October 2011 - Fractint - mailman.xmission.com

FOTD 17-10-11 (Bare Singularity [7])
by Jim Muth 18 Oct '11

18 Oct '11

FOTD -- October 17, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image is the third one created with an exponent of 1.05, though today it is positive Z rather than negative Z that we raise to the power of 1.05. The parent fractal was created by calculating the expression Z^(1.05)+C at a level of 0.31... turns down the complex logarithmic hyperspiral with the 'recip' function applied. The surprise in the image is the existence of a minibrot. The minibrot lies at the center of a disorganized spiral, which is another surprise. Most spirals appear boring because they continue unchanged all the way down to infinity; today's spiral however comes to a definite end at the central minibrot. I named the image "Bare Singularity". I almost named it 'neutron star', but the singularity name has more impact. I'm not sure a bare singularity could actually exist. Any singularity would necessarily have an event horizon around it, and would therefore lie unseen inside a black hole, but it is fun to try to imagine what a bare singularity might look like. The rating of a 7 is about what the image is worth. A little extra effort on the colors might have rased the rating to a 7-1/2. The calculation time of 7 minutes starts to drag before the image is finished. Avoid the dragging by viewing the image on the web site. The official FOTD web site is at: <http://www.crosscanpuzzles.com/Archives.html> where the finished image is posted. or the high-definition web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original web site may be accessed at: <http://www.Nahee.com/FOTD/> Light rain fell during the night here at Fractal Central, but by daybreak the sky was clear. The rest of the day brought full sun with only a few passing clouds, and a temperature of 64F 18C. The fractal cats approved of these conditions, at least during the times when they were not distracted by a large orange tomcat that wandered onto the back porch. The world of the humans featured only routine stuff not worth reporting. The next FOTD is due to be posted in 24 hours. Most likely it will be posted on schedule. Until then, take care, and if nothing can escape from an (almost) black hole, how does the gravity get out? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Bare_Singularity { ; time=0:07:09.90-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotBC3 function=recip passes=1 center-mag=-2.109365353519732/+2.80890231424387/\ 1.629783e+011/1/-85/0 params=1.05/0/-0.31034272286\ 14155/0 float=y maxiter=5000 inside=255 logmap=700 periodicity=6 mathtolerance=0.05/1 colors=000GWeXmjNdgGWe8Pb0Ha0AZ03X00V00W00W00W00W0\ 0W00W00W00X00X00X00X01X01X01X01Z02Z02Z02Z02Z03Z03Z\ 03Z03_05_05_05_05_06_06_06a06a07a07a07a07a08a08b08\ b08b09b09b09b09b0Ab0Ad0Ad1Gl1Cd1Cd2Cm2Cd3De3De3De5\ Me5Me6Me6Me5Md6Me6Me6Me7Me7Me7Me7Me8Me8Hl8Me8Gv99u\ 9Mu9GuAMuAMuA9uAMuCCuCEuCMuC9uDMuD9uDEuEMuEDuEHuEG\ uGEuGEuGDuGCu8DuHAuHGuC8sH9uGHuDAuEJuDIuDAuCCmAImA\ 9o9Fo8Co8Do7Go6Ho6Io5Do2Cp3Do5Eo5EoLJo6GoLQh7Ao8Co\ 8Po9Do9IoASoAEoCOmCGmDHjDMjEIhELhGJgGJgHPeHMeLQeIN\ eJNeJPeLPeLQeMQeMSeNSdNTdPTdPVdQVdQWdSVdSWeTWeTWfV\ WfVXgWZgWXgXZhXZhZ_fZ_g_ag_agachabgbegbeidgodglehm\ ejoglqglzhmzhpzjpzjozlozlozmozmozopxopxppxppxrpxrp\ xsrxsrxurxurxvrxvsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxx\ sxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsx\ xsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxsxxs\ xxsxxsxxsxxsxxsxxsxxsxzzz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END PARAMETER FILE=========================================

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FOTD 16-10-11 (A Bigger Surprise [8!])
by Jim Muth 17 Oct '11

17 Oct '11

FOTD -- October 16, 2011 (Rating 8!) Fractal visionaries and enthusiasts: How low can you go? Yesterday's image brought a big surprise when I found actual chaotic detail in the (-Z)^(1.05)+C Julibrot. Today's image brought an even bigger surprise when I found chaotic detail in the (-Z)^(1.0025)+C Julibrot, which is 20 times closer to unity, and this is exactly what I named it. The rating of an 8! expresses my surprise at this unexpected turn of events, and I would not be surprised to find the biggest surprise as I continue to lower the exponent. In addition to the unexpected detail, the image shows a surprising overall pattern of radiating arms and curving loops. And yes, the background is filled with a large variety of detail. The calculation price for all this surprise is an unwieldy 15-1/4 minutes. But the web sites will eliminate this problem. The finished image is posted at: <http://www.crosscanpuzzles.com/Archives.html> in 640x480x256 resolution. The hi-def version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site is at: <http://www.Nahee.com/FOTD/> A sunny morning was followed by a cloudy afternoon here at Fractal Central. The temperature settled around a comfortable 66F 19C for most of the day, keeping the fractal cats content until we brought a new chair into the living room. When we set the chair in its place, Nicholas checked it, seemed satisfied, and walked away. Cassie checked the chair and immediately laid claim to it. She will probably make it her own catsonal chair, where Nico will be permitted only with her permission. The next FOTD will be posted in 24 hours. Until then, take care, and if we took the money from the ridiculously wealthy one-percent and distributed it evenly among the remaining 99-percent, everyone would have about double what he now has. The demand for goods and services would then double, which would cause the prices to double also, cancelling the extra wealth. The only change would be a lack of ridiculously wealthy people. My solution to the problem of the unequal distribution of wealth is to ****** the ******* so that ******* ** ******** **** ***** would be equal. And then everyone would be satisfied. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_Bigger_Surprise { ; time=0:15:14.06-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=1 center-mag=2.7\ 2198/0/3.20013/1/-90/0 params=37.5/0/37.5/0/1.1513\ /0/0/0/1.0025/0 float=y maxiter=32767 inside=0 logmap=-668 periodicity=9 colors=000OG0QI0SK0TN0VQ0XT0XW0YZ0Wa0Ud0Sg0Qj0Mm0O\ p0Qr0Rr0Tq0Up0Wp0Xo0Zo0_n0am0bm0dl0ek0gk0hj0jj0ki0\ mh0nh0pg0qg0nd0lb0j_0gY0eW0cT0aR0ZO0XM0VK0TH0QF0OC\ 0MA0J60K80KA0KC0LE0LG0LI0MK0MM0MO0NQ0NR0NT0OV0OX0O\ ZzP`zPbzPdzQfzQhzQjzQkzOizNhzLfzKezIczHbzGazK_zNZz\ RXzUWzXUz`TzcRzgQzjOzmNzmNzmOzmOzmPzmOzmPzmPzmPzmQ\ zmQzmQzmRzmRzmRzmSzmSzmSzmTzmTzmTzmUzmUzmUzmVzmVzm\ WzzYzz_zzazzczzezzgzzizzkzzmzzozzqzzszzuzzwzzxzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzblzc\ mzdnzdozeqzfrzfszgtzhvzhuzixzjwzjzzhvzgwzfuzetzdtz\ cqzbrzaoz`oz_lzZmzXizWjzVfzUgzTdzSdzRazQbzP`zO_zNZ\ zLXzKWzJUzITzHSzGQzFPzEOzDNzCLz8NzBLzDNzGNzIPzLSzN\ UzQXzSZzU`zT_zTZzTYzTYzTXzTWzTVzSVzSUzSTzSTzSSzSRz\ SQzRQzRPzROzRNzRNzRMzRLzRLzQKzQJzQIzQIzQHzQGzQFzPF\ zPEzCizEhzGfzHdzJbzLazN_z } 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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FOTD 15-10-11 (The Big Surprise [?])
by Jim Muth 16 Oct '11

16 Oct '11

FOTD -- October 15, 2011 (Rating ?) Fractal visionaries and enthusiasts: Rarely does a parent fractal become Fractal of the Day, but today is the second consecutive day on which a parent fractal has been featured. In yesterday's image we saw that the (-Z)^(1.05)+C Julibrot apparently holds no interesting semi-chaos, at least not in the area of Seahorse Valley. In today's image we find that first impressions are sometimes wrong. Today, we check the hump that passes for East Valley in the Mandelbrot aspect of the Julibrot. We check it at an angle double rotated 37.5 degrees toward the Julia direction, and what we find is total chaos. While all the edges in yesterday's image were smooth, today's image shows nothing but chaos in its eastern parts. To add to the interest, this chaos consists of discontinuities, which vary widely in character in different parts of the image, yet have a similar theme in restricted areas. Such a mixed-up Julibrot surely has many additional curious slices in this East Valley area. I'll be checking other slices over the next few days, and I would not be surprised if some slices achieved FOTD image status. The name "The Big Surprise" expresses my feelings when I checked the 37.5,37.5 angle of today's slice through 'east hump'. The rating of a question mark shows my indecision. The mathematical interest is certainly there, and would rate about an 8, but take this math interest away and the artistic value falls short of FOTD reference standard. The redeeming feature is the super-fast calculation time of 50 seconds, which will give no one a reason to regret the wasted time if the image falls flat with them. To view the image without the bother of calculating it, visit the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> To see the image in high-definition, visit: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> To see all the images since April 1997, go to: <http://www.Nahee.com/FOTD/> Conditions were windy here at Fractal Central today. The gusts near 50mph, 80kph kept the leaves swirling. Otherwise the partly cloudy skies and temperature of 64F 18C were harmless. The fractal cats were also pretty harmless, sleeping as they did through a good part of the afternoon. FL and I stopped by a local 'occupy' demonstration around noon. Somehow I found myself holding a we're-not-going-to-take-it-any- longer sign and getting honked at by passing cars. Luckily, no harm was done to my middle-of-the-road political reputation, since all sides apparently agree on the same problem, if not the solution. We then spent the rest of the day on a short antiquing expedition. The next FOTD will be posted in 24 hours. Until then, take care, and when the time is right, the answers will become obvious. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Big_Surprise { ; time=0:00:50.15-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 center-mag=1.07545/0/\ 0.3427852 params=37.5/0/37.5/0/1.1513/0/0/0/1.05/0 float=y maxiter=15000 inside=0 logmap=yes symmetry=xaxis periodicity=9 colors=000blYcmXdnXdoWeqWfrVfsUgtUhvThuSixSjwRjzRh\ vQgwQfuQetPdtPcqPbrOaoO`oO_lNZmNXiNWjMVfMUgMTdLSdL\ RaLQbKP`KO_KNZJLXJKWJJUIITIHSIGQHFPHEOHDNGCLG8NHBL\ GDNGGNGIPGLSGNUGQXGSZGU`GT_FTZFTYFTYFTXETWETVESVES\ UESTDSTDSSDSRDSQDRQCRPCROCRNCRNCRMBRLBRLBQKBQJBQIA\ QIAQHAQGAQFAPF9PE9PD9PD9PC9PB8PA8OA8O98O88O77O77O6\ 7O57O57P68Q69R7AS7BS8CT8DU8DV9EW9FWAGXAHYBIZBJ_BJ_\ CK`CLaDMbDNcEOcEPdEPeFQfFRgGSgGThHUiHVjHVkIWkIYlJ_\ mIanGcoEeqCgrAis8ku6mv4ox2qz0sy1ux2ww2ww3ww3ww4ww4\ ww5ww5ww6ww6ww7uw8sw8qw9ow9mwAkwAiwBgwBewCewCewDew\ EfwEgwFgwFhwGhwGiwHiwHjwIkwIkwJlwKluKmsLmqLnoMomMo\ mNpmNpmOqmOqmPrmOsmPrmPqmPpmQomQomQnmRmmRlmRlmSkmS\ jmSimTimThmTgmUfmUfmUemVdmVcmWczYaz_`za_zcZzeXzgWz\ iVzkUzmTzoRzqQzsPzuOzwMzxLzzKzzJzzIzzGzzFzzEzzDzzB\ zzAzz9zz8zz7zz5zz4zz3zz2zz1zz2zz2zzfzzezzezzdzzczz\ czzbzzazzazz`zz`zz_zzZzzZ } 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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FOTD 14-10-11 (An Old Smoothie [No Rating])
by Jim Muth 15 Oct '11

15 Oct '11

FOTD -- October 14, 2011 (No Rating) Fractal visionaries and enthusiasts: The exponent of (-Z) in today's image is 1.05, a value that would be expected to create little in the way of interesting fractals. But it is negative Z that we are iterating today, not positive Z, and when it comes to fractals with an exponent of Z between 1 and 2, negative Z wins hands down. The parent fractal, with an exponent only 0.05 above unity, already has some halmarks of the Mandeloids -- a prominent period-2 bud on the negative X-axis and a very well-defined Seahorse Valley. To produce today's image I found the Julia set of this valley, which is an empty featureless figure-eight shape, and double rotated the view 0.5,0.5 degrees. The result is a figure eight nearly filled with the bloated Mandelbrot valley. Searching for interesting semi-chaos, I increased the maxiter to 500000, but when I saw that no chaos was to be found, reduced it to the present 75000, which is still quite large enough. The name "An Old Smoothie" refers to the smooth edges of everything in the scene. Since the image is the second similar one in a few days, I declined to give it a rating. The result is probably not worth the calculation time of 11-1/2 minutes, so thank goodness for the FOTD web sites. The finished image is posted in SF5 resolution at: <http://www.crosscanpuzzles.com/Archives.html> and in higher resolution at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic, FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> A series of heavy thunder-showers plagued Fractal Central through the night and most of today, with about 3 inches, 7.5cm of rain falling in that time. The fractal cats checked the window several times, but when the thunder grew too sharp, they ducked for cover in the closet. FL simply endured the conditions, while I rather enjoyed the action. At least, the temperature of 64F 18C pleased human and cat alike. The next FOTD will be posted in 24 hours. If an antiquing expedition arises, it might be late however. Until whenever, take care, and don't worry about who might be the next U.S. president. You'll never notice a difference. The international corporate conglomerate is actually running things and will continue doing so. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= An_Old_Smoothie { ; time=0:11:29.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 center-mag=-0.3568/0/1 params=89.5/0/89.5/92/-0.736/0.03/0/0/1.05/0 float=y maxiter=75000 inside=0 outside=tdis logmap=75 periodicity=9 colors=000Q86R56R26R06Q17Q27Q28Q38Q49Q49Q5AQ5AQ6BQ\ 7BQ7CQ8CP9CP9DPADPAEPBEPCFPCFPDGPEGPEHPFHPFHSIFVKE\ XMD_OBbQAdS9gV7jX6lZ5o`3rb2td1qc6obBlaGjaLh`Qe_Vc_\ _`ZcYYaVY_SXYQXWOWUMWSKUQIUOGUMGUKHUIHUGHTEGRDFPCE\ NFDLHCKJBIMAGO9ER8CT8BV9DYAF_BHaBJdCLfDNhEPjERmFTo\ GVqGWsFVqFVpEUoEUnDTmDTlCSkCSjBRiBRhAQgAQf9Pe9Pd8O\ c8Ob7Na7N`6M_6MZ5LY5LX9QTDVQGZNKcJNgGRlDUpAXqB_rBa\ sCdtCftDiuDkvEnwEpwFsxFuyGxzGzzGzu9zp3zm4zj4zj4zk4\ yk4xl4wl5vm5umAtnFsnKroMqoOpoQooSnoUmoWon_rlZtkYvj\ OxiIzh5uf8qdAmbCiaEe_GaYIYWLUVNQTPMRRIPTEOVGMZIKaK\ IdMHgOFjQDmSBpTAsWDqZGo`ImcLlfOjhQhkTfnWepYcs`aub`\ vebvgdvjfvlhvojvqlvtnwwwuuusssqqqooommmkkkiiigggee\ ecccaaa___Y_YW`WUaUU_SUYQUWOUUMUSKUQKUPMUROUTQUVSU\ XTUZVU`XUbZUd_UfaUhcUjeUlfUhhUejUblUZnUWpUTrUQtUbd\ UnQUzBUZVU7mUCdUGWUKNUOYUPWbQV_RUXSTUTSRUROVQLWPIX\ OFYNCZM9_L7_KUE1UD2UD2UC2 } 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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FOTD 13-10-11 (1-1/2 Seahorses [8])
by Jim Muth 14 Oct '11

14 Oct '11

FOTD -- October 13, 2011 (Rating 8) Fractal visionaries and enthusiasts: Believe it or not, today's image is a scene in the Seahorse Valley area of the (-Z)^(1.5)+C Mandeloid. Actually, the scene is very close to a Julia set of the valley, being double-rotated only 0.4,0.4 degrees from the true Julia direction. The wedge- shaped feature almost filling the outer figure-8 shape is a grossly enlarged view of the Mandelbrot Seahorse Valley. Iterating (-Z) rather than straight (Z) makes a great difference in the fractals with a fractional exponent of Z between 1 and 2. While positive (Z) results in tiny bean-shaped fractals, negative(Z) produces much larger fractals, with recognizable Seahorse Valleys and much more interesting surrounding semi- chaos to explore. I rendered the scene with the outside set to 'tdis'. Some of the other outside options also produce interesting versions of the scene. The name "1-1/2 Seahorses" refers to the exponent of Z, not to any sliced up seahorses that might be lying around. The rating of an 8 includes a full point for the coloring. This might be a bit excessive, but why not reward myself? I must have put almost an hour into working out the colors. The calculation time of 8-3/4 minutes is on the slow side. Most of this time is caused by the large maxiter of 32767, which was the maxiter limit of early versions of Fractint, and which I still use as a standard setting. But wait! There is no need for the 8-minute delay. Calculation may be avoided by viewing the image already calculated on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> And by viewing the high-definition version 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/> Heavy clouds and intermittent showers continued here at Fractal Central on Thursday, while the temperature of 63F 17C was on the mild side for the season. The fractal cats, being warm weather fans, enjoyed the conditions. The humans spent the day doing routine things, which make for a peaceful day to live through but rather dull reporting. The next FOTD is scheduled to be posted in 24 hours, and it might actually be ready. Until next time, take care, and if we ever defeated the terrorists, who would we then blame our problems on. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= 1-1/2_Seahorses { ; time=0:08:47.48-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot5 passes=t inside=0 center-mag=-0.305312/0.00434276/1.123196 params=89.6/0/89.6/92/-0.742/0.05/0/0/1.5/0 float=y maxiter=32767 outside=tdis logmap=3 periodicity=9 colors=000TL_SKYRJWQIUPHSOGQNFOMEMLDKKCIJBFIACH99G\ 86F73D50C30700800900000000000000000000000000ZVKb`D\ fe6lx_iwaevcbvf_uhWtjTslQsoMrqJqsGpuDpwIqrMrmQshUt\ cYuZauUzMHvJMsGRpDWlA`i7ef4iY3`P2SG1J71BJ4DU6Fd9Ho\ BJzDLwJPtPTqVWn`_kfbhlffridojbmk`jl_hmYenWcoV`oTZp\ RWqPUrORsMPtKMuJKuLMsNNrPPqRQpTRoVTnXUmZWk`XjbYid_\ hf`ghbfjcekddlbelaem`em_emZejachcbfe`cg_aiY_kXXnWV\ pUTrTctRmvQzxPmqNcjMScKSXJTQHUJGRKJOKMLKPJKSGKVDLX\ AL_8Lb5Le2Lh0Lj1Mg1Md2Mb2M_2MX3MV3MS4NP4cc4cc5cc5c\ c6cc6cc6cc6cc6cc6cc6cc6cc6cf6cl6cr9cpBmoDmnGmlImkK\ mjNmhPmgRmfUmdWmcomYcmZ9mgwmuqmmkmfemzkmzgmzcmz4mz\ LmzcmzamzZmz_mz_mz`mzNmzSmzXmzemzcrzarzDrzSrzXrz9r\ zGrzNrzUrz0rzJrzDrzPrzcrzbrzarzmrzmrzmrzmrzmrzmrzm\ rzmrzmrzmrzmrzmwzmrzmrzmrzmrzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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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time theory, addendum
by Sebastien helie 14 Oct '11

14 Oct '11

Planet_time { reset=2000 type=formula formulafile=fr2011.frm formulaname=10_10_2011_2 center-mag=1.89737/-1.28214/0.8503401 inside=fmod outside=imag invert=-0.75/1/-0.75 decomp=64 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzzzLzzz000555<3>HHHKKKOO\ O<3>ccchhhmmmssszzz00z<3>z0z<3>z00<3>zz0<3>0z0<3>0zz<2>0GzVVz<3>zVz<3>zV\ V<3>zzV<3>VzV<3>Vzz<2>Vbzhhz<3>zhz<3>zhh<3>zzh<3>hzh<3>hzz<2>hlz00S<3>S0\ S<3>S00<3>SS0<3>0S0<3>0SS<2>07SEES<3>SES<3>SEE<3>SSE<3>ESE<3>ESS<2>EHSKK\ S<2>QKSSKSSKQSKOSKMSKK<2>SQKSSKQSKOSKMSKKSK<2>KSQKSSKQSKOSKMS00G<3>G0G<3\ >G00<3>GG0<3>0G0<3>0GG<2>04G88G<2>E8GG8GG8EG8CG8AG88<2>GE8GG8EG8CG8AG88G\ 8<2>8GE8GG8EG8CG8AGBBG<2>FBGGBGGBFGBDGBCGBB<2>GFBGGBFGBDGBCGBBGB<2>BGFBG\ GBFGBDGBCG000<6>000 } Planet_time{;sinpix z=pixel: x=z*z^c y=1/x a=sin(z/2) b=x+y+a z=z+b/x+(1/(z+b/x)) } I like time theory it's like duality, or the concept of (essai and error) set into amelioration. First somewhere in the electro-magnetic world we can imagine and anticipate that we all have a linear time memory of our individual life (since TeraByte memory!!smile). Attempt to remember everything,is impossible,my girl friend can get down when she had 3 year old, what i found impressive. Then from this theorical individual linear time line, we got to see the collective, who is probably like fractal geometrie has object, from this life attempt #2 will give a different result(geometric) end than attempt #1 just cause you know it, and act according to. Could be fun to get down time, dividing i guess the conscious and the not conscious of the fact?! smile... let's bad trip, i like negative speculation. Your back in time, suddenly you encounter a geometric break in the time structure(happen in fractal), you do not existe in the society anymore, no friend no family, nothing else that your self... Could be a good thing to simulate in the peace society!. We can, by playing with time end up all counscious in our own and individual conscious cell awared and alone... No problemo i know for math-eux [= mathematician hobbist] but got to get ready for long periode of solitude i'am certain.... and futur? plus social utopia, when it's clear to me that since a long time same people come back... Just come from the museum with a exposition about Rome, to figure than Constantin really look like one of my old boss has exemple.... anyway both are For people with lot's of energy, adventurer.. one thing sure... my grand-parent are not this kind of triper. pray your fractal result. sebastien Helie

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FOTD 12-10-11 (Reckless Driving [No Rating])
by Jim Muth 13 Oct '11

13 Oct '11

FOTD -- October 12, 2011 (No Rating) Fractal visionaries and enthusiasts: Today's image is a blow-up of a tiny hole in the upper right part of the 'infinite ocean' image of October 10. Out of curiosity I checked to see what the hole was about, and to my surprise found the fog shrouded midget car being driven quite recklessly by the driver whose head is clearly visible through the mist. As soon as I saw the driver and his car, I knew the name of the image must be "Reckless Driving". Actually the mini car is a Z^sqrt(2)+C minibrot that exists in its full form in the Mandelbrot aspect of the East Valley of the parent fractal, which resembles nothing quite as much as a kidney bean. The holes in the fog obscuring the mis-shapen car and driver are basically Julia sets of what lies under them. Since the entire image is kind of a joke, and the calculation time is a cumbersome 34-1/4 minutes, I gave it no rating. The calculation may be avoided by viewing the finished image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high definition image is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The classic FOTD web site is at: <http://www.Nahee.com/FOTD/> Today's weather left much to be desired here at Fractal Central. Heavy clouds and occasional rain spoiled every outdoor activity, not that any were planned, while the temperature of 57F 14C kept the fractal cats in cold weather mode. The local humans, FL and I, spent the day doing what needed to be done, and did it without powdermilk biscuits. If all goes according to plan, the next FOTD will be posted in 24 hours. If not, who knows? Until whenever, take care, and if we took the money from the top one-percent of wealthiest people in the US and distributed it equally among the rest, how much would each person receive? (Poverty cannot be significantly reduced by making the wealthy people poor.) Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Reckless_Driving { ; time=0:34:12.35-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.257646/\ 0.768567/43.47637/1/-55/0 params=89.99/0/89.99/\ -78.25/0.13/0.00037/0/0/1.4142/0 passes=1 float=y maxiter=100000 inside=0 logmap=248 periodicity=10 colors=000m8Jh9KcAMZBOUCQPDSMEUKFVLGWMHXNIYOJZPK_Q\ LaRMcRLdSLeSKfTJgTJgUKgUJgUJgVKgWLiXLkYMlZNmZQmZSl\ ZUj_YiY_hW`fTbeQddMebKgaGh`DhZAiY6kX2jY3kW3lU3lS3l\ Q3mP3nN3nL3nJ4nI4nG4nE4oC4oB4o94o74o54o43p83qC3qF3\ rJ3rN3sQ3sU3tY3t`3sd3rh3qk3oo3mr4jo4gm5ei5cf6ac6_a\ 7Y_7WZ8UX8SU9QS9OPAMNAKKBIIBGFCEDCDBDCDEDEFEFGFGHG\ HIHIJIKKJLLKMMLNNMOONPPORQPSRQTRRUSSVTTWUUYVYZdb_X\ U`YUaZVb_Vd`WeaXfbXgzYKlZidZidZjcYkbYkaXlkXzaXmbWm\ cWmcWncVncVocUocUocUpcTpcTqcTqcSqcSrcRrcRscSscTsbU\ taUt`Uu_UuZUuYUvXUvWUwVUwUUxTUySUzRUzQZzPZzOZzNZzM\ ZzLZzKZzJZzIKmHKmGKmFKmEKmDKmCKmBKmAKm9Km8Km7Km6Km\ 6Km6Km6Km6Km6Km6Km6Km6Km5Km5Km4Km4cz4cz3cz3cz3cz6c\ z8czAczAczAczAczAczAczAczAczAczczzczzczzczzczzczzc\ zzczzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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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FOTD 11-10-11 (Conventional Limits [8])
by Jim Muth 12 Oct '11

12 Oct '11

FOTD -- October 11, 2011 (Rating 8) Fractal visionaries and enthusiasts: Today's image is named "Conventional Limits". The name refers to the image's magnitude of over 3*(10^13), which is right at or a little beyond the useful limit of the conventional math routine. The image is a very high iteration scene rather deep in the north branch of Seahorse Valley. The logmap value of 91500 is perhaps the largest in FOTD history, though I do not keep a record of this. The maxiter of 1000000 has been exceeded many times however. The record is 2147483647, which is the maximum value permitted by the program. The calculation time of only 5-1/4 minutes is due to the speed of the type=mandel formula on my 2000mhz machine. On the old 200mhz unit, which still sits idly on a nearby table, the image would take well over an hour to finish. (An arbitrary-precision version would take about one week on the old machine.) The rating of an 8 is the highest in several days, once again showing that the wonders of the Mandelbrot set are nowhere near being exhausted, and never will be. (Regardless of how much is taken from infinity, an infinite amount always remains.) The completed image is posted on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> A high-definition version may be found at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site, with images back to April 1997, is at: <http://www.Nahee.com/FOTD/> Today began with dense fog here at Fractal Central. The fog lifted in the late morning, revealing a partly cloudy sky. The temperature of 73F 23C was pleasant for mid October, but the pleasant conditions will soon end. The forecast is for rain tonight, as well as Wednesday, Thursday and Friday. The local farmers prayed for rain all through June and the first half of July. With the 32 inches 80cm of rain that has fallen since the middle of July, I feel their prayers have been adequately answered. (And from what I hear on the local news, so do they!) The fractal cats, who always keep their paws dry, spent the day plotting mischief, while FL and I kept the mischief from happening. The next FOTD will be posted in 24 hours. Until then, take care, and how will the world ever agree on peace when it can't even agree on which religion is true? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ConventionalLimits { ; time=0:05:16.54-SF5 on P4-2000 reset=2000 type=mandel passes=1 float=y inside=0 center-mag=-0.74999775055745050/+0.003016340258101\ 39/3.2935e+013/1/-37.5/0 params=0/0 maxiter=1000000 logmap=91500 periodicity=10 mathtolerance=0.05/1 colors=000cWkuWkuYiu_fuadudbuf`uhZujWulUunSupPurNu\ tLuvJuxHuzHsxHqvHptHnrHmqHkoHjmHhkHfiHegHceHbcH`aH\ __HXYHVTHTQHROHPNHNMHMLHLKJLKHLKHMLHOMHROHUQHWSHYU\ H_YHaaHdeHfiHhmHjqHltHnvHpyJrzLszNtzPtzRszTszVrzWq\ zWqzWqyWpyWpxWowXowXnvXnuXnuXmtXmsXlsYlrYkqYkqYjpY\ joYjoYinZimZhmZhlZgkZgkZgj_fi_fi_eh_eg_dg_df_ce`ce\ `cd`bc`bc`ab`aa``aa``a`_a__a_ZaZYaZYaYXbYWbXWbXVbX\ UbXUbWTbWTbVSbVRbTQaURbVRcWSdXTeYTfZUg_UhaVibWjcWk\ dXleYmfYngZohZpi_qj_rk`slatmaunbvobvpcvsevqcvobvm`\ vk_uiZsgYreWpcVoaUm_SlYRjWPiUOgSNfQLdOKcMIbKH`IG_G\ EYEDXCBXDCWECVEDVFDUGETHESIFRJFQJGQTYPmYhlsekvcxH5\ pLIgPUZTfQXrUSmXNh_IcbDZe9UP7E800S7Bk9MxBXxNauYeph\ infcmeZkcTjbOhaIg_NeZUdYcXScQMcJHAQFEXDHcBLi9Op7Sw\ 5Vx4YiAMQFB6K5QQHiVXx_lx_mu_nu_oKGPLHOMHNNIMOILOJL\ PJKQKJRKISLHTLGTMFUMEVNEWODXPCYQBZRA_T9_V8`X8`Y7aY\ 6bY5cY5cY5dY5eY5eY5fY5fY5 } END PARAMETER FILE=========================================

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FOTD 10-10-11 (The Infinite Ocean [6])
by Jim Muth 11 Oct '11

11 Oct '11

FOTD -- October 10, 2011 (Rating 6) Fractal visionaries and enthusiasts: The rating of a 6 that I gave to today's image might be a bit conservative. The image trick is one I have often used before, and this repitition held down the rating a point or two. The outer shape is a Julia set of East Valley of the Z^(1.4142)+C Mandeloid. The chaotic stuff along the 'horizon' inside the Julia set is a grossly enlarged view of the north shore line of the East Valley, rotated so that its edge cuts straight and level across the scene. The sickle-shaped stuff scattered about the lower part of the Julia set is made of the same stuff fractal trees are made of. In fact, only a small tweaking of the parameters will produce a fractal tree. The name "The Infinite Ocean" means just what it implies. The number of fractals is infinite, and the individual fractals are also infinite. This produces a total of (infinity)*(infinity) possible fractals. But do not be too overwhelmed. Infinity multiplied by infinity is still infinity. (Infinity must be raised to the power of infinity to produce a higher infinity.) Today's image finishes on my 2000mhz machine in 13 minutes -- quite slow for an image with a rating of a 6. Visiting the web site defeats this slowness however. The official FOTD web site, now totally back up and running, may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> The finished image is available at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic FOTD site is at: <http://www.Nahee.com/FOTD/> The day began with fog here at Fractal Central. The fog lifted by 10am, but the sun was filtered by a veil of higher clouds for the rest of the day. The temperature of 75F 24C left nothing to be desired however. The fractal cats were exhausted by yesterday's boisterousness, and spent most of the day sleeping. The human beings, being human, did human things. The next FOTD, an abstract thing, will be posted in 24 hours. Until then, take care, and I really do enjoy the way this crazy world keeps getting crazier. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Infinite_Ocean { ; time=0:13:02.47-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=t maxiter=100000 center-mag=-0.187793/0/0.8130081/1/-90/0 float=y params=89.99/0/89.99/-78.25/0.13/0.00037/0/0/\ 1.4142/0 inside=0 logmap=yes periodicity=10 colors=000D8JE9KFAMGBOHCQIDSJEUKFVLGWMHXNIYOJZPK_Q\ LaRMcRLdSLeSKfTJgTJgUKgUJgUJgVKgWLiXLkYMlZNmZQmZSl\ ZUj_YiY_hW`fTbeQddMebKgaGh`DhZAiY6kX2jY3kW3lU3lS3l\ Q3mP3nN3nL3nJ4nI4nG4nE4oC4oB4o94o74o54o43p83qC3qF3\ rJ3rN3sQ3sU3tY3t`3sd3rh3qk3oo3mr4jo4gm5ei5cf6ac6_a\ 7Y_7WZ8UX8SU9QS9OPAMNAKKBIIBGFCEDCDBDCDEDEFEFGFGHG\ HIHIJIKKJLLKMMLNNMOONPPORQPSRQTRRUSSVTTWUUYVUZWU_X\ U`YUaZVb_Vd`WeaXfbXgcYhdZidZidZjcYkbYkaXl`XlaXmbWm\ cWmcWncVncVocUocUocUpcTpcTqcTqcSqcSrcRrcRscSscTsbU\ taUt`Uu_UuZUuYUvXUvWUwVUwUUxTUySUzRUzQZzPZzOZzNZzM\ ZzLZzKZzJZzIZzHZzGZzFZzEZzDZzCZzBZzAcz9cz8cz7cz6cz\ 6cz6cz6cz6cz6cz6cz6cz6cz5cz5cz4cz4hz4hz3hz3hz3hz6h\ z8hzAhzAhzAhzAhzAhzAhzAhzAhzAhzAmzAmzAmzAmzAmzAmzA\ mzAmzAmzAmzAmzAmzAmzAmzAmzAmzArzArzArzArzArzArzArz\ ArzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAwzAw\ zAwzAwzAwzAwzAwzAwzAwzAwz } 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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FOTD 09-10-11 (Julia in Mandelbrot [6])
by Jim Muth 11 Oct '11

11 Oct '11

FOTD -- October 09, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image shows Julia sets of a point on the west shore line of the large period-3 north bud of the Mandelbrot set. I say Julia *sets* because the image is filled with countless Julia sets. All the tiny orangish things spotting the deep blue background are smaller Julia sets. But don't bother checking them. They all appear the same as the large set filling the frame. The image is actually a scene in a 'perturbed' Mandelbrot set. The perturbed sets are slices through the Julibrot in the Mandelbrot orientation, but they have starting points other than 0,0. (For some reason, the type=mandel formula starts the points at the square root of the value assigned the parameters, but IMO, the formula is so fast that this is only a tiny, easily- worked-around flaw.) In this particular area of this particular perturbed set, the low-iteration stuff appears to be moth-eaten, filled with holes of varying size, while the high-iteration stuff remains mostly hidden beneath the low-iteration stuff, with only small patches showing through the moth-holes. The curious thing is that the moths who ate the holes were very well-educated, and ate holes in the shape of Julia sets. To see the true Julia set of this area, reset the parameters to 0,0 and, without waiting for the image to finish, strike the space bar twice. A skeletal Julia set will result. At this point, reset the logmap to 1 to see the surface Julia set or leave the logmap at minus-4375 and do an inzoom or two to reveal another version of the large Julia set that appears in today's FOTD lurking in the depths, just a bit too small to be visible at the surface. The name "Julia in Mandelbrot" accurately describes today's image. The rating of a 6 is a bit low to fully justify the 7-1/4 minutes required to run the parameter file. To avoid all this tedious calculation, check the finished image on the official FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> Or check the high definition at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original, now classic FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> Morning fog and afternoon sun earned mixed reviews for the weather in the Fractal Central area today. The temperature of 79F 26C was about as perfect as it can get however. The fractal cats were apparently energized by the perfection, and spent a good part of the afternoon playing hide and seek games on the book shelves in the hallway. The humans, who always knew the location of one another, spent the day dreaming of things to come, such as the next glorious FOTD, which will be posted in under 24 hours. Until then, take care, and from what I read in a magazine recently, the Limerick: A crusty old codger named bright, Could travel must faster than light. He took off one day, In a relative way, And came back on the previous night. just might be true. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Julia_in_Mandlbrot { ; time=0:07:16.13-SF5 on P4-2000 reset=2004 type=mandel passes=1 center-mag=-0.2176\ 546382061398/+0.7252284839096655/6.042805e+009/1/\ -145/0 params=-0.984435560167241/-0.220313119907224 float=y maxiter=2500000 bailout=9 inside=255 logmap=-4375 periodicity=0 colors=00055H55H56H45H46H45H36H35H36H36H26H26H25H1\ 5H14H14H14H45J76LA7NC8PF9RIATLBVNBWMCVLCVKDVJDVIEU\ IEUHFUGFUFGTEGTDHTDHTCISBISAJSbSDcRCdQCdPCePCeOBfN\ BgMBgMBhLAhKAiKAjJAjIAkH9kH9lG9mF9mE8nE8nD8oC8oC8p\ D9pD9pE9pE9pF9pF9pF9pG9pG9pH9pHApIApIApIApJApJApKA\ pKApKApLApLApMBpMBpNBpNBpNBpOBpOBpPBpPBpPBpQCpQCpR\ CpRCpSCpSCpSCpTCpTCpUCpUCpVDpVDpVDpWDpWDpXDpXDpXDp\ YDpYDpZEpZEp_Ep_Ep_Ep`Ep`EpaEpaEpaEpbEpbFpcFpcFpdF\ pdFpdFpeFpeFpfFpfFpgGpgGpgGphGphGpiGpiGpiGqjGrjGsk\ GtkHulHvlHwlHxmHymHznHznHznHzoHzoIzpIzpIzqIzqIzqKz\ rKzrIzsKzsKzsKztUzuUzvUzwUzxUzyUzzUzzczzczzczzczzc\ zzczzczzczzczzczzczzczzczzczzczzczzmzzmzzmzzmzzmzz\ mzzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzwzzwzzwzzwzzwzzwz\ zwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzw\ zzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzz\ wzzwzzwzzwzzwzzwzzwzzwzzw } END PARAMETER FILE=========================================

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