose it. The words just kind of popped into my head when I shut off everything else. The included parameter file calculates in one minute. Those who do not calculate will find the finished image posted at: <http://www.crosscanpuzzles.com/Archives.html> The image is available in high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site with the entire library of past FOTD's is at: <http://www.Nahee.com/FOTD/> My plans are to eventually post all the past images on my own web site, but judging from the way things are presently going, I may never finish the job. Heavy clouds and a temperature of 63F 17C cast a pall over Fractal Central on Saturday. The rain was barely enough to dampen the sidewalk, but it did dampen the spirits at the fair for the benefit of the local volunteer fire company. The fractal cats, who were left alone all afternoon, had their spirits dampened also, and gave the humans a sound scolding when they returned. The next FOTD will be posted in 24 hours. Until then, take care, and some claim that everything is a dream. If this is so, then who or what is the dreamer? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Many_Happy_Returns { ; time=0:01:06.24-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 center-mag=-1.746803722\ 297722/+0.00001106402990913/2.52e+007/1/-57.5/0 params=0/0/0/0/0/0/0/0/2.003/0 float=y maxiter=1500 inside=0 logmap=198 periodicity=6 colors=000HEWCAO87G438fGaWCSL8JA49ipk8rs1I60D40930\ 411ch0Zb0UX0PS0KM0FG0AB055IcM9KBixhGXLAME5B7gSg_N_\ TITMEME9E747q25JqSC_I6I9j8hd7bZ6XT5SN4MH3GB2B5150r\ i0g_0XR0MI0B92bR1JDaOIVKFPGCJC9C866436jdWP6LG4A82O\ TLKOIHKFDGCeHKgEGiBCk88fABbBDZCFVDHQEKMFMIGOEHQiUF\ mj5tm8jgBk_ElZGkaIkdJjgLjjMimOipPhsRhvSbuVXtYSs`Ms\ cGrfBqi5pl0poOMvPSrQYnRbjShgTmcUs_UxXTmXTcXTUXTKXT\ AXQQcNejLtpMqqNnrOksOhsPetQbuQ_uSXtUVtWSsYQs_Nr`Lr\ 8X3AZAC_HDaOFbVHdaIehKgoLhvQcvV_vZWvcRvgNvlJvpFvjD\ qeBm`9hW8dQ6`L4WG2SB1O75L48J1BHSCOrDUhAP_8KR6FI4A3\ 10925`jcOVQCFDm3Kc2GU1CK18A041cM0QE0D7xv7pn6hg5a_4\ UT3MM2FE1770nholvM_gGOTBCE5sbmiWd`QXSJPIDG968ApC8g\ A6Z85Q63H4182GwmDneBeZ9YS6PL4HE287gY1h0k`0cU0cM0cF\ 0m70muDmgJm`GmVDmPAmI8mC5m62mhz5_z4Rz3Iz29z1GzVAzK\ 5zAtzRlzNezKZzGSzDLzAEz67z3zzwzzUzzszzkzzczzWzzOzz\ Gzz8zzhzzXzzMzzBzzszzkzzc } frm:SliceJulibrot5 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=(-z)^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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Recent FOTD's
by Brian Prentice 14 May '11

14 May '11

Jim, Your recent postings have been exceptional. Here are 6 more details from the area you have been describing: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01a.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01b.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01c.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01d.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01e.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01f.png Brian Prentice

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FOTD 14-05-11 (Cubic Action [7])
by Jim Muth 13 May '11

13 May '11

FOTD -- May 14, 2011 (Rating 7) Fractal visionaries and enthusiasts: The classic Mandelbrot set might be the greatest of all fractals, but let's not forget the Z^3+C Mandeloid, the cubic figure, which is almost as great and in addition holds some features with no analog in the classic set. To be honest, the parent fractal of today's image is not exactly the Z^3+C Mandeloid. It is the Z^(3.003)+C Mandeloid. The differences are very small however, and I'm sure that a virtually identical scene could be found in the pure Z^3 set. I stumbled upon the scene by accident while searching for rectangles in the Julia sets. Instead of rectangles, I found today's image, a fair consolation prize. When all the pluses and minuses were figured in, I gave the image a rating of a 7. The name "Cubic Action" needs no explanation. The calculation time of 3-1/2 minutes is a small drag, but why worry about running a parameter file when the finished image may be viewed already calculated on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image is available in glorious high-definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> A heavy gray overcast and temperature of 66F 19C muffled things here at Fractal Central on Friday the 13th. The fractal cats, not believing in bad luck, took things in stride, and worked off their excess energy chasing each other up and down the hallway. The humans had another un-notable day, where everything went along pretty much according to schedule. The next FOTD will be posted in 24 hours. As always, if an antiquing expedition comes up on Saturday, the next FOTD might be late. Until next time, take care, and if the solutions to the world's problems are as simple as some people say, why haven't the problems been solved? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Cubic_Action { ; time=0:03:31.19-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=-1.096032374971432/-0.000000000036281\ 81/6.781329e+011 params=0/0/0/90/0/0/0/0/3.003/0 float=y maxiter=2700 inside=0 logmap=428 periodicity=6 mathtolerance=0.05/1 colors=00090`80a70a90_A0ZC0YD0XF0WG0VI0UJ0TL0SM0RN\ 0QO0PO0PP0PP0OP0OQ0OQ0OQ0NR0NR0NR0NO0QL0SI0UF0WC0Y\ 90_C0bF0dI0gL0iO0lR0nU0qX0s_0vb0xc0sc0na0j`0d_0__0\ U_0OZ0RX0UU0XR0_O0`K0bG0dC0f80g90i50k10m30n60lD0jF\ 0hH0fJ0dL0cN0cP0bQ0aR0_S0YT0WV0UX0SV0QT0OR0MP0KN0K\ L0KK0KI0KG0KF0KF0KC0KB0KA0KC5PDAUEFZEKcFPhGUmHSlHR\ kIPjJNiKLhKJgLHfMFeNDdNCcRLXVTQZaKbiDfq7bkD_fIW`OT\ WTQRYRU_RW`RYaR_bRacRcdSefSggSihSkiSmjSokSqlQniPlf\ OjdNhaMfZLdXKbUI_RHYPGWMFUJESHDQECOCEQEFSGHTIIVKJW\ MLYOMZQO`SPaUQcWSdYTf_UgaSibQjbPlcNmcModKpdIqdHseF\ teEvfCwfBxfUmiccchhhmmmooorrrtttwwwvwzuuuptpnormqn\ jnkgkhdgeadb_a_TXWMSTFOQHWWJcaLkfOlcQlaTlZVmXXmV_m\ SamQcnOfnLhnJjnHhkFghEffCdcBc`9bZ8c`7da7db7ec6ed6f\ e6ff5gg5gh5hi4hj4ik4il4hm8gmBfmzemzdmzcmzbmzanz`nz\ _nzZnzYnzXnzWnzVzzUzzUzzTzzmzzmzzmzzmzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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<Jim>Is the rectangle somewhere in this image?
by Hal Lane 13 May '11

13 May '11

Jim, You said, in your FOTD -- May 13, 2011 (On-Stage Pyramids): > ...the rectangle is located at the top of the central > pyramid, where it butts against the ceiling. I wasn't able to tell for sure where the rectangle was. I did a zoom into the top of the pyramid in your FOTD. I put it in the file: F110513A.gif on this page: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd_2011_05_May.html or: http://tinyurl.com/top-of-pyramid-in-F110513A Is the rectangle somewhere in this image? - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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FOTD 13-05-11 (On-Stage Pyramids [7])
by Jim Muth 12 May '11

12 May '11

FOTD -- May 13, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows the curious rectangle in its Parabolic aspect. Well, it's not exactly the Parabolic view, since the slice is rotated 30 degrees toward the Julia orientation. It might be difficult to pick out the rectangle at first glance. Actually, the rectangle is located at the top of the central pyramid, where it butts against the ceiling. A good part of the image, including the pyramids, consists of 'inside' stuff made visible by the 'bof61' inside fill. The 'outside' stuff fills the top part of the frame. I named the image "On-Stage Pyramids" when I had the impression of a theater stage filled with living pyramids performing their routine. But performing pyramids can be a rather dull act to watch, so I could rate the image no higher than a 7, which BTW is FOTD average. The calculation time of 2-1/2 minutes may be avoided by viewing the completed image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-fefinition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And the original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> If I had three wishes, and it was forbidden to wish for extra wishes, the first wish would be to gain the ability to visualize the fourth spatial dimension without resorting to the trick of using time as the fourth dimension. I know all the parts of simple 4-D objects such as the hypercube and hypersphere, but even after all these years I am unable to connect the parts into a single hyper-object. Then I wonder how a person would react if they suddenly found themselves with a 4-D body living in a 4-D world. If they could survive the sensory overload, would they recognize the things they previously could picture only one 3-D section at a time? Would they recognize a hypercube or hypersphere, and what about that strange 4-D object with no analog in 3-D space, the 24-cell? How would they cope with the experience of walking on a planet where the horizon appears as a sphere surrounding them in all directions, even the directions we in 3-D space call up and down? Oh well, I guess it's a nice dream. Too bad I'll never be able to fulfill it. It's all very frustrating, so to whom do I complain about this inability to visualize the higher spaces that physicists are now claiming actually exist? Spring was in full swing here at Fractal Central on Thursday, as the temperature reached 79F 26C under bright sun. The fractal cats spent the day chasing the sun around the kitchen floor. The humans had one more in a long series of typical days, which seem to pass with nothing worth telling taking place. It should hardly be necessary to tell that the next FOTD will be posted in 24 hours. Until then, take care, and seek the answer where you least expect to find it. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= On-Stage_Pyramids { ; time=0:02:37.36-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 periodicity=6 center-mag=0/0.00603022/67.66976/0.1261/180 params=-30/90/90/0/-1.7435/0/0.00019/0.07388/2.003\ /0 float=y maxiter=750 inside=bof61 logmap=yes colors=0008FF9EG9EH99NADKADLACMBCNBBOBBPCARCASD9TD\ 9UD8VD5YE7YE7ZF6_F8`DA`FC_HEYIGZKIYLKWNMVPOUQQSSSR\ TTPVUEWWDYYB__A`a8bc7ce5eg4gi3ik1kl0mm0on0qo0sp0uq\ 0wt0zw0zz0zw0zu0zs0zq0zo0zm0zk0zi0zg0ze0yc0xa0w_0v\ Y0uW0tU0sS0rQ0rO0rM0rK0sJ0sI0sH0sF0sE0tD0tC0tB0tA0\ t90t80u70u70u70u70u70u70u70u70u70u70u70u70u70u70u6\ 0u60u60u60u60u60u60u60u60u60v60v60v60v60v50v50v50v\ 50v50v50v50v50v50v50v50v50v50v50v50v40v40v40v40v40\ w40w40w40w40w40w40w40w40w40w40w40w40w40w40w40w40w4\ 0w40w40w40w40w40w40w40t40r50o60m70k80Kb6Kb6Ka6Ka6K\ a6Ka6K`6K`6K`6K_6K_6K_6K_6LZ6LZ6LZ6LY6LY6LY6LX6LX6\ LX6LX6LW6LW6MW6MV6MV6MV6MV6MU6MU6MU6MT6MT6MT6MT6MS\ 6NS6NS6NR6NR6NR6NR6NQ6NQ6NQ6NP6NUUNUUNUUOUUOUUOUUO\ UUOUUOUUOUUOUUOUUOUUOUUOUUPUUPUUPUUPUUPUUPUUPUUPUU\ PUUPUUPUUPUUPUUQUUQUUQUUQUUQUUQUUQUUQUUQUUQUUQUUQU\ UQUURUURUURUURUURUUWC6WB6 } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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<Brian>That's a great set of images!
by Hal Lane 12 May '11

12 May '11

Brian, That's a great set of images! And really super colors, too! Am I correct in assuming that the images are 256 color images? - Hal Lane ######################### # hallane(a)earthlink.net # ######################### ----- You Wrote: ------------------------------ Author: Brian Prentice Date: 2011-05-11 08:53 -400 To: Fractint and General Fractals Discussion Subject: [Fractint] Recent FOTD's Jim, Your recent postings have been exceptional. Here are 6 more details from the area you have been describing: http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01a.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01b.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01c.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01d.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01e.png http://linuxenvy.com/bprentice/Fractals/Set%2016/BP_16_01f.png Brian Prentice ------

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FOTD 12-05-11 (It Has No Symmetry [8])
by Jim Muth 12 May '11

12 May '11

FOTD -- May 12, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a view of the curious Julia rectangle as it appears in the Oblate plane, which is determined by the real(Z) and imag(C) axes. When viewed from this angle and given an appropriate amount of stretching and skewing, the rectangle pretty much retains its rectangular shape. The name "It Has No Symmetry" accurately describes the image. At first glance, the image does indeed appear to have origin symmetry, but a close inspection will reveal small discrepancies. The rating of an 8 could have been a half point or so higher if I had not re-used a previous color palette. The calculation time of 3 minutes is well within reason, but all the fuss and bother that goes with setting up and calculating a parameter file may be forgotten by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The image may be seen in hi-def at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Paul's original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> I find the inability of the human mind to visualize the fourth dimension most curious. Computers have no problem converting the math of the fourth dimension to spatial coordinates and manipulating the resulting spatial figures exactly as they do with everyday 3-D figures. It would even be possible to construct a monitor with a 3-D viewing surface, ready to be enjoyed by a 4-D viewer. Unfortunately, a normal 3-D man with his 2-D retinas would be able to view such a screen only from the 'edge-on' direction and would be unable to enjoy the 4-D show any more than he could enjoy viewing a normal flat screen edge on. Why are we limited to visualizing three dimensions, when such fascinating things as double rotation and undistorted Klein bottles exist only one dimension higher. It is impossible for us to imagine even a 2-D flatland or a 1-D line without automati- cally mentally embedding these lesser spaces in a surrounding 3-D space. The limitation is not due to the math, which merely grows more tedious as the number of dimensions increases, with nothing of a totally new nature appearing. There is a theory, not entirely scientific, that our inability to visualize 4-D figures is a limitation of our level of con- sciousness, which is stuck at the 3-D level. This would imply that a being with a higher level of consciousness might be able to visualize the fourth dimension, or might even interpret the sensory impressions of the world he lives in as possessing four spatial dimensions. If so, he would not be around too long to enjoy his advantage. Stable planetary orbits are impossible in a space of four dimensions with its inverse-cube law, and if our math is correct, a planet in 4-D space would either spiral into its star or spin off into interstellar space. But then again, maybe a 4-D man would have different laws. The days keep getting better here at Fractal Central. Wednesday featured cloudless skies, gentle breezes and a cat-pleasing temperature of 77F 25C. The fractal cats, totally pleased, spent the day sleeping and dreaming of what they might do if they ever get to go outside. The humans had more mundane things to attend to. The next FOTD will be posted in 24 hours. It will likely be another view of the rectangle. There is still much yet to be discovered in the vicinity. Until then, take care, and Nostradamus says the world will end in 589 days. It's got ME worried. I thought we had 5-1/2 billion years. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= It_Has_No_Symmetry { ; time=0:03:04.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0\ /1130/0.02072/0/77 params=0/90/90/90/-1.7435/0/\ 0.00019/0.07388/2.003/0 float=y maxiter=15000 inside=0 logmap=62 symmetry=none periodicity=6 colors=000FDHFDJFELFCNFCPFCRGCSIETKGUMIXOK_QLbSNeU\ OhWQkYSm_ToaUqcTseSugRuiRukQvmPvoOvqOvpStrWst_rvcq\ xhpzmozrpzvszzvzzzzzzzzzzzzzzvzzrzzmzzgzzdzyazxazw\ azw`zv`zu`zt_zt_zs_zr_zqZzqZzpZzoYznYznYzmYzlXzkXz\ kXzjWziWzhWzhWzcSzZOzUKzPGvKCrF8mB5hC8cDBZEEUFHPGK\ OGMRHPUISXJV_KYaK_dLbgMejNhmOkoOmmRkkTjiVhgXgfZed`\ dbbb`daZf_YhZgh_ph_dcTTZMHUF5P99SEDUJHXOLZTO`XN_YN\ ZYNYYNYYNXYNWZNWZNVZNUZNUZNTZMS_MS_MR_MQ_MQ_Q9mQ9m\ P9cP9cO9cOAcNAcNAcMAcMAcLAcLAmKAmKAcJAcJAcIBcIBcHB\ cHBcGBcGCcFDcFEcEFcEGcDHcDIcCJcCKcBKcAKmAKmAKm9Kz9\ Kz8Kz8Kz7Kz7Kz6Kz6D65D65D54D54D53D53D42D42D42D47U8\ CiCHyGGzFGzFGzFGzFGzFGzFFzFFzFFzEFzEFzEFzEFzEEzEEz\ EEzEEzDczDczDczDczDczDczDczDczCzzCzzCzzCzzCzzCzzCz\ zCzzBzzBzzBzzBzzBzzBzzBzzBzzBzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all 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), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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