February 2010 - Fractint - mailman.xmission.com

Splotch.jpg
by Jay Litwyn 21 Feb '10

21 Feb '10

http://ecn.ab.ca/~brewhaha/img/Splotch.jpg I used an outside=atan rendering together with a two-colour outside/inside mask, plus an off-center PaintShopPro gradient for that. I had a gallery owner tell me that my work was "so...symmetrical". She was probably holding back loud, which is why I offer monochromes, plus monochromes work well as backgrounds. http://ecn.ab.ca/~brewhaha/Fractal_Gallery.htm Splotch { ; If you save an image with gray.map, then it will contain ; sixty-four unique colours. If you use altern.map, then ; you will get 256. Conclusion: fractint is still rounding ; colours off to a multiple of four. ; Fractint Version 2004 Patchlevel 4 reset=2004 type=formula formulafile=fractint.frm formulaname=MandelBroh function=sqr/conj passes=t center-mag=-0.250612/-0.257234/1.02894/1.7614 params=2/8/0/-0.75/0/0.75 float=y maxiter=1024 inside=0 outside=atan invert=0.0471796195166667/-0.11771965045/0.0255761745 periodicity=0 colors=(a)altern.map } MandelBroh { ; Anglicized spelling. I recommend sticky functions. z=fn1(pixel) +P2, c=fn2(pixel) +P3: z=z^real(P1) +c |z| <= imag(P1) }

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FOTD 19-02-10 (A Slipped Disk [7.5])
by Jim Muth 19 Feb '10

19 Feb '10

FOTD -- February 19, 2010 (Rating 7.5) Fractal visionaries and enthusiasts: Today's image is named "A Slipped Disk". This does not refer to a medical condition; it refers to the Siegel disks in the fractal, which have suffered some kind of slippage. Actually, there are no Siegel disks at all in the image. Siegel disks are purely Julia objects, while today's image, which is rotated 0.02,0.02 degrees from the Julia orientation, comes close but wins no cigar. In this case, the tiny rotation makes a world of difference. Actually, I have never had a clear idea of exactly what makes a Siegel disk. I know the disks appear in the Julia sets of points on the edge of the Mandelbrot set, but just what parts of these Julia sets are called Siegel disks? Well, I guess it really doesn't matter. As today's image shows, not-quite-Siegel disks can make interesting images, especially when they are rendered with the inside set to 'bof61'. The rating of 7.5 includes a small bonus for the coloring. The calculation time of 30 seconds will pass in a flash, as fast in fact as the trip to view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Thursday featured partly cloudy skies and a temperature of 39F +4C here at Fractal Central. The fractal cats, who dislike partly cloudy weather with its on-and-off sunshine, spent only a few minutes on their sun-shelf before seeking the artificial heat of the large radiator in the hallway. My day was close to normal; tomorrow should be the same. The next FOTD will be posted in 24 hours. Until then, take care, and speak with some wisdom. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Slipped_Disk { ; time=0:00:29.86-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=0/0/0.94 params=89.98/0/89.98/0/-0.390541/-0.586788/0/0/2/0 float=y maxiter=500 inside=bof61 logmap=yes symmetry=none periodicity=6 colors=000hkNjlRlmUmnYoo`qpcrqgtrjvsmwtqyutzvwzzzw\ wwuuuyrhyodylayhYydUy`RyXNyRJyPGsTHnXIh_JccKYfLTjM\ OmMGfK8_I0UG6SMCQRHOXNMaTKgYIlcGrhEweCrbAn`8jaAgbC\ dbEacFZcHWdJUdLReMOfOLfQIgSGgTDhVAhX7iZ4i_2gb8edDc\ gIaiN_lSZnYXqbVsgTvlRxqQzvMowIdxEUyAKzDLsFMmHNgJOa\ aazbZxbWwbTvbQubNtbLsbIqbFpbCob9nb6mb4l`5k_6kZ7kY7\ kX8kW9kV9kUAjTBjSCjRCjQDjPEjOEjSHiVKiYNiaQidShgVhk\ Yhn`hqbhq`fqZeqXdqVcqUaqS`qQ_qOZqNYmO_jO`gOacOc`Pd\ YPeUPgRPhOQiKQkHQlEQmLcXSqGUkMVeRW`WYVaZPf_KkVIiRG\ hNEfJDeFBcB9b78a9UlBnvEnsHnqJnoMnmOnkRniTngWneZnc`\ nacn_enYhnWjnUmnSonQppSpqTprUqsVqtXquYrvZrw_rx`mwY\ ivWeuTatRYsOUsMQrKMqHIpFEoCAnA6n87oD8pI8qN9rS9rWKh\ TV_QeQNoHKkNNhTQdZTadWYjZVo`RpZNpYJqXFqWBqU7rT3rS0\ rR7kSEdTKYURRVYKWcDXj6Yp0Zq6_qC_rH_rN`rS`sY`sb`sha\ tmatsatxaikZZ_WONTEBQA8N75L42J10z8hzF`cGVzHPcIJzJD\ cK7zK2cfezTMbF2z2vzKmzV0m } 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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FOTD 18-02-10 (In on Something Big [No Rating])
by Jim Muth 18 Feb '10

18 Feb '10

FOTD -- February 18, 2010 (No Rating) Fractal visionaries and enthusiasts: As the FOTD nears its 13th anniversary, the fractals are showing no signs of running out. Actually, when I posted the first FOTD image, I expected to continue posting fractals for a week or two. I guess I under-estimated my interest in fractals. Today's image shows a grossly bloated part of East Valley of the large minibrot on the main stem of the Z^2.000001+C Mandeloid. The valley has broadened into a wedge, the bloated edge of which is visible in the interior of the outer near-Julia set. Some fractalists may wonder if I have discovered a way to get more magnification out of the standard math routine. Don't get your hopes up. These magnified images do little more than shift the decimal point and lose resolution at a much lesser magnitude. There is little or no art in the image, so I gave it no rating. Actually, I am currently more interested in finding unusual math- ematical fractal things than creating wannabe works of art and saying, 'Look Ma, I'm an artist'. The name "In on Something Big" could refer to the greatly enlarged wedge, only a tiny part of which is visible inside the Julia shape. The calculation time of 5-3/4 minutes is slow enough to make the trip to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> worth the effort. Cloudy skies interspersed with snow flurries and a temperature of freezing made Wednesday less than ideal here at Fractal Central. The fractal cats must not have liked it any more than the humans. They were quite testy most all day. My day was rather busy but still under control. FL did get a bit annoyed at lunch when I told her I was not the slightest bit disappointed with Super-prez. I expected him to do nothing and he has done nothing. The next FOTD will be posted in 24 hours. Until then, take care, and if you expect nothing from your frac- tals, you might actually get *something* and be surprised. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= In_on_SomethingBig { ; time=0:05:46.45-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t inside=0 center-mag=0/0/8.8/1/90/0 params=89.99996/0/\ 89.99996/0/-1.74999826/4.55e-006/0/0/2.000001/0 float=y maxiter=4200 outside=tdis periodicity=0 colors=000PbnMbnIcnFdnBen8fn5fnBhmGjlLklQmkVnk_pjd\ riisinuhsvhtwdtwauwYuwVuwSvwOvwLwwHwwEwwBxvDxuExtG\ xsHysJyrKyqLypNyoOzoQznRzmTzlUzlVwiTufSsdRqaQo_PlX\ OjVNhSMfQLdNKeKLbLJ`LHZMGXMEVMCTNBRN9G83PN8Vb9XaCZ\ `E`_Gb_IcZLeYNgYPiXRjWUlWWnVYpU_qUas_etdhQXYuikrgh\ offlecjcagbZdaXb_U_ZSXYPVWNSVKPUINSFKRDHQAFP8HRCJT\ FLVINXLPZPQ`SSbVUdYWfaYhd_jg`ljdh`heSlaIpZ9m_Cj`Fg\ aIdbLacOZcRWdUTeXQf_NgbKjjLgeMd`NaWOZSPWNQTIQRENXI\ LbLJhOHnRMjSQfSUbTY_TaWUeSUiOVmLVqHWuDWz7VyAWxDWwF\ XwIXvLYuNYuQYtTZsVZrY_r`_qb`pe`leWpg`tiexkjxjixihx\ hgxgfxfexedxecxdbxcaxb`xa_x`ZzcWx`YvYZtV`rTapQcnNd\ lKfnKjjIggHedGbaE`ZDYjLZWCWrE`H4UI6TJ8TJATKCSKESLG\ SLIRMJRMLRNNQNPQORQOTPPVPQUMPWPPYSO_VOaYNc_NebMgeM\ ihMkjQehU_fYUd`PbZReXSgWUiUVkSWmRYoPZqO_sSTmWNgZHa\ bBWd4Pe5Re5Se5Te5Ve5We5Xf5Zf5_f5`f5bf5cf5df5edAabE\ Z`JWZNTYSQWWNU`KSdHQiEPmB } 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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Random Dot Stereograms
by Jay Litwyn 18 Feb '10

18 Feb '10

I think it is a matter of deleting the depth factor. The default of one hundred is too much. If I reduce it to thirty (about what it was for stereograms that were once printed every week in comics, here), then simplify the code according to a constant depth, then I will probably find the bug in it, too. Then I can either put the depth factor back in or let someone else do a good job of it. What is daunting is the sophistication of the code, now, since I see that there are graduations between most heights. Maybe I should see if the code can make steps between all heights. So, in sum, it is like: 1. Delete depth factor code. 2. Delete edge-blending code. 3. Choose a minimum and maximum depth that make for 256 heights that blend when only one difference in colour is. 4. Consider making it scale and interpolate, again. 5. Start with what I actually promised to do, elsewhere. :) _______ http://ecn.ab.ca/~brewhaha/img/STEREOD.GIF Stereogram diagnostic--256 numbered (and coloured) shades of gray that should look like a mountain road in RDS. It would be trivial to arrange it in a square spiral, which might be more informative, yet. Fun: Try reducing the colours in a 24bit grayscale to the map in that diagnostic. The hue will always be wrong, so you will get a lot of noise to diffuse. (order.map)

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FOTD 17-02-10 (The Big Wheel [No Rating])
by Jim Muth 17 Feb '10

17 Feb '10

FOTD -- February 17, 2010 (No Rating) Fractal visionaries and enthusiasts: Laziness took a setback Tuesday when a new job came in, but a fractal still appeared, almost by magic. The fractal is another of the near-Julia Seahorse Valley kind -- this one of order 15. Most of the effect was achieved by rendering the scene with the outside set to 'tdis', and also by the coloring. With nothing new in the image, I could not give it a rating. The name "The Big Wheel" refers to the circular arrangement of fifteen smaller buds around the circumference of the large bay. The calculation time of 2-1/3 minutes is surprisingly fast; the trip to see the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> will be even faster. But before surfing, give Paul a chance to post the image. Light snow continued Monday night here at Fractal Central. By the time it ended at 10am Tuesday about 1-inch 3cm had piled up. Tuesday afternoon turned mostly sunny, while the temperature hovered around freezing and the fractal cats took things easy. The next FOTD will be posted in 24 hours. If all goes well, it will be something new. Until then, take care, and if a fractal isn't broke, don't try to fix it. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= The_Big_Wheel { ; time=0:02:21.75-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0/0.928 params=89.95/0/89.95/42.6/\ 0.003/0.87909/0/0/15/0 float=y maxiter=15000 inside=255 outside=tdis symmetry=none periodicity=6 colors=000000cUBzcMsFPoGRkHThHVwIc`JZYJzXQYWWVVaSU\ gPTmMSsJSyHWgD_Q9b86dAEfCMhDUjFalHinIqmNnlSklXikaf\ jfcjkaipZiuXbmZXf_Q_`KSbDLc7Ed8Jf9Ng9RiAVjB_kBcmCg\ nCkoElkGmgHncJo_KpWMqSNrPTiOY`ObSNgJNlAMq1Mi6KaBIU\ GGNKEFPC7UA0Y8C`GNcOYeWhhcsjjhejZ`jPWjFRj5Mj8GcABX\ C5QE0KD6JCBJBHJAMJ9RJ8XJ7aJ6fJViFrlCdr`Rxytuktwotx\ sqtpopnmlljhjhdhf`fdXdaTa_P_YLYadjidnqdqxdtqbsj`rc\ ZqXXpQVoJTnCSnHVhLXbQ_XUaSYdMbfGfiAjk5fhEbeNZbWV_d\ RXmNVvKYqH`lEcgBfcIkUOpKVuA`z1ct6fnAhhEkbInXMpRQoP\ OoOMoNKnMInLGnKEhMIcNLYPOTQRORVITYDU`8Vc7Yf7_h6aj6\ cl5en5gpAbmEZkIViMRgQNeUJcYFaaB__H`ZN`XTaWYaUZ`R``\ Pa_Mb_Kd_HeZFfZDgZCeYCdYCbYCaYC_YBZYBXYBWYBUYBTYBS\ YGV`LXcQZfU`iZclceohgrliujfvidvhbwg`wfZweXxdVxcTxb\ RyaPy`Ny_Sq_XiZabZfVYkNYoGWiKVcOUYRTSVSNZRHaQBeP5i\ O0ld5iuAfaJdIRcGP`FNYDMWCKTAJR9HO8GMAJKCMIEPHGRFIU\ EKXCM_BOa9Qd8Sg6Ti5Od6HFK } 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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Random Dot Stereograms
by Jay Litwyn 16 Feb '10

16 Feb '10

I think it is a matter of deleting the depth factor. The default of one hundred is too much. If I reduce it to thirty (about what it was for stereograms that were once printed every week in comics, here), then simplify the code according to a constant depth, then I will probably find the bug in it, too. Then I can either put the depth factor back in or let someone else do a good job of it. What is daunting is the sophistication of the code, now, since I see that there are graduations between most heights. Maybe I should see if the code can make steps between all heights. So, in sum, it is like: 1. Delete depth factor code. 2. Delete edge-blending code. 3. Choose a minimum and maximum depth that make for 256 heights that blend when only one difference in colour is. 4. Consider making it scale and interpolate, again. 5. Start with what I actually promised to do, elsewhere. :) _______ http://ecn.ab.ca/~brewhaha/img/STEREOD.GIF Stereogram diagnostic--256 numbered (and coloured) shades of gray that should look like a mountain road in RDS. It would be trivial to arrange it in a square spiral, which might be more informative, yet. Fun: Try reducing the colours in a 24bit grayscale to the map in that diagnostic. The hue will always be wrong, so you will get a lot of noise to diffuse.

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FOTD 16-02-10 (Ray of Futility [No Rating])
by Jim Muth 16 Feb '10

16 Feb '10

FOTD -- February 16, 2010 (No Rating) Fractal visionaries and enthusiasts: Today's image does the same thing with the northern Seahorse Valley of the Z^3+C Mandeloid as yesterday's image did with the single Seahorse Valley of the classic Mandelbrot set. I named the result "Ray of Futility" for reasons known only to myself and already forgotten. I could do this same thing with Mandeloids of every higher order, though the result would soon devolve into higher-order sameness. I might try just one more however, perhaps of a fractional order like 2.5 or 1.5. Sameness is boring, so I decided to give no rating to the image. The calculation time of 9 minutes is more than I think the image is worth, so to make life easier I recommend viewing the already finished product on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Monday, Presidents' day, here at Fractal Central began sunny, but the pleasant conditions didn't last long. By midday threat- ening clouds moved in and at 3pm snow arrived, while the tempera- ture hovered within a degree or two of freezing. Early in the afternoon the fractal cats gave up waiting for the sun, and spent the rest of the afternoon finding the coziest sleeping places in the house. My day was about average, though far more active than the past two days, when I did nothing at all. All who would like to see another glorious fractal will have their wishes fulfilled at this same place in 24 hours or so. Until then, take care, and technology is the answer to all problems. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Ray_of_Futility { ; time=0:09:02.37-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0.175365/0.93633 params=89.98/0/89.98\ /90.5/0.005/0.7698185/0/0/3/0 float=y maxiter=15000 inside=0 outside=tdis periodicity=7 colors=0009BS9DU8FU8HU8JU8LU8NU7PU7RT7TS7VQ7WP7UQ7\ TQ7RQ7QQm8Ue7WY6YR5_SFaSOcSYdSffSphSyiRwhRvgRufRte\ RsdRqcRpbRoaQn`Qm_QkZQjYQiXQhWQgVQfUOaUMYUKTUIOUGK\ UEFUM4UH8U2JU4IU5HU7GU8FUMlzOjzPlzQozSrzTtzUwzVyzX\ wzZwz`vzbvzcvzavv`vr_umYuhXucWu_VvWTwVSwURxTPySOyR\ NzQMzQHnRCmR7mS3mS6mQ8mPAmOCmNEmLGmKJmJLmINmGPcFRc\ ETcDVcCVcIVcNVcSUcVUhYTm_TmbSmdSmgRmiRmlRmnPmjOmgM\ mcLm`JmXImUGmQFmNHmMJmLLmKNmKPmJRmITmIUmHWmGYmG_mF\ amEcmEemDgmChmCdmTdmSemRemPemOemNemLfmKzDJzAHz8Gz6\ Fz7Kz7Pz8Uz8Zz8cz9hz9mz9qzCozmmzmkzmiiKziMziOziQzh\ TzhVzhXzhZzh`zhbzhdzhfzibzjZzkVzkRzlOzmKzmGznCzo8z\ o5zoGzoRzoazolzowzOJzYVzffzoqzhmzbm`XmZRmXLmVFmT9m\ R3mP4mS5mU6mW7mZ7m`8mb9mdAmgBmzBmkCmmDmpEmrFmtFmvK\ msOmqSmoWmm_mkcmigmgkmeimcgmbezzdzzbzz`zz_zzYzzWzz\ VzzTzzRzzQzzOzzMzzLzzQzzMzzJVzGLziOzTHzcvz_ozWhzSa\ zOVzKOzGHzMozHVzNGzIDz9Vz } 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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FOTD 15-02-10 (Seahorse Holiday [No Rating])
by Jim Muth 15 Feb '10

15 Feb '10

FOTD -- February 15, 2010 (No Rating) Fractal visionaries and enthusiasts: I spent the day Sunday enjoying how pleasant it is to actually spend a day doing nothing of importance. Despite the attack of laziness, I did manage to find a fractal. The fractal is simply another version of the effect I demonstra- ted in yesterday's FOTD image, where the grossly bloated image of a tiny part of the Mandelbrot set is seen lying in its corres- ponding Julia set. This time I chose a scene in the southern branch of Seahorse Valley to enlarge and fit into its Julia set. A careful tweak- ing of parameters placed the enlarged valley straight through the center of its Julia set. The name "Seahorse Holiday" has a kind of fun-fantasy ring to it. The lack of a rating indicates that I took the lazy way out when finding the image. The calculation time of under 3 minutes will make life easy for all but the most impatient fractalists. These impatient few may find immediate viewing pleasure on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> where the finished image is or soon will be posted. Peace prevailed here at Fractal Central on Sunday, both among cats and humans. The weather was peaceful also, as the clouds failed to drop their snow and the temperature reached freezing. The next FOTD, very likely another venture into the abstract world of four dimensions, will be posted in 24 hours. Until then, take care, and fight the latest epidemic -- the epidemic of fractal addiction. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Seahorse_Holiday { ; time=0:02:52.38-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0\ /0.8810318 params=89.9/0/89.9/89/-0.75007/-0.01/0/\ 0/2/0 float=y maxiter=32767 inside=0 logmap=yes periodicity=9 colors=000PHZSGYVFXYDW`CVcBUf9Ui8Tl7So5Rr4Qu4Px4Pv\ AQuGRsMSrRSqVToZUnbUlgVkjWjkWljXmhXnfXocXp`XqYXrWX\ sTXtQXuNXvKXwHXxEXyCXpHOhLG_Q8SU0NPBIKLDFV8Bd9Ab9A\ `A9ZA9XB8VB8TC7RC7QD6OD6ME5KE5IF4GF4EF4DJAIMFNQKRT\ PWXU___dcdhfimjnqmsvpxzrruslqtglvahwWcxR_uTarVcpXd\ mZfj`hhaieckbem`gnYipWjqabgfVZkNQpFHu78rCFpGLmLRkP\ XhUbfYhcbnaft_jzZhrYfkXdcXbXW`QVZIUXBUV4VX5WY6XZ6Y\ `7Za8_b8_d9`e9afAbhBciBdjCdkCfjCgiChhCjgCkfCSiQShM\ ThIThLThPSfUReZQdcPchObmNarM`wL_wKZwJYwIXwHWwGWwFX\ wEYwDZwC_wB`wAaw9br3cm8dhCecGfZKgUPhPTiKXjF`kGUlIN\ mLCnOGoNJpNNqNQrNUsNXtN`uNcvNgwNjxNcxNcxNcxNcvMcuL\ ctKcsJcqIcpIcoHcnGQmzQmzRmzSmzSmzTmzUmzVmzVmzWmzXm\ zYmzYmzZmz_mzXmz_mzbmzemzgmzjmzmmzomzrmzumzxmzwmzw\ pzvwzvwzvwzuwzuwzuwztwztwztwzswzswzuwzswzrwzpwzowz\ mwzlwzjwziwzgwzfwzdwzcwzawz`zz_zzVzzQzzIzzLzzNzzPz\ zRzzTzzVzzXzzZzz`zzbzzdzz } 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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FOTD 14-02-10 (A Crazy Angle [6])
by Jim Muth 14 Feb '10

14 Feb '10

FOTD -- February 14, 2010 (Rating 6) Fractal visionaries and enthusiasts: Not surprisingly, the antiquing bug did bite on Saturday, which explains why this FOTD is late. The name "A Crazy Angle" refers to the orientation of the image slice through the 4-D (Z^2+C) Julibrot. In the background of the image we see a grossly magnified version of the normally insignificant period-30 bud on the south shore of East Valley of the Mandelbrot set. The ridiculous enlargement is due to the angle at which the image cuts the actual 4-dimensional bud-complex. The closer the orientation lies to the true Julia direction, the greater the enlargement, and since today's image is cut 0.015,0.015 degrees from the actual Julia, the enlargement is spectacular indeed. (At the actual Julia orientation, the enlargement is infinite, and the same point of the bud is reflected in the entire scene.) Do not try to visualize how an object may be magnified in two dimensions by simply varying the direction in which it is sliced. It's another of those 4-D mysteries, like exiting a completely closed room by stepping around the wall, that make no sense in 3-D space. I rated the image at a 6, mostly because of the mathematical interest. The calculation time of 4-1/4 minutes is slower than I would have preferred, but with the image maxiter at 120,000 it is quite reasonable. And of course, the finished image, for all it is or is not worth, is posted for immediate satisfaction on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Partly cloudy skies, a high temperature of 30F -1C and a few flakes of snow made for a typical midwinter day here at Fractal Central on Saturday. The fractal cats passed the day sleeping. The next FOTD will be posted in 24 hours. Until then, take care, and free your mind from the bonds of convention. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= A_Crazy_Angle { ; time=0:04:14.06-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t center-mag=0/0\ /1.182144/1/90/0 params=89.985/0/89.985/20/0.26065\ /-0.0022/0/0/2/0 float=y maxiter=120000 inside=0 logmap=yes periodicity=6 colors=000PHZSGYVFXYDW`CVcBUf9Ui8Tl7So5Rr4Qu4Px4Pv\ AQuGRsMSrRSqVToZUnbUlgVkjWjkWljXmhXnfXocXp`XqYXrWX\ sTXtQXuNXvKXwHXxEXyCXpHOhLG_Q8SU0NPBIKLDFV8Bd9Ab9A\ `A9ZA9XB8VB8TC7RC7QD6OD6ME5KE5IF4GF4EF4DJAIMFNQKRT\ PWXU___dcdhfimjnqmsvpxzrruslqtglvahwWcxR_uTarVcpXd\ mZfj`hhaieckbem`gnYipWjqabgfVZkNQpFHu78rCFpGLmLRkP\ XhUbfYhcbnaft_jzZhrYfkXdcXbXW`QVZIUXBUV4VX5WY6XZ6Y\ `7Za8_b8_d9`e9afAbhBciBdjCdkCfjCgiChhCjgCkfCSiQShM\ ThIThLThPSfUReZQdcPchObmNarM`wL_wKZwJYwIXwHWwGWwFX\ wEYwDZwC_wB`wAaw9br3cm8dhCecGfZKgUPhPTiKXjF`kGUlIN\ mLCnOGoNJpNNqNQrNUsNXtN`uNcvNgwNjxNcxNcxNcxNcvMcuL\ ctKcsJcqIcpIcoHcnGQmzQmzRmzSmzSmzTmzUmzVmzVmzWmzXm\ zYmzYmzZmz_mzXmz_mzbmzemzgmzjmzmmzomzrmzumzxmzwmzw\ pzvwzvwzvwzuwzuwzuwztwztwztwzswzswzuwzswzrwzpwzowz\ mwzlwzjwziwzgwzfwzdwzcwzawz`zz_zzVzzQzzIzzLzzNzzPz\ zRzzTzzVzzXzzZzz`zzbzzdzz } 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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FOTD 13-02-10 (Negative Pi [5])
by Jim Muth 13 Feb '10

13 Feb '10

FOTD -- February 13, 2010 (Rating 5) Fractal visionaries and enthusiasts: Today's venture into the world of Pi takes us to the negative X-axis area of yesterday's parent fractal, where we find a cluster of Pi-minibrots in an intricate network of interlaced filaments. I decided to rate the image at a 5, mostly to point out that I put almost no effort into it. The name "Negative Pi" has no meaning, but it was very easy to think of. The calculation time of 1-1/2 minutes will pass swiftly. But I leave it to the viewer to judge whether the time is well spent. The finished image is posted on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A perfect midwinter day prevailed here at Fractal central on Friday, with near clear skies, a high temperature of 34F +1C, and light winds. The fractal cats enjoyed the sunshine that flooded their window shelf most of the afternoon. My day was, believe it or not, spent mostly in relaxation -- something I have seen far too little of recently. When FL saw me slouched in my overstuffed chair, she said it's about time I slowed down. The next FOTD will be posted in 24 hours. But if an unexpected antiquing trip comes up tomorrow, the FOTD might be delayed until Feb 15, but it will eventually appear. Until whenever, take care, and we had best look into mind travel to the stars, because we will never make it there physically in the clumsy inefficient contraptions we call chemical rockets. Jim Muth jamth(a)mindspring.com jimmuth(a)aol.com START PARAMETER FILE======================================= Negative_Pi { ; time=0:01:32.21-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=FinalDivideBrot function=recip passes=1 center-mag=-1.468318766312069/+0.0010893028439826/\ 2.322823e+012/1/71.5/0 params=3.14159265358979/\ -3.14159265358979/0/0 float=y maxiter=1650 inside=0 logmap=106 periodicity=6 mathtolerance=0.05/1 colors=000kAKg7Kd8Ka9FZA9Y70UB4RE8NHCKKLHNKGOPFQOK\ SNUVMcXLmZKvaJzcIvbCmeIchNUkSKmXBpcBshAvnByzAxsAxl\ AweAwZAvSAvMAuF2w5Au9HqDPmHWhLcdPhcQj`SlYUmVWoSYpP\ _rMamPbhUccZdZceUhfPigKjhKiiKkhKlhKnhLohNphPrhRshC\ vaSthgrovqvpppjojend_mZWpSVlUVhVVeXUcYUc_ecUUc`Icg\ 6cn5ci4cd4c_3cV2cQ2cL1cG1cC4cD6cE9cFBcGDcHGcIIcJKc\ JKcLKcMKcNObPR_QVXRYUS`RTdOUgLVjIWnFXqCYt9ZqDYoGYm\ JYjMYhPYfSYdVYaYY_`YYcYVfYTiYRlYPoYRmZSk_Ui`VgaXea\ Ycb_bc``dbZdcXeeVffTggSgeTdcTbaT`_UZYUXWUVUUTSVRQV\ POVNMVLNXOOYRP_UQ`XQa_RcbSdeTfhUgkUhmdmbhmckmdomer\ mfumgqmbmmZimVemRamNYmJUmFVmHWmIXmJYmKZmL_mM`mN`mO\ amPbmQcmRdmSemTfmUfmVbmWZmWVmWRmWzzXzzXzzXzzXzzXzz\ XzzXzzXzzXzzXzzXzzXzzXzzUzzRzzPBzzCzzDzzFzzGzzHzzK\ zzNzzPzzSzzUzzYzz`zzczzfzzjzzmzbpzeszivzlozkhzjazj\ VziOzhHzhAzg4zg7zc9z`CzXEzUGzQJzNLzJNzGPzHQzHSzHTz\ HUzHWzIXzIZzI_zI`zItzhpzb } frm:FinalDivideBrot { ; Jim Muth z=(0,0), c=pixel, a=-(real(p1)-2), esc=(real(p2)+16), b=imag(p1)+0.00000000000000000001: z=(-b)*(z*z*fn1(z^(a)+b))-c |z| < esc } END PARAMETER FILE=========================================

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