March 2010 - Fractint - mailman.xmission.com

FOTD 04-03-10 (Half-and Half [7])
by Jim Muth 03 Mar '10

03 Mar '10

FOTD -- March 04, 2010 (Rating 7) Fractal visionaries and enthusiasts: If the Julia set of a Z^(2.003)+C Mandelbrot rectangle is an octagon, what would we see if we checked half-way between the Julia orientation and one of the other orientations -- a hexagon? Actually, when the octagon is double-rotated halfway toward the Mandelbrot direction, it has long since become a perfect rectangle. In fact, it morphs into a rectangle well before the double rotation reaches one degree from the Julia plane. Today's image shows how our Julia octagon appears when its orientation is rotated only 0.000065 degree toward the Rectangular direction. It certainly does not appear as an octagon, though the eight vertices are still vaguely discernible, and it is nowhere near appearing as a rectangle. In fact, it is hard to believe that the weird shape will ever morph into a rectangle. But strangeness is a way of life in the world of fractals, and with quite a bit of stretching and a bit of skewing, the pointed shape in the center of today's image will be a near-perfect rectangle by the time it is rotated to the Oblate direction. The name "Half-and-Half" does not refer to coffee creamer. It means that the shape in the image is halfway between its Julia shape and the Oblate shape. The rating of a 7 is above average, which makes the image's calculation time of just under 2 minutes reasonable enough. The most reasonable way to view the finished image however is to view it on the FOTD web site, which for another 10 days or so may be accessed at both the following addresses: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or <http://www.Nahee.com/FOTD/> Wednesday began with light snow here at Fractal Central. The snow ended by midday, leading to a cloudy afternoon with occasional sprinkles of rain and a temperature of a seasonable 43F +6C. The fractal cats would have preferred more sun, but a special treat of salmon (we were out of tuna) eased their disappointment. My day was normal. FL is still watching the continuing 24-hour earthquake coverage on TV-Chile. (It looks riveting; it's too bad I don't understand Spanish.) If all goes well, and why should it not, the next FOTD will be posted in 24 hours. Until then, take care, and if one wants nothing, he is certain to get everything he desires. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Half-and-Half { ; time=0:01:51.21-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.000001843\ 04564558/-0.00000312570156525/33523.52/1/-120/0 params=89.999935/0/90/0/-1.743397953167458/1.66204\ 6652e-005/0/0/2.003/0 float=y maxiter=1800 inside=0 colors=000pYRr`TsdVthXulZvo`vmavkbvibvgcvedvddvbev\ `fvZfvXgvVhvUhsRiqPioNilKijIihGieDicBia9i_7iZAfZCc\ YE`YGZXJWXLTWNQWPOfQMXVWN_dDdmHYbKRTPXUTaVYfWakX_l\ WYlVWmVUmUSmTQnTOnSNnSLoRJoQHpQFpPDpOBqO9WW8VW7UW7\ TW7SW7RW7QW7PW7OW7MX7JY7DZ8GX8IW8LU8NT8QR8SQAVOEXN\ I_LMaKQaIY_HbYFgWElU9qS5mQ6gP7aO8XN9RLAMKBKJCKIDK9\ 7K11K34K56K78K9AKBCKDFJFHHHJFJLEKNHNMKQMNTLQWLSYKV\ `KYcJ`fJbhIekIhnHkqHnvDmsHlpLlmPkkTkhXje`jcci`giYk\ hWohTsgQwgOzbMuZKpVIkRGfMEaICXEASA9OAANBBLBCKBDJBE\ IBFHBGGe`mZWfTS_NOTHKMLL9JKBHJCFIDDUE1YA2`B3_B4YC5\ WC5UC6SD7RD8PE8NE9LEAJFBHF85L98JAAIACHBEGahXZeVXbT\ U`SSYQPVONTNKQLzNJzLIzIGzbpzXfzRYzzOzzJzzIzzIzzHzz\ HzzGzzGzzFzzEzzFzzFzzFzzFzzFzzFBOFBKFsGAoGBlGBhGCe\ GCaGCZGDVGDSGEOGELGEHGFEGF1sA4iC6_D9QEyFewGduGcsGb\ qGaoG`nG_lGZjGYhGXfGWdGVcGUaGT_GSYGRWGQVGPTGORGNPG\ MNGLLGKKGJIGIGGHmMLnQNoUP } 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 03-03-10 (Octagon Tendencies [!!])
by Jim Muth 03 Mar '10

03 Mar '10

FOTD -- March 03, 2010 (Rating !!) Fractal visionaries and enthusiasts: Yesterday's image showed a Minibrot in the Z^(2.003)+C Mandeloid with strange rectangles surrounding it. Today I checked the Julia set of one of these rectangles. The rating of a !! (double bang) reflects how I felt when I saw the Julia set. Instead of the Julia rectangle, I found a near- perfect octagon. To add to the surprise, the Julia octagon is surrounded by the rectangles that were expected all along. All I can say about the situation is 'who knows what wonders lurk in the hearts of fractals'. I'll check further into this situation tomorrow, and if anything interesting turns up, (most likely it will), it will appear as tomorrow's FOTD image. Today's image is named "Octagon Tendencies". A quick glance at the image will reveal why I chose this name. The calculation time of 2 minutes is well within reason. The trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image is equally reasonable. For the next 2 weeks or so, the FOTD web site can be accessed at both the old address given above and the new address, which is: <http://www.Nahee.com/FOTD/> after that, the old address will be discontinued. Cloudy skies here at Fractal Central on Tuesday were made more pleasant by the relatively mild temperature of 46F 8C. At least the fractal cats assumed it was so as they spent several hours on the window shelf even though no sunlight was falling on it. My day was uneventful though a bit busy. The next FOTD will be posted in 24 hours, come heck or tsunami. Until then, take care, and rational skeptics know they are right. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Octagon_Tendencies { ; time=0:01:59.34-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/30147.06 inside=0 params=90/0/90/0/-1.743397953167458/\ 1.66204665216e-005/0/0/2.003/0 float=y maxiter=1800 colors=000pYRr`TsdVthXulZvo`vmavkbvibvgcvedvddvbev\ `fvZfvXgvVhvUhsRiqPioNilKijIihGieDicBia9i_7iZAfZCc\ YE`YGZXJWXLTWNQWPOfQMXVWN_dDdmHYbKRTPXUTaVYfWakX_l\ WYlVWmVUmUSmTQnTOnSNnSLoRJoQHpQFpPDpOBqO9qN8qN7_P7\ YQ7WR7US7ST7QV7OW7MX7JY7DZ8GX8IW8LU8NT8QR8SQAVOEXN\ I_LMaKQaIY_HbYFgWElU9qS5mQ6gP7aO8XN9RLAMKBKJCKIDK9\ 7K11K34K56K78K9AKBCKDFJFHHHJFJLEKNHNMKQMNTLQWLSYKV\ `KYcJ`fJbhIekIhnHkqHnvDmsHlpLlmPkkTkhXje`jcci`giYk\ hWohTsgQwgOzbMuZKpVIkRGfMEaICXEASA9OAANBBLBCKBDJBE\ IBFHBGGe`mZWfTS_NOTHKMLL9JKBHJCFIDDHE1cA2aB3_B4YC5\ WC5UC6SD7RD8PE8NE9LEAJFBHF85L98JAAIACHBEGahXZeVXbT\ U`SSYQPVONTNKQLzNJzLIzIGzbpzXfzRYzzOzzJzzIzzIzzHzz\ HzzGzzGzzFzzEzzFzzFzzFzzFzzFzzFBOFBKFsGAoGBlGBhGCe\ GCaGCZGDVGDSGEOGELGEHGFEGF1sA4iC6_D9QEyFewGduGcsGb\ qGaoG`nG_lGZjGYhGXfGWdGVcGUaGT_GSYGRWGQVGPTGORGNPG\ MNGLLGKKGJIGIGGHmMLnQNoUP } 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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FOTD 02-03-10 (Mandel Rectangles [8])
by Jim Muth 02 Mar '10

02 Mar '10

FOTD -- March 02, 2010 (Rating 8) Fractal visionaries and enthusiasts: As I said in yesterday's discussion, the strange rectangles exist in the East Valley area of the large split-apart minibrot on the negative X-axis of the Mandelbrot set of the formula Z^(2.003)+C. And to prove my point, today's image shows a minibrot surrounded by a whole flock of rectangles. I have highlighted the rectangles by rendering the image with the inside set to brilliant white. I rather enjoy the overall pattern surrounding the minibrot, which would be worth a FOTD even without the rectangles. With the rectangles included, the image rates an 8. The name "Mandel Rectangles" explains itself. The calculation time of 1-1/2 minutes will pass like greased lightning. A trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is posted for instant happiness, will pass even faster. But note that in a few days the address of the web site will change. I will post the new internet address in tomorrow's FOTD. The partly cloudy skies and temperature of 45F +7C here at Fractal Central on Monday kept the fractal cats leaping on and off their window shelf. They finally gave up trying to catch the sun and settled for an extra treat of tuna. My day was rather busy. The next FOTD will be posted in 24 hours. Until then, take care, and walk with your heads held high. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Mandel_Rectangles { ; time=0:01:35.43-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 float=y center-mag=-1.743397952568624/+0.00001662025822986\ /1.66e+008/1/-60/0 params=0/0/0/0/0/0/0/0/2.003/0 maxiter=1800 inside=255 logmap=212 periodicity=6 colors=000AFFAEGACHAAIA8JA6KA4LA3MA5NAAO5KPCQRJWTQ\ `VWdXbdbibfp`kv_oqVgmQ`iLUeGNLQX1_e3Xg4Vh5Th7Qh8Oh\ 9MhAKfCHeDFdEDcFBcH8dI6eJ4gK2iL5eL8bMB_MEXNHWNKUON\ SOQQPTMPWIQZEQaAQd6Mg8JjAGmCCnEmpz6rImsJ6qzmqImpzm\ pHzozmoGznGznzmmFmmFXmzmjCQcANXKJQ6GJKDC2A5KF4KJ4A\ N4ER4JW3O_3Xc3cg3hl2mpArtKvzSzzUzzSzzMzvGsrKmmNlhK\ ecHZZESUBLK600000000000JH7RO9ZWBfcDnjEdkEWlEMlEDmE\ 4mD6lC7lB9kAAk9Bj8Dj8Ej7Fi6Hi5Ih4Jh3Lg2Mg2Ng6IYAEP\ EAGH67SLLaZYbYZcY_cX`dXaeWbeWcfVdfVdgVehUfhUgiThjT\ ijSjkSkkSkfTkbUkYUkUVkPVkLWkGXkCXk7Yk3Yk6_g8`cAb_C\ cWEdTFfRGgQHhPIiOJjNKkMLzLMzJNzIOzHPzGQzFRzESzDTtC\ SzBRzBzzBm`AQWAPRAPMAOH9OC9N79N29R3DV3HZ3Lb4Pf4Tj4\ Xn5`r5dv5hy5laYzE0zD0zD0zC0zC0zC0zF0zI0zK0zN0zQ0zS\ 0zV0zY0z_0zZ0zZ0zZ0zZ0zY0zY0zY07Y05Y04X08W0CV0GU0K\ U0N_0Vd0bj0jo0rt0zs0ys0xs0xs0ws0vr0vr0ur0tr0tr0sr0\ se0tU0tI0tJ0qK0nL0lM0izzz } 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), 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] pakman fractal
by JackOfTradeZ＠comcast.net 01 Mar '10

01 Mar '10

. Jay - are YOU the original author of theFRM/PAR file for the pakman? If so I will credit you on my website. Let me know. And yes, I did vary the parameter as you suggested - just over a wider range. .

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Re: [Fractint] Ansers to Queshuns
by JackOfTradeZ＠comcast.net 01 Mar '10

01 Mar '10

. ""There's also a *nifty visual effect* caused by the brain's visual system that appears after watching the video. (See below for more about this.)"" It was the 1st thing I noticed; You also get this with some of my other viddies that have prolonged rotation sequences, like "cyclone" and "waltz of the pixels", to name just 2. This phenomenon is well known for a long time, the web is FULL of videos to trick your eye/brain. ""Does anyone else feel this 'out of control' vertigo effect?"" As for vertigo, uhh ... no, I don't get that. But then I am used to climbing 500 foot cliffs and jumping out of airplanes so I don't get perturbed so easy ... ""JackOfTradeZ, I'm curious as to why you zipped your WMV video file"" Old habits die hard. I always zip attachments for upload. Previous compression codecs made a difference; for some people a 30 vs 26 MEG file can make the download decision for them. This was a new codec, with the most recent MS Media Encoder; yes it appears very efficient. And some security suites block multimedia files (they can contane malware, and often do). But there is always an exception for ZIP since it's so common. The MAP: yes it's cool; I may use it in future work. Unfortunately, most of the colors didn't come out in the animation, except near the very center with the pakman image. ""Pakman Fractal Authorship"" No, it wasn't clear who to credit from the initial post, I just figured it wasn't a Muth thing. So I left it open on my web site. (I can always edit it later). ""Are the sequences of Fractint keystrokes I include in some of my posts ever of any use to anyone?"" I'm not sure what you are talking about. Anyone who has been using fractint for a while knows the keys? .

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FOTD 01-03-10 (Rectangularitis [6])
by Jim Muth 01 Mar '10

01 Mar '10

FOTD -- March 01, 2010 (Rating 6) Fractal visionaries and enthusiasts: Just when I thought I had seen all aspects of the Z^2.003 rectangle and had a vague comprehension of its full 4-D shape, I made a slight parameter change and the rectangle went crazy. It became a zig-zag thing better seen than described. The rectangle exists in its most perfect form in the Julia plane. Similar much smaller rectangles exist in the patterns around the minibrots in the Mandelbrot plane, but the original Julia rectangle totally vanishes in the Mandelbrot orientation. The Julia rectangle also extends into the Oblate and Rectangular orientations, and in the rotations between these orientations, though some degree of stretching and skewing is necessary to pre- serve the rectangular shape. I have not yet carefully checked the Elliptic and Parabolic planes, though I have no reason to doubt that traces of rectangularity exist there also. Such rectangles exist only in fractals with exponents of Z very close to 2.003. I have checked the Julia sets of the same area of the Z^4.003 Mandeloid and found no traces at all of a rectan- gle. As to why the Z^2.003 Julia sets seem so blessed with rec- tangles, I have no idea. Only the deity of numbers knows why, and he isn't talking. I named today's image "Rectangularitis" and rated it at a 6, which in my perhaps too-humble opinion is what it's worth. The calculation time of just under 3 minutes seems to be pretty standard for rectangle views when the maxiter is set at a some- what excessive 32767. All this calculation may be avoided however by viewing the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But keep alert if you view the images on the FOTD web site! The internet address of the site will change in about one week. Sunday here at Fractal Central began with a heavy snow shower that left 2 inches or 5cm of fresh fluffy snow on the ground. But when the sun came up, the snow melted away as fast as it had fallen, and by midday the streets were totally clear. The fractal cats took it in stride. My day was acceptable; FL spent most of the day watching the earthquake coverage on TV-Chile. The next FOTD, maybe or maybe not more rectangular stuff, will be posted in 24 hours. Until then, take care, and except for those who put their faith in reason, it's irrational to believe that all questions have a rational answer. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Rectangularitis { ; time=0:02:53.85-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/4508.257\ /0.0159/90/-55 params=0/90/0/90/-1.7435/0/0.00019/\ 0.07682/2.003/0 float=y maxiter=32767 inside=0 logmap=63 periodicity=6 colors=000CD6DE7DF8DG9DHADIBDJCEKDELEEMFENGEOHBPID\ QJERKFTNGWRIYVJ`ZKccLehNhmOkrPnvHpzMqzQqzUrzYrzasz\ mzzzzzetzarvYmrUjmRfhNbcJZZFVUBSP8PK9MF9KA9I8FG6KE\ 4PC3UF5ZI6cK8hN9mPBrSCvUEzXFzZGvZHrZImZJhZKcZKZZKU\ YLSXLTXLVWMXWMYVM_VMaUNbTNdTNfSOgSOiROmSGjROgQWdPc\ aOkRCwWIt_NrcSohYmlbjpghxnktlfqjanhYkfThdOtw0ecKRK\ bCEaC1uE6pGBkIGgKLbMQZOVUQ_QSdLUiHWnCZt2Ys8YrEYqKY\ pQYpVYo`YnfYmlcuuYmqSfmMZiGSeAKa4AX5DY5GZ5JZ5M_5P_\ 5S`5V`DZXLbUTfR`iNhmKpqHzzAxwCwtEvrGuoItlJsjLrgNqd\ PjwMmlOpbQsSRvITx8Ux7Rx6Px6Mx5Kx4Hx4FpCGhJHaRIUYJZ\ q1NdK9UfBTdCSbER`FQZHPXIOVJNTLMRMLPOKNPJLhHNZILQJJ\ 29RAEMHJHOOCTP4jfllbjm_inXhoUgpRfqOevEatIcrLdpOfnR\ gmUikXji_lgbmdjsegpfengblh`jiZhjcfkcdlcamc_ncYocWp\ cUqcSrmQpmOnmMmmKkmIimGhmEfmCzzAzz8zz6zz3zz5zz6zz8\ zz9zzBzzCzzEzzFzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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), c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(p5)+c |z|<=9 } END PARAMETER FILE=========================================

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