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Fractal Music
by Albrecht Niekamp 21 Oct '13

21 Oct '13

HI, although not being a registered member anymore I would like to present one of my latest musical creations: Pelog_Rock. The name is taken from the pentatonic Gamelan scale used. The music was created by an automatic algorithm scanning the "Springtime" image which came about in the preliminary stages of my multifractal project. For scanning the phantastic Swirl5.IFS shown in Fractint was used. : Albrecht : https://www.dropbox.com/s/2phqpwq5jgw56d0/Pelog_Rock.mp3 https://www.dropbox.com/s/mbzs7aq8jupaw1d/springtime.bmp https://www.dropbox.com/s/e8kz1b0nlwvbhaj/Swirl5.gif

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My versions of Jim Muth's FOTDs & their parent fractals for Oct 13 - 16 are up.
by Hal Lane 19 Oct '13

19 Oct '13

My versions of Jim Muth's FOTDs and my investigations into their parent fractals for October 13 - 16, 2013 are on my site now. Please use this link to keep my counters up to date -- thanks: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html - Hal Lane ######################## # hallane(a)earthlink.net ######################## --- This email is free from viruses and malware because avast! Antivirus protection is active. http://www.avast.com

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FOTD 18-10-13 (First Light From Vega [A-7,M-6])
by Jim Muth 18 Oct '13

18 Oct '13

FOTD -- October 18, 2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: Today's fractal lies in the same parent fractal as yesterday's. To find today's image, I checked a filament in the East Valley area of the obvious minibrot just north of the main body of the parent instead of yesterday's tiny spike on the positive X-axis. What I found near the minibrot is mostly typical East Valley features, but with enough extra decorations to make a deeper view worth the effort. I eventually settled on a tiny minibrot -- the one that appears at the center of today's image. I colored the scene to give the appearance of a series of ridges surrounding the minibrot, but unfortunately, the coloring is not enough to raise the art rating above a merely adequate 7. Since we have been on the same math theme for a couple weeks, the math rating is only a 6. The name "First Light From Vega" has no relation to the image. It is the name of a long forgotten drawing I did many years ago. I have no idea why the name popped into my head today, but it sounds kind of arty, so this will be the name of today's fractal. The calculation time of 4-1/4 minutes borders on being unacceptably slow, but is still within reason for those with fast machines that can do DOS. Visiting the web sites will make the task of viewing the image simpler and faster however. The finished image is posted on the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> A cloudy morning gave way to a mostly sunny afternoon here at Fractal Central today, with a seasonal temperature of 61F 16C. The fractal cat, Nicholas, was more interested in the new arrival, an all-black little girl named Jasmine, than in the outside conditions. He considers the 7-week-old an unwanted newcomer, and lets her know who is boss with occasional apparently harmless hisses and growls. The newcomer is still frightened of the oversized resident fractal cat with the foul mouth, but when the big guy is out of sight, she is quite eager to explore her new surroundings. It will take some time for them to grow accustomed to each other's behavior. Other than keeping an eye on the fractal cat situation, the fractal humans had an uneventful day. We're taking a trip back to Old Fractal Central tomorrow, so the next FOTD will not be posted until at least October 20. Until the next FOTD time actually arrives, whenever that might be, take care, and most people agree that something is wrong with the direction in which our culture is taking the world. Now let's try to agree on exactly what is wrong with us and our culture, and what if anything might be done about it. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= FirstLightFromVega { ; time=0:04:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=+0.4566637948436287/+2.124420312062973/\ 8.337e+011/1/72.5/0 params=0.5/1/0.5/-1/0.5/2/0.25\ /3/-1.176222776541/0 float=y maxiter=1750 inside=0 logmap=189 periodicity=6 mathtolerance=0.05/1 colors=000G00F00E00D00C00B10A209308407506505504503\ 50250150050msIhrCcq6ZpKUoMQlJMgGKbDJZBHU8FP5DK2CF0\ BA0A00900800700600zzzzz0qw0kt0iqEbmBWf8Pc5Ib`UbbR_\ XOWRMRMJNGHJBEF5CB4A73842601400200000rTOkRKePH_NDU\ KAOF6IC3835A54A73A83DA2GC1FD1DF0mj6ge5ba4XX3ST2MO1\ HK0w9eoBZgCS_DLSEEKF7BgdCcZC_TCWNCSHCOBCK5A_XBXSBV\ OBSKBQGCNCCL8CI4B9yoG1aG0PG0TJVQIPNIKKHFHHAEG5DegC\ `_CXTCTMCOECK7mOEhNCcMAZL8VK7QJ5LI3GH1FaZEYTEUNDRH\ DNBCJ5_hQSZHKP8_hhWcaT_WPWPMSJIOCFK6bdxWYhPSUIMFtf\ uYTTvsGnlDfeAPoCSlHViMYfQRacLXqKZnJ_lI`iHagcUpzMxw\ WqudjsmcpgZnbVkYRiTMfOIdJEbEAgKFkQJpWNt`R2gn3ei4dd\ 5c_6bV7aQ8`L9_G9ZBBhPchachnchpchrmptmmvmbTmabmRJmc\ lmSOmszmlomeem_VmTLmMAmiHmdEm_BmV8mQ5mL2mU7mP4mK2m\ lFmgDmcBm_9zW7zS5zOczKczOczMczKzzJzzHzzDzzEzzFzzGz\ zVzzSzzQzzNzzLzzIzzYzzPzz9zzAzzBzzCzzDzzEzzFzz1zz4\ zz6zz8zzAzzCzzEzzDzzFzz5z } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END PARAMETER FILE=========================================

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FOTD 17-10-13 (Things That Might Be [A-6,M-6])
by Jim Muth 17 Oct '13

17 Oct '13

FOTD -- October 17, 2013 (Rating A-6,M-6) Fractal visionaries and enthusiasts: The iterated expression that created today's image is the same one that created yesterday's image. The difference is that in today's image, Z is initialized to a different critical value, which is -1.176... This value creates a parent Mandeloid much like yesterday's but rotated 180 degrees so that the mostly obscured M-set now faces east, with East Valley on the west side. In addition, there are two large minibrots, one just north and the other just south of the main body of the parent. They might be worth a check. A tiny bud and spike extends east along the X-axis from the main body of the parent. Today's scene lies near the tip of this spike. I named today's image "Things That Might Be". When I thought of the name, I was pondering the big question of whether fractals are real, unreal, or something in between. The artistic and math ratings of an everyday 6 show that I think the image could be better. If I had not put so much time into playing with the new kitten, I could probably have worked the image into one that would rate at least one point higher. The calculation time of 15 seconds makes the job of running the parameter file a virtual breeze. The web sites, where the image has already been calculated and posted, can create the actual breeze. The web sites are located at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> The day began with a sky half filled with clouds, but the clouds blew away by mid-morning, leaving a mostly sunny sky for the rest of the morning. The clouds returned in mid-afternoon however, and rain began shortly after. The temperature of 72F 22C was more like September than mid-October. The established fractal cat spent the day trying to decide what to make of the new kitten arrival in the house. At the present time, he is both interested in her and wishes she would go away. Meanwhile, the humans had another normal day. The next FOTD will surely be posted; the question is when. Twenty-four hours from now is the best bet. Until that magical time arrives, take care, and the use of common sense is quite common in the world. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= ThingsThatMightBe { ; time=0:00:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident center-mag=+0.5814917617012194/0/9.23049e+010/1/180 params=0.5/1/0.5/-1/0.5/2/0.25/3/-1.176222776541/0 float=y maxiter=500 inside=0 logmap=34 symmetry=xaxis periodicity=6 mathtolerance=0.05/1 colors=0005gl5dk5aj4Zh4Wg4Tf3Qd3Nc3K`2HY2EU2BP18K1\ 5F12A36A59K6DS8G_AJ`BNaDQbFTcGXdI_eKbfLfgNihOliGeP\ 9Z5HV6PS6WO6cL6jH6rE6yB6tIBoPGjWKebP`iUXoYZl_`iabf\ cdcefafhZhjWjlTlnQnpOorLqtIsvFuxCwzAxxBrwBmvBguBbt\ BXrBSqBMpBHoBBnB68bODdPIePNfQSgQWhQ`iRejRjkSolSsmS\ tlTtlTtlUtlUtlVtlVukVukWukWukXukXukXriYphZng_kf`id\ agcadbbbac`_dYZeWYeUXfRVgPUhNTiLSiLgYLvNMsQNpSOnVP\ kXPh_QfaRcdS`fTZiTWkUTnVRpWOsXLuXJwULlRNaOPRLRGIS5\ Fa8CkAAuCCsGEqKGpOInSJmVLkZNjbPhfQgiSemUdqWbuXaxZY\ s`VobSkdPgfLbhIZjFVkCRgHUdMWaQYZV_W_bTcdQhfNlhPkhQ\ jhRieSibUi_VhXXhUYhRZgO`gLagIbgF`hEZhDXiCViBTjARj9\ Pk8Nk7Lk6Jl5Hl4Fm3Dm2Bn19o08p0Aq4Br7DsBEtEGuIHvLJw\ PKxSLyVNzZOzaQzeRzhTzlUzoVzrTzVRz7Pz6Oz6Nz6Mz5Lz5J\ z5Iz4Hz4Gz4Fz3Ez3Cz3Bz3Az29z28z20z17z15z14z13z02z0\ 1z05zO3zI2zCMzWIzTEzQAzN7zKGzMPzOYzQfzSozUwzWszYoz\ ZjzWfzTazQYzNUzKPzHLzEHzB } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END PARAMETER FILE=========================================

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FOTD 16-10-13 (Mutated Seahorses [A-7,M-6])
by Jim Muth 16 Oct '13

16 Oct '13

FOTD -- October 16, 2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: The farther I delve into these 4-part fractals, the more interesting they become. It's too bad I'm not math literate enough to write a formula that will automatically initialize Z to one or all of the critical points like the 10-year-old 2-part MandAutoCritInZ formula does. But the parabolic-plane method I use works well enough. Today's curious image was created with a combination of straight Z, (1/Z), Z^2 and Z^3, with initial Z set to a critical point of 0.6029... The resulting parent fractal resembles the eastern third of the main bay of an oversized Mandelbrot set, with an entire skeletal M-set where the rest of the bay should be. Today's scene lies in the north branch of the strangely solid Seahorse Valley of this skeletal M-set. There is not much to be said for the image, which speaks well enough for itself, even without being turned into fractal 'music'. If I had more time to work on the colors, the art aspect of the image might have rated more than the actual 7. The math aspect remains a 6, which is good enough. I named the image "Mutated Seahorses" because of the unexpected transformation the seahorse elements have undergone. The down side is the calculation time of 5-3/4 minutes, which will start to drag, especially on slower machines. The drag may be eliminated by visiting the FOTD web sites. The web sites may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Cloudy skies, a few small drops of rain, and a temperature of 64F 18C kept spirits under control here at Fractal Central today. The old fractal cat was too busy checking the 7-week-old new fractal cat through a cracked door to pay much attention to the weather, while the humans kept an eye on the feline situation. So far, the two have not decided what they think of each other. The next FOTD will be posted when the right cosmic time arrives. Until then, take care, and what are skeptics the most skeptical of? Is it space aliens visiting earth in UFO's, bigfoot creatures, lake monsters, mental telepathy, spontaneous human combustion, ghosts, reincarnation, the existence of a conscious and transcendental creative power called God, or everything that lacks the solid approval of conventional materialistic science? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mutated_Seahorses { ; time=0:05:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=-0.9416268908362115/+0.0097462448978816\ /6.419e+010/1/40/0 params=0.5/1/0.5/-1/0.5/2/0.25/\ 3/0.602906705069/0 float=y maxiter=1600 inside=0 logmap=249 periodicity=6 mathtolerance=0.05/1 colors=000lgcjfage_edYcbWa`UYWRVSPSNLPJINGFJCBF97A\ 58545046558A6CF7FK8JP9MTAPUCRUDUVEWWFZWG`XHbXIcWGZ\ WEVVCQVAMU8HU6DU49R5FP6KN6PL7VJ7_H8dF8iJ7gM6eQ5cT4\ aW4__4Yb4Wf4Ui4Sl4Qp4Os4Mv4Km4Le4MX6NP9OGCP8MQPQMP\ _IQiDQm8ei4odAoZ8pS7mM6dK5XL6QJ7LM9FSBBVDFUCISBMQA\ PP9TN8WM7ZM7`RAbWCd`EffGhkIjpKluMgsOcqQZpSVnUQmWMk\ YIj_LiZOhYRgXUgX_dbeahk_nqXtvVypUykTyeSy`RyVQyQQyR\ TnSVdSXVT_KUaAUc0bZ4jV7rRAtOJvMSwK`zXzuaypeykjygny\ hemiXajOQkFEl63w4Lx4Qy4Vz4`z4ez5jz6pz7uz8zyBwtDtnF\ qiHndJlZMiUOfOQcJS`EUZlY2iZ8g_De`JcaOaaT_bZYccWdiU\ enSesPcqNboL`nJ_lHYkFXiDVgBUf9Sd7RcCZdGfdKndOudRtb\ Us`XsZZrXarVdqTfqRipPloNnoLqnJtnHvmFymDzlBzlAzkCzk\ EzjFzjHyjJxiKwiMvhOuhPthRsgTrgUqfWpfYpfZqgaqhdqigq\ jjrkmrlprmsrouqprpqoorlnsinvfmvclv`kvYkvWkvTkvRkvP\ kvNkvLkvJkvHkvEkvCkvAkv8kv6kv4kv2fvBbvKYvSUv`QvhSv\ gTvgUvgVvgWvgXvgYvgRvNQvI } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END PARAMETER FILE=========================================

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FOTD 15-10-13 (Sly Trickery [A-7,M-6])
by Jim Muth 15 Oct '13

15 Oct '13

FOTD -- October 15, 2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: To create today's image I combined various reiterated portions of Z^2, Z^3, Z^4 and Z^5, and initialized Z to a critical point of -2.445... The parent fractal that results is in two parts -- a Mandelbrot set rotated 180 degrees and an extra Mandeloid on the X-axis some distance east of the M-set. At first glance, this Mandeloid does not appear critical, but a closer check will reveal that it is filled with perfect minibrots. Today's image lies near the tip of one of the filaments extending from the eastern end of the main spike of the extra Mandeloid. The name "Sly Trickery" is a comment on the rendering method, where instead of the usual outside=iter, I reset the outside to 'tdis', which creates the effect of terraces surrounding the central minibrot. This trickery took a full point from the art worth, dropping it to a 7. The overall effect is not in the math, it is in the program. The math aspect is worth only a 6. The calculation time is a very fast 45 seconds, but the inconvenience of setting up and running the parameter file still exists. A quick trip to one of the web sites will eliminate this chore and make life easier. The web sites may be accessed at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> The day began with fog, but when the fog cleared off around 9am, it led to a perfect day with total sun and a temperature of 70F 21C. The fractal cat enjoyed the conditions fully, then retired to my favorite chair to spend the afternoon sleeping. The humans passed the day as just one more in a near endless string of similar days. The next FOTD will be posted in a number of hours. Until the number is revealed, take care, and before you look to the light for enlightenment, be sure it is the right light. Remember that the world is filled with wrong lights. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Sly_Trickery { ; time=0:00:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident center-mag=-1.752840469303519/+0.0457707436589533/\ 3.507371e+009/1/-175/0 params=1/2/0.2/3/0.1/4/0.04\ /5/-2.445428353012/0 float=y maxiter=1500 inside=0 outside=tdis periodicity=6 mathtolerance=0.05/1 colors=000IUJLUJOVKRVLVWLYWM`XNcXNfYOiYPlYPdURYQTQ\ MUJIWBEY4AZBE_HH_NL_UO`_S`eV``ZYWbWSfTNjRInPErM9vK\ 5yIFoSOeaMbbL_cJXdIUeGRfFPfJWYMbPPiGQjHQjIRkJRkJSl\ KSlLTmLTmMUmNUnNVnOVoPWoPWpQXpRXpRKV5IS6GP6EN7CK7A\ I88F86C94A9277000576DF8JN7PS7VY6`c5fh5ln4rt3wy3tp6\ qg9nZBkREhIGe9J91LH0bP0tSKuWUuZaub_v`Zv_XvYVwXUwVS\ wURwRVwOZwLawIjwFswzvwzzwzzwmzwczvZzuUztKzs4ur4tq4\ tp4to4sn4sm4rl4rk4rj4qi4qh4qg5nh5ki6ii6fj7dk7Xk7Pl\ 8Im8Am93n95o9DoCKpEQpHRqJTqMUqOVrRXrTYsWZsY`s`atbb\ tedugeuifugesfdqecocbnbala`j`_hZZgYYeXXcWWaUV`TUZS\ TXRTWKQOEOH7LA1J37K5DL7JM9C4iC4kC4mB5oB5qB5sB5uGAu\ KFuPKuTPuYTuaYufbujguoluzpuziozfnzcmz`lvYkzWjza`zf\ SzlJzqAzv1zq6zmBziGzeLzaQzYUzTZzPczLhzHmzDrz9vzAtz\ BszBrzCqzDpzDnzEmzElzFkzGjzGhzHgzIfzIezJdzJczygzcv\ zavzZvzXvzVuzSuzQuzOuzLuzJuzHuzIqzJnzKkzLhzMdzNazN\ ZzOWzPSzQPzRMzSJzSGzTHzTI } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END PARAMETER FILE=========================================

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J.S. Bach -- Crab Canon on a Möbius Strip
by Paul N. Lee 15 Oct '13

15 Oct '13

Here is something a bit different, which I found quite enjoyable and intriguing. Well worth the three+ minutes of your time (in my opinion): http://youtu.be/xUHQ2ybTejU Sincerely, P.N.L. -------------------------------------- http://www.Nahee.com/PNL/Fractals.html http://www.Nahee.com/Fractals/

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FOTD 14-10-13 (Raspberry Riot [A-8,M-6])
by Jim Muth 14 Oct '13

14 Oct '13

FOTD -- October 14, 2013 (Rating A-8,M-5) Fractal visionaries and enthusiasts: In today's image I mixed together various portions of (1/Z), (Z^2), (Z^3) and (Z^-4). With this strange combination, the only critical value I could find for initial Z is -0.6926... The resulting Mandeloid appears as an undersized Mandelbrot set located well out on the positive X-axis. Today's image lies on the eastern edge of the north branch of Seahorse Valley of this remote M-set. The large-scale shape of the image elements is routine Seahorse Valley stuff that can be found in Seahorse Valley of the classic M-set, but the small-scale texture is unique to the particular exponents that were combined into today's image. This texture could (most likely) never be found in the M-set with the outside set to 'iter' as it is in today's image. The name "Raspberry Riot" is obviously based on the eight brilliant red elements surrounding the central minibrot. The artistic rating of a superior 8 indicates that I put extra effort into the coloring. The math rating of a humdrum 5 shows that IMO the math trick is beginning to grow stale. The drawback is the calculation time of 9-3/4 seconds, which is slow indeed. But the web sites are always there to ease the impatience. So don't be impatient! Check different versions of the finished image at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> An un-notable mix of sun and clouds prevailed here at Fractal Central today, with a near average temperature of 68F 20C. The fractal cat, who may soon find himself with a new companion, enjoyed the conditions well enough. The humans, with other things to do, neither enjoyed nor were annoyed by the weather. The next FOTD will be posted before too long. Until then, take care, and let's put all the political losers out to pasture. If we did, I wonder who would be left to run things. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Raspberry_Riot { ; time=0:09:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=+1.59666112836225/+0.00220736012223885/\ 8.321261e+011/1/-56.5/0 params=4/-1/2/2/-1/3/0.5/\ -4/-0.692615048216/0 float=y maxiter=2250 inside=0 logmap=418 periodicity=6 mathtolerance=0.05/1 colors=0002GP2JU2MZ8PcLThWVniXtt_zmYwfVt_SqTPnMMkE\ JgzRE3rT41683CD5IH7PM9VQA`UCgZEmbGsgIzPi22505A17G2\ AL3CR4FW4Ha5Kf6Ml7Pq8Sw9UqK596AIDFRJK_QPhWHUb5KE5E\ C4A06C1AE1DF2HJ2KN3OR3RV4VZ4Yb5af5dj6hn6cr7Zm8UhUP\ cMKZXFUiASe8VmAShCPcEMZGJUIGPKDKMAHO7FR8HU8JX9KcAM\ pBOzCQ635C6AIAFODKUGP_KUiNZqRcwRzzMmz8iq0Sm04c18_2\ AY3CU3AQ48S56W60_7Kc7Ug8ck9moAtsBzz4zz9zvE5rI7mN9h\ MBcLDZKFVJHVI3VH6VG9VFCVEFVDIWCLWBOWARW9UZ9XaA_eBc\ 1423855D86HB8LEAQH0410921E31I42N52S63W73`84e94iA5n\ B5sC6xE10330740B60F80J90NB0RD0UE0YG0aI0eJ0iL0mN1q8\ 64GC8OICXPHdVLl`PugU31N63i543A86FDALHDQLHVUK`XOhaR\ ofXohYuka51DA2QG4b4868GCDPI2525B47G7AM9DRCFXEIaHLg\ JNlMQrOTxR650CA1JG1PL2VQ3aW3g`4nf5LU1fU30W20Y40_60\ a91bB1cD1dF1eI1fK2gM2hO2iR2jT2kV3lY2m`4nc6of8piAql\ EroIsrMtvQuwUvwYwwaxweywizwmzzrzzvzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END PARAMETER FILE=========================================

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FOTD 13-10-13 (Mystic Night-Sky [A-8,M-6])
by Jim Muth 13 Oct '13

13 Oct '13

FOTD -- October 13, 2013 (Rating A-8,M-6) Fractal visionaries and enthusiasts: To create today's FOTD, I quadrupled the portions of the exponents of Z that created the most recent image, that of October 11. In today's image the two wings sprouting from the East Valley area of the original parent have degenerated into two zig-zagging filaments strung with a kind of flower buds. Today's scene is located rather deep in East Valley, in a flower bud on the southern filament. The name "Mystic Night-Sky" describes the mood of the image, with its overall deep somber grayish and bluish tones. The implication is that there is a lot more going on up there in the sky than is visible to the eye. Not being limited by rational scientific skepticism, I have a far easier time believing in spirit beings in the sky than aliens from the stars in their warp-drive material space craft. And invisible spirit beings certainly are mystical. The artistic rating of an 8 and math rating of a 6 might be a little conservative, but the theme is starting to grow old. The calculation time of 1-3/4 minutes is fast enough, though a visit to the web sites can speed up things even more. To avoid the calculation, check the web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> Cloudy but bright weather made the day with its temperature of 68F 20C rather pleasant here at Fractal Central. At least the fractal cat thought so, as he spent an unusually long time in the southwest window, his entertainment center. The fractal humans spent the day doing nothing much, which could hardly be better. The next FOTD will be posted in the near future. Until that vague time arrives, take care, and keep a sharp eye on the world of fractals as well as the sky. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Mystic_Night-Sky { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident center-mag=+0.3274631404590703/-0.0003459273012306\ /4.86033e+007/1/-32.5/0 params=2/1/1/2/0.666666666\ 6666667/3/0.5/4/-0.9999999999999999/0 float=y maxiter=900 inside=0 logmap=134 periodicity=6 colors=000KA_F9XE8UD7SC6PB5NA4K93I82F71C60B50A4093\ 082071060060050040030020010000000000008mZ7hV6cS5_P\ 5VM4RJ3MF2IC2D91E60F31GY2HX3IW4JV5KUALTGMSKNRLOQIN\ PELMAJP5GR1EN1BK18G16D04A026013`z8Tm6M`4E_37b11YXT\ TGNaCHS9BJ6593_d0W`0TX0QT0MQ0JM0GI0DE09B0670030AZG\ KUNUUUcUZmUcmUhmKmnAppBsrDvpFnpKgpP_qUTqZMrcKtcIzc\ GzcFzcSzZdzUazU_zcYzhWzmTzmRzmPzmNzmUzrczwmzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzCDa50`50_50Z50Y50X50W50U50S\ 50Q50O50M40L30K20I10G00F00C00A008006004002FjXDdSBZ\ O9TK7NG5HC3B8154VqVQiQMZMHMHDDDzzzzzzzzzosxfovYitQ\ crIYpKSnIQlGOjEMhDLfCKdBJbAI`9HZ8GX7FV6ET5DR5CP4AN\ 49L38I37F26C249135123011xkUcWKKGAaUXZUUWUSTUPRUNOU\ LLcIJcGILeLJiNHlPFoRDrTBuVAxXCuYDr_Ep`FmbHkcIhdJff\ KcgMaiNZjOXkPUmQRnSPpTMqUKrVHtXFuYCwZAxc7yc5umBqmH\ mmNimSeoYarcYuiVwnTxkSxhRxePzbOz_NzXLzUKzSJzPHzMGz\ JFzGDzDCzABz8Ez9Gz9Iz9Kz9 } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END PARAMETER FILE=========================================

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FOTD 11-10-13 (Vision in the Sky [A-9,M-6])
by Jim Muth 11 Oct '13

11 Oct '13

FOTD -- October 11, 2013 (Rating A-9,M-6) Fractal visionaries and enthusiasts: Those who have no interest in the fourth dimension should skip to the start of the fractal stuff 12 paragraphs below. The image is pretty good, at least in my humble opinion. The fourth spatial dimension, where the Julibrots live, holds many things that defy common sense when they are squeezed into our everyday three dimensional space. One of the most curious is the strange motion known as double rotation, in which a 4-D object such as a hypersphere may rotate around two absolutely perpendicular planes at the same time, with each plane rotating on itself independently of the motion of the other plane. In 3-D space, when two rotations are applied to an object, the rotations combine into a single resultant rotation, but a double-rotating 4-D hyper-object is in an entirely different condition. This strange motion is impossible to visualize in 3-D space, but with some effort I have worked up a crude visualization of a hypersphere subject to double rotation. Hopefully, my description will communicate at least some of my visualization. The trick is to rotate the view in 4-D space. I begin by visualizing a 3-D sphere like the earth. On the curved 2-D surface of this 3-D sphere, it is possible to move away from the equator at a right angle in only two directions. On the earth these directions are straight north and south, and following these two geodesics one will reach the polar points of the rotating sphere. But on the curved 3-D surface of a 4-D hypersphere it is possible to move away from the equatorial circle at a right angle in any direction in a plane perpendicular to the equatorial circle. Regardless of the direction one chooses, if he sets out at 90 degrees to the equator and follows a straight geodesic line on the surface of the hypersphere, he will intersect the polar circle. The direction in which he sets out determines the point of the polar circle he will intersect. I now drop a dimension and rotate the view 90 degrees. The equatorial circle vanishes except for the point at which the explorer is standing. He now sees himself as standing at a pole of the sphere. The great circle he sees circling the spherical slice of the hypersphere at 90 degrees from his location is the actual polar circle. This is as close as I can come to visualizing a hypersphere. I do it one 3-D slice at a time. Rotating back so that the entire equatorial circle is again in view, the explorer sees that the visible part of the hypersphere is rotating exactly as the earth does, with the equatorial circle rotating on itself. He now is observing a 3-D slice of a hypersphere in a state of a single rotation, and though he cannot see it, he knows that every point of the the polar axis-plane is remaining stationary while it turns in place. Now the fun begins. There is nothing to prevent the polar axis from rotating on itself also, with the equatorial circle as its axis, and when it does, the two rotations are totally independent. The resulting motion of the hypersphere is called double rotation and like everything else in 4-D space, it is impossible to visualize. But to make an effort at visualization, let's assume that, just as on earth, the equatorial circle is rotating on itself once every 24 hours. So far, so good. But now let's assume that the polar circle is rotating on itself once every hour. While standing very near the equator, the explorer finds his location on the hypersphere rotating around the closest point of the equator while being carried forward with the equator and tracing out a kind of helix. The explorer sees the point where he stands rotating around the equator 24 times every time the equator makes one revolution on itself, but the point is not tracing out a simple 3-D helix looped into a ring, only a close approximation. The farther from the equatorial circle he wanders, the stranger the motion becomes. If the explorer were standing very close to the polar circle, he would find the point rotating around the entire hypersphere 24 times before it rotated around the polar circle once, tracing out something like a twisted garden hose, and if he stationed himself at a point halfway between the two axis circles, the point would trace out something that could be visualized only by a being with 4-D vision. The incredible part is that the hypersphere remains rigid while subject to double rotation, undergoing no strain or distortion. A vague idea of the motion of double rotation can be found by observing the 3-D shadow of a double-rotating skeletal 4-D hypercube. Such projections are probably on the internet, though I have not yet searched. The fun does not end here however. In six-dimensional space, triple rotation is possible, but that's a story for another day. Now let's get to today's fractal. To create today's image I cut the portions of Z of yesterday's formula in half. This keeps the critical point unchanged. The resulting parent Mandeloid is larger than yesterday's, with more prominent 'wings'. Today's scene lies near a minibrot northeast of the north wing of its parent. This minibrot is connected to the main body of the parent by a broken filament, but unlike almost all minibrots, which are connected to the main body of the parent at their East Valleys, this minibrot is connected at the southern branch of its Seahorse Valley. Today's scene lies in this strange Seahorse Valley connection. I named the image "Vision in the Sky". Something about it reminds me of a dream I had long ago, where I saw a similar object in the sky. The math interest rates only a 6, but the artistic value is a superior 9. The rather lengthy calculation time of 4-1/2 minutes is a drawback. The web sites will remove this problem however. Enjoy freedom from calculation pains by viewing the finished image at one of the web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> After a night that brought 3.25 inches, 8cm of rain and some minor flooding, today dawned cloudy with light rain still falling. The rain ended before noon and the sky brightened in the afternoon, but the sun failed to appear. The temperature of 64F 18C gave no cause for complaint. The fractal cat, who does not like water, spent the day checking the outside conditions and sleeping under the chair cover. The humans were thankful that the heavy rain resulted in only a few small puddles in the fractal basement. The next FOTD fractal will be posted in the proper time, October 13 is the best guess. Until whenever, take care, and don't be concerned if you fail to understand what I have written say about the fourth dimension and double rotation. I don't understand it myself. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Vision_in_the_Sky { ; time=0:04:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident center-mag=+1.075076292720345/+2.073914299796522/\ 3.727144e+011/1/18.75/0 params=0.5/1/0.25/2/0.1666\ 666666666667/3/0.125/4/-0.9999999999999999/0 float=y maxiter=750 inside=0 logmap=339 periodicity=6 mathtolerance=0.05/1 colors=00050`50_50Z50Y50X50W50U50S50Q50O50M40L30K2\ 0I10G00F00C00A008006004002FjXDdSBZO9TK7NG5HC3B8154\ VqVQiQMZMHMHDDDzzzzzzzzzosxfovYitQcrIYpKSnIQlGOjEM\ hDLfCKdBJbAI`9HZ8GX7FV6ET5DR5CP4AN49L38I37F26C2491\ 35123011xkUcWKKGAa2XZ1UW1ST1PR1NO1LL1IJ1GG0ED0BA09\ 807504202X2LU1JR1HP1GM1EK1CH1BF09C08A06704503201up\ FqlEmhDieCeaBaZAYV9US8RO7NL6JH5FE4BA3772331OuGGaA8\ J5U4IM3DF29714lM4hK3eJ3bH3ZG2WE2TD2QB2MA1J81G71D51\ 9406203102Fd1Ea1DZ1CX1BU1AS19P18N17K06H05F04C03A02\ 70150023EP2BK18F15A025h3N_2IR1DI199048mZ7hV6cS5_P5\ VM4RJ3MF2IC2D9196043z4Zr3Uj3Qb2LV2HN1DF18704EZYAQP\ 7HH38820R10N10K10G10D00A006003`z8Tm6M`4EP37C11gXTk\ GNaCHS9BJ6593_d0W`0TX0QT0MQ0JM0GI0DE09B06703307ZG6\ WE5TD5QC4OB4L9q9mqApqBsqCvpCnpcgpc_pcTpcMrcKtcIzcG\ zcFzcSzwdzsazo_zkYzgWzdTz`RzzPzzNzzKzzIzzGzzEzzCzz\ FzzIzzLzzOzzRzzUzzXzzZCDa } frm:MandelbrotMix3a {; Jim Muth z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=real(p3), h=imag(p3), j=real(p4), k=imag(p4), l=imag(p5)+100: z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| <=l } END PARAMETER FILE=========================================

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