September 2013 - Fractint - mailman.xmission.com

Re: [Fractint] Three Details
by Hal Lane 14 Sep '13

14 Sep '13

Brian, The color map in your: http://bprentice.webenet.net/Fractal%20Images/Set%2018/BP_18_33.png makes the palm tree-like shapes almost look like they have a warm sunset glow behind them. - Hal Lane ######################## # hallane(a)earthlink.net ########################

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Re: [Fractint] Fractal Music Project
by Hal Lane 14 Sep '13

14 Sep '13

Albrecht, I really like both the drumming and the melodic pieces a lot. I was especially pleased to find that the melodic piece was not "aimlessly" wandering. This makes your piece much more approachable for me than some other fractal music. My son liked the melodic piece, too. - Hal Lane ######################## # hallane(a)earthlink.net ######################## ================================================== Author: Albrecht Niekamp Date: 2013-09-13 05:30 -400 To: Fractint Subject: [Fractint] Fractal Music Project HI, : after a long time of silence IÂ´m back again with a new project. After my Multifractal Project which has remained unique as it still is the only software creating fractals using up to five formulas simultaneously here is my Fractal Music project, possibly the only one which deserves that name, there are some details they have in common: : It uses a single algorithm to automatically create music of theoretically indefinite size which never repeats itself. The rhythm is my own definition of an endless shifting rhythm originally inspired by Steve Reich ("Drumming") and Terry Riley ("In C") and on their side by African native music for instance by the pygmies. : The melodies- of course being the other half of the structure "shifting melodies" - are created using pixels of a Bitmap (BMP) fractal, which is scanned using the dots and lines of a freely designed IFS fractal. : The basic software - in and out and conversion of a pixel into musical parameters of a single note - originates in the nineties, author David Strohbeen and is not available anymore. : In addition to the image the music is influenced to a high degree by the IFS fractal used, a pyramid for instance creates a harder rhythmic structure, a spiral a softer melodic structure. Listening closely and relaxed you may well find that the general atmosphere of the music is that of the originating fractal. : I converted JimÂ´s "End of the World" image, FOTD Aug27, loved it at first glance. Thanks for that, Jim. Including links of the WAV files - mp3 is not satisfactory - and the original MID files. Be careful when using Midi: The sound depends on the fonts used and therefore maybe disapointing.The soundfont used is WeedsGM3, google for it. Use only a player that does not change the parameters. The creative player destroys the music, Winamp is ok. : Albrecht Niekamp] : SPIRAL1.IFS { 0.788 -0.424 0.242 0.860 1.649 5.431 0.896 -0.121 0.258 0.152 0.053 -6.722 1.377 0.052 0.182 -0.136 0.091 0.182 6.086 1.568 0.052 } : http://www.crosscanpuzzles.com/Aug13/082713.html https://www.dropbox.com/s/1c7bl26vc44lqy6/120913D3.MID https://www.dropbox.com/s/kvastwz6oopb900/120913D3.wav https://www.dropbox.com/s/odhd6582zzu6cy1/11091301.MID https://www.dropbox.com/s/94mlkbmmdwvydlp/11091301.wav =========================================================

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FOTD 13-09-13 (The All-Seeing Eye [A-5,M-9])
by Jim Muth 13 Sep '13

13 Sep '13

FOTD -- September 13, 2013 (Rating A-5,M-9) Fractal visionaries and enthusiasts: Today's image shows what happens in the fractal that results when the whimsical expression (Z^1.5)+(1.5*Z^2)+(2*Z^2.5) +(2.5*Z^3)+C is iterated with Z initialized to the assumed critical value of -0.3968... Zero appears to be a second critical value, but I have not yet checked this fractal. The parent fractal of today's image looks not at all critical. It consists of little more than a roughly circular open bay with an area of sandy debris along its western shore line. So far, so good, but look at today's image, which shows what lies buried not very deep in this debris. About 15 years ago I discovered a near-perfect rectangle. In today's image I have found a near-perfect equilateral triangle. This raises the math value to a superior 9. With little more than sand, not very attractive filaments, hurried coloring and a triangle going for it, the artistic worth remains mired at a humdrum 5. The name "The All-Seeing Eye" came to mind when I happened to notice the back of a one-dollar bill, which has the image of an unfinished pyramid with an eye printed on it. I guess the Masons are in town. The calculation time of 1-3/4 minutes will pass in two flashes, even faster on the FOTD web sites. For peace of mind, check 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> Much cooler air brought a refreshing relief to Fractal Central today. With a mix of clouds and sun, a temperature of 70F 21C and much drier air, the day could hardly have been improved upon. At least the fractal cat thought so. The humans always find a way the day could have been better however. The next FOTD will be posted, that's a promise, but there is no guarantee of the exact time. Until whenever the time comes, take care, and see you then. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_All-Seeing_Eye { ; time=0:01:45.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident float=y center-mag=-0.6614804957/+0.0746736023/5347/1/-119\ /0 params=1/1.5/1.5/2/2/2.5/2.5/3/-0.3968321221967\ /0 maxiter=1000 inside=0 logmap=29 periodicity=6 colors=000DDLCCK9BI6AH39F78EB7BE69H57K45M38O3AR3DV\ 3FY3H`3KZ3MX2PV2RT2TR2WO2YR2`T2bV2dX1gZ1i`1lb1nd1p\ f1sh1uj1wi2vi2vi2vi2vi2vi2vh2vh2vh2vh3vh3vh3vg3vg3\ vg3vg3vg3vg3vi5uj6ul7um8uo9tpAtrBtsCttDtpHllLehPZd\ Tz`XzX`zWZzWYzWWzVVzVUzVSzURzUQzUOzTNzTMzTKzSJzSHz\ SGzRFzRDzRCzQBzQ9zQ8zQ7zOUzQUzSUzTUzVUzWUzYUzZUz`U\ zaUzcUzeRzfPzhMziJzkGzlDznAzo8zbIzRSzFaz3jz5hq6gq8\ fr9erBdsCcsDbtF`tG_uIZuJYvLXvMWwNVwRRuVOsZLqbIofEm\ jBkn8ir5gu2er6ep9enCelFejIehLefOecSeaVe_YeY`eWceUf\ eSieSjcTjaTk`UkZoGLpFKqFJrEIsDHtCGuBFvBErAGnAHk9Ig\ 9Jc8K`8LX7MT7NQ6OM6PI5QF5RB4S74T44U69T8DTAHSCLSEPR\ FURHYQJaQLePNiPOmPMlQKlRJkRHkSGjTEjTDiUBiVAiVBhTCh\ SChRDgPEgOEgNFgLGfKGfJHfHHfGIeFJeDJeCKeBLd9Ld8Md7M\ d6KcEJcMIcTHc`GcgFcoEcvGauH`uI_uJZuKYtLXtMVtNUtOTt\ PSsQRsRQsSOsTNsUMrVLrWKrXJrYIrZJn_KkkQdiQbfRadR_aR\ ZZSXXSWUSUSSTPTRMTQKTOHUN } 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 11-09-13 (Island Universe [A-6,M-7])
by Jim Muth 13 Sep '13

13 Sep '13

FOTD -- September 11, 2013 (Rating A-6,M-7) Fractal visionaries and enthusiasts: Today's image takes us to the second critical point of the current parent Julibrot, which is -0.26... The resulting parent Mandeloid again appears much like the non-critical one that results when Z is initialized to zero. Today's scene lies in a bit of debris inside the period 2 bud on the NNW shore line of the main bay of the parent. (The 'bud' on the negative X-axis of the parent Mandeloid is not a true bud.) I named the image "Island Universe". The name refers to the central fractal complex, which because of the coloring, appears to be an island. Today's ratings have dropped from those of the previous FOTD fractal. The reason is partly the growing familiarity of the theme and partly the image itself, which is adequate, but not really good or great. Perhaps the best feature of the image is the calculation time of a fireball 40 seconds. This high-speed calculation will leave no spare time for impatience to raise its ugly head. As is always the case with FOTD images however, satisfaction with the result is not guaranteed. The web sites will make satisfaction more likely however. Those who prefer doing it the easy way may view 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> Exciting weather prevailed here at Fractal Central today. Until 5pm it was partly cloudy, very hot and humid, with a temperature of 95F 35C. But things changed by 6pm when a whopper thunder- storm moved in with high winds, torrential rain, crackling lightning and even a few small hailstones. The fractal cat weathered the storm well enough until lightning struck a transformer a half block away, causing a brief power outage, when he sought a more secure place. After the storm, the temperature was a far more comfortable 72F 22C. As one who enjoys wild weather, I had an enjoyable day. FL endured the action until the storm died down. The next FOTD will be posted in the proper time. Until whenever that might be, take care, and to bomb or not to bomb . . . that is the question. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Island_Universe { ; time=0:00:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident center-mag=-0.0938330879721098/+0.8852092567717744\ /1168124/1/35/0 params=0.1/2/1/3/0.5/6/0.01/-1/\ -0.2602855645470608/0 float=y maxiter=500 inside=0 logmap=13 periodicity=6 colors=000000000000000WzvSpoOhhKc`GWQCNA8E34610000\ 00000zJZzIXzHWzGUzRKzVKzYJzaJzdJzgJzqJzwJzzJzwLzmM\ zeNzaPzYQWURVQTVMUVJVWIUXITYISZIS_HR_HQ`HPaHPbGOcG\ NcGMdGMeFLfFKgFJgFJnEVtDfuFeuGevHevIewJewKelWYbfRT\ qKRpJPpINpHLzGKzFIzEGzEEzDDzCBzB9zA7z96z99zCBzFDzI\ FzLHzOKzRMzUOzXQz_Sza`zgizmNzrPzpQznRzlSzjTzhUzfVz\ dWzcUzaYz_ZzY_zW`zUazSbzRbzLazGZzKWzNTzRQzUNzYKz`H\ zdEzgBzk9znGzdMzVKzRIzOGzLEzHCzEBzBDzCFzCHzDJzDLzE\ NzEPzFQzFRzIRzLRzOSzRSzUSzXTz_TzbUzdVzRWzTXzUYzWZz\ XZzgZzqWzmUziRzfPzbMz_KzWHzTFzPCzMAzI8zFAzzCzHEzIG\ zJHzKJzLLzLNzMPzNQzOSzPUzQWzRXzRZzS`zTazTczUdzUfzV\ gzWizWjzXlzXmzYozZpzZrz_sz_nzZizYezX`zWXzVSzUOrUPp\ SPoQQnPQmNRlLRkKSjISiHTgFTfDUeCUdAVc8Vb7Wa5W`4`b6e\ d7je9ogAtiCyjDuaIqTMmLQlLPkKPiKOhJNgINeIMdHLcHLaGK\ `GJ_FIYEIXEHWDGUDGTCFSCFSCEQBEPADOACM9B00zK8AI89H7\ 9G68E67D57C56A45944834623 } 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 12-09-13 (Floating Star [A-7,M-6])
by Jim Muth 13 Sep '13

13 Sep '13

FOTD -- September 12, 2013 (Rating A-7,M-6) Fractal visionaries and enthusiasts: Today's image returns us once again to the Julibrot of the past several days. Today we check the Mandeloid created when Z is initialized to the third critical value, which is -0.975... This Mandeloid shows the greatest degree of difference from the non-critical one that results when initial Z equals zero. Yesterday's image rather resembled a minibrot totally isolated from its 'outside' surroundings. The image was a sham, since the disconnection was achieved by the coloring. Today's image is the real thing however. It was found inside a strange mini Mandeloid just inland of the northwest shore line of the parent fractal. This mini Mandeloid has a bit of disconnected debris in its center, with today's scene lying in this debris. The result is a minibrot totally cut off from the rest of the fractal by a ring of 'inside' stuff. The minibrot is actually doubly disconnected. And yes, the open hole that contains the minibrot and its 'star' is symmetrical, as is true of almost all features surrounding minibrots. Since the minibrot's immediate 'outside' surroundings are shaped like a star, I named the image "Floating Star". The heavily blue cast I gave to the image emphasizes the stellar appearance. The ratings could have been a point higher if the theme were not becoming so shopworn. The calculation time of 7-1/4 minutes might be a bit much to ask to see the image. Visiting the web sites is a better deal. The finished image is posted 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> Today was partly cloudy and very humid until mid-afternoon, with a temperature of 84F 29C. But then a heavy thunder shower suddenly arose and dropped the temperature to 72F 22C. The crackling lightning striking within 100 meters or so sent the fractal cat scurrying for cover again. He came out as soon as the all-clear was sounded. Other than the excitement of watching the big storm, the fractal humans had an uneventful day. The next FOTD will be posted when the same particle entity can be in two different places at the same time. Since this is already the case, the FOTD will be posted in the near future. Until bilocation occurs, take care, and real magic might be irrational, but according to quantum science, it does exist. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Floating_Star { ; time=0:07:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=-0.1354452771282252/+0.7340443868840427\ /414258.8/1/-35/0 params=0.1/2/1/3/0.5/6/0.01/-1/\ -0.9753887460956279/0 float=y maxiter=1500 inside=0 logmap=12 periodicity=6 colors=000FazDOzBbzCPzC0c6lz9EzUUzsszcgzVXzLMzJvzF\ ZzvmzjmzdUzjmzpmzvmzImz9UzEmzJmzOUzSUzVmzYUzVmzoUz\ dmzVmzLmzqmzsmz2mzumzKmzImzGmzEmznmzVmzsmzdmzQmzZm\ zRhzJSzxXzr`zXOzwKzkHz_FzODzmcz9bzBPzdmzcEzQCztMzY\ GzKezD0z4iz6`z8SzAJzkHzbFzUEzLCzvgzjZzZRzNJzQVzJLz\ _DzOCzJWzFLzjizJwzxYzgQzSIzn4zGazEOzUNzPKzLHzGEz1m\ z7UzIfzGWzELz5sz9XzWxzPgzIRzlCzwgz_RzHizESzGxzu2zi\ 5zZ7zN9zQyzjizHYz9VzAOzBHzFjzEZzDNzbpzWezPWzILzBfz\ CRzbVzWQzPLzIGzFTzbEzUDzLCz23z77zFczEWzDPzCIzngzaX\ zPMzT9zNAzHBzhrzSXz52z75z97zB9zN1zK4zH6zE9zBnzCdzC\ VzCLzImzlFzUDziuzYezNQzZFzOlzn2zV7zRZzMRzHJzQFzZxz\ N_zzNzAizB`zBSzCJz78zAAzgZzSNzmDzVCz6lzpjzbZzPNzOe\ zeRzYNzRJzJFzJLzGHzEEzxDz_CzEFzYfzNRz4Lz8GzUvzLZzL\ tz6GzMpzJezHWzELzNKzHFz`nzOVzAzz5pz7ez9WzBLzunzidz\ ZVzNLz3_z8Nz76z98zBAz_FzUEzODzICzBezP7zL8zI9zFAzF6\ zE8zD9zCAztgzhZzYRzNJzHoz } 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 10-09-13 (Points Revealed [A-7,M-8])
by Jim Muth 11 Sep '13

11 Sep '13

FOTD -- September 10, 2013 (Rating A-7,M-8) Fractal visionaries and enthusiasts: While yesterday's fractal was a non-critical loser, today's fractal, which is critical, is a notable improvement. It is a scene in the fractal that is generated when yesterday's fractal is re-calculated with Z initialized to the first of the three critical values of the iterated expression. This value appears as the real(p5) parameter of today's image. At first glance, today's parent fractal, which is critical, appears little changed from yesterday's image. In its depths however it is totally different, with intact minibrots lurking where least expected. Today's image, which I named "Spiraling Onward", lies on the west side of the north branch of what could be called a kind of Seahorse Valley. The math value remains a superb 8, while the artistic value has risen from an abysmal 3 to a very respectable 7. The three critical values of initial Z in yesterday's loser image were found by entering the same parameters into the CriticalPoints formula, which appears in today's parameter file. This calculates the Parabolic plane of the iterated expression and creates an image that is a rough graph of the expression. All that is then necessary is to find the 'Y' coordinates of the tips of the three obvious though distorted parabolic curves. I always choose the place where the default red adjoins light blue. The tedious part is continually stretching the curves horizontally to determine the exact 'Y' coordinates. The second image, named "Points Revealed", shows the resulting image-graph that must be analyzed. The method is tricky, especially with negative and fractional exponents, and sometimes does not work, but it is still better than trying to write a formula to do the job or finding the points by hand calculation. The calculation time of 2-2/3 minutes is somewhat slow, and I'm not sure the result is worth the wait. Luckily, the web sites can speed up the viewing. Save time and effort by checking the finished images 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 mix of sun and clouds, and a temperature of 88F 31C made today quite summer-like here at Fractal Central. The fractal cat was undecided whether to stretch out or curl up, and finally settled half stretched in my favorite chair. The fractal people passed the day getting things done. The next FOTD will soon be posted. To see how soon, check back here frequently, and before you know what happened, the next fractal will be here. Until whenever the fates decide, take care, and let's admit it -- according to science, objective reality is probably an illusion, which means that our mighty scientific method is founded on nothing more than an illusion. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Spiraling_Onward { ; time=0:02:40.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident passes=t center-mag=-0.511568295107038/+0.05469492019194518\ /1.23e+010/1/140/0 params=0.1/2/1/3/0.5/6/0.01/-1/\ 0.2246790860663939/0 float=y maxiter=1750 inside=0 logmap=138 periodicity=6 mathtolerance=0.05/1 colors=000AIA8J68K3CL2JK2QK2WK1bK1iK1oK1VG6XF7ZG7`\ I3aL0eP6eVBcYFdZJeZMfZPgYSgWVhUYiR_jObkLekJhlGkkEn\ iBqe9saAlWBfNB`IBWFAQC8O87K65G44C420228zz4rp5mk4if\ 4ea3dX3cU3cQ2cM2cI1cF1UB1K70c306m55h45c44Z44U34P33\ K33I23G22E22C11A1181160040020ZyFWoEThDRcCPZBNUALR9\ JP8HM7GK7EI6CG5AD48B3793562341120M`zKYmJWcHUUGRKFP\ ADN1CK1BI19G08D06B0590460240120PmVNiTLfRKcPI`NHYLF\ VJESHCPFALD9IB7F96C7495363131SqTQmROjPMfNLcLJ`JHXI\ FUGERECNCAKA8G97D75A5363131pQjjNddK_ZHVTEQNBKH8FB5\ A5256zn5ti4nd4h`3cW3YR2SN2MI1HD1B9054KK0II0HH0FF0E\ E0CC0BB0AA0880770550440220110ltcOSKjceNKLQzbMqXIhR\ E_MBRG7IB395Xw7Mc4BK2oPukNpgLlcJh`UdXU`TUXQUTMUOIU\ KEcGBcC7c83c4xchhmXUmMFmBwmcdmlczhczdcz`czXmzUmzQm\ zMmzImzFmzBmz7mz3mzSmznzzizzdzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ 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 } Points_Revealed { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=CriticalPoints function=ident passes=1 center-mag=0/0/0.6666667 params=0.1/2/1/3/0.5/6/0.01/-1 float=y maxiter=500 inside=0 periodicity=6 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\ zLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmsss\ zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\ 00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\ VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\ lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\ lhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70S\ E0SL0SS0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLES\ OESSESSEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLES\ OESSEOSELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKS\ SKQSKOSKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0G\ G0CG08G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0C\ G08G04G88GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8C\ G8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBD\ GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\ G000000000000000000000000 } frm:CriticalPoints {; Jim Muth z=imag(pixel), c=fn1(real(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): z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c, |z| < 10000 } END PARAMETER FILE=========================================

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FOTD 09-09-13 (Not Critical [A-3,M-8])
by Jim Muth 09 Sep '13

09 Sep '13

FOTD -- September 09, 2013 (Rating A-3,M-8) Fractal visionaries and enthusiasts: I have received a couple inquiries over the past few days about critical points and their relation to fractals, and also how I use Fractint to graphically find critical points. This will be the topic for the next several FOTD discussions. Hopefully, my limited math knowledge will be equal to the task. To begin, a critical point is a point on the graph of a function where the rate of change is zero and the tangent is therefore parallel to the X-axis. This point can appear as the tip of a parabola or a point of inflection, where the direction of curvature changes. In fractals, when Z is initialized to a critical value, the fractal will consist of undistorted Mandelbrot stuff, such as appears all around the edges of the classic Mandelbrot set, and the fractal's depths will be filled with intact minibrots. In the classic M-set, the critical value is zero, but in today's fractal, in which Z is initialized to zero, the result is distinctly non-critical. No perfect minibrots lie in its depths, and no undistorted buds lie along the edges of the large bays. For those who cannot wait, if any, today's fractal has three actual critical points. These are: +0.2246790860663939 -0.2602855645470608 -0.9753887460956279 If one of these values is entered as the value of real(p5), the resulting fractal will closely resemble today's non-critical version, but it will have many critical areas, especially along the negative X-axis, with intact buds, and minibrots in their depths. The name "Not Critical" is a simple truism. Since the math, which rates a lofty 8, is the chief topic of today's image, I put little effort into the coloring, which rates a lowly 3. The fractal is a parent fractal, this is true by definition, but it holds little of interest. The thin vertical column in the center of the main bay is created by the 0.01 part of (1/Z) in the iterated expression. I will resume this topic tomorrow, when I will describe my rather convoluted technique of finding critical points graphically with the Fractint program. The calculation time of a fireball 20 seconds will cause no grief. The web sites can bring extra assurance of satisfaction. The finished image is posted 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 day passed with little fanfare here at Fractal Central today. The sky was mostly cloudy, but the clouds were thin enough to give the impression of a mostly sunny day. The morning temperature of 45F +7C made sweaters comfortable, but the afternoon high of 73F 23C was near perfect. The fractal cat slept through most of the afternoon, while the fractal humans accomplished what needed to be done. The next FOTD will be posted in the appropriate time. Until we see what is appropriate, take care, and, "I think that crocodile is still alive!" Tom said off-handedly. Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Not_Critical { ; time=0:00:20.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandelbrotMix3a function=ident passes=1 center-mag=-0.12/0/0.8 symmetry=xaxis params=0.1/2/1/3/0.5/6/0.01/-1/0/0 float=y logmap=1 maxiter=500 inside=0 periodicity=6 colors=000D1iD1lD1nH3oK4pN5pR6qU7qX8r_9rcAsfBtiCtm\ DupEusFvvGvsJrpLomNlkPihSeeUbcW_`YXY`TWbQTdNQfKOiG\ LkDImAGo7Fn8Fn8Fn8Fn9Fn9Fn9Fn9EnAEnAEnAEnBEnBEnBEn\ BbqXXp`SpdMphHplKmiNjgPgeSdcVaaX___XYbUWdRUgOSiMQY\ jPXfQXcRX_SXXTWUUWQVWNWWKWXMVXNUXOTYPTYQSYSRZTQZUQ\ ZVP_WO_YN_ZN`_M``L`aK`bKZ`JX_JVYITXIRWIPUHNTHzRGzQ\ GzPGzNFzMFzKEzJEzIEzLJzONzQRzTWzW_zYczeVzlNmsFmz7m\ sAmlCzeEzZGzSIzVKzXLzZNz`OzcQzeRzgTziUzh_ozSnzSmzS\ lzSOzJQzLRzNTzOUzQWzSXzUZzW_zXazZbz`dzbezcbzd_zeXz\ fUzgSzgPzhMziJzjGzkEzkBzl8zm5zn2zo0zo4zn7znAzmDzmG\ zlJzlMzkQzkTzjWzjZziazidzhgzhjzhhzffzddzcbza`z_ZzY\ YzWWzUUzTSzRQzPOzNMzLKzKIzIHzGFzEDzCBzA9z97z75z53z\ 31z10zo0zg0z`0zT0zM0zE0z7wzXrzUmzRizPdzM_zKWzHRzFN\ zCIzADz79z54z2IzBHzAGzAFz9Fz9Ez8Dz8Dz8Cz7Bz7Bz6Az6\ 9z59z58z57z46z46z35z34z24z23z22z12z11z00z0JzlHzgFz\ bDzYBzT9zOJzLKzJKzHLzFLzD } 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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Re: [Fractint] AOTD 9_7_2013
by Hal Lane 09 Sep '13

09 Sep '13

> Animation of FOTD August 26, 2013: Undersea Scene is posted: > http://www.fractal-animation.net/vid/xenomorphs.zip > It is 2 min 21 sec runtime, 40Meg download. That's a great video! I especially like the yellow sparkles on the dark purple background at about a minute in. There was a lot of suspense the first time I watched it as to whether it could possibly keep zooming in and finally arrive at an M-set or not! I didn't see the "pumping" up and down of the color map in this video: Did you have another value in Logmap other than 2? <---<< - Hal Lane ######################## # hallane(a)earthlink.net ######################## Author: JackOfTradeZ Date: To: fractint Subject: [Fractint] AOTD 9_7_2013 . Animation of FOTD August 26, 2013: Undersea Scene is posted: http://www.fractal-animation.net/vid/xenomorphs.zip It is 2 min 21 sec runtime, 40Meg download. -----

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AOTD 9_7_2013
by JackOfTradeZ＠comcast.net 08 Sep '13

08 Sep '13

. Animation of FOTD August 26, 2013: Undersea Scene is posted: http://www.fractal-animation.net/vid/xenomorphs.zip It is 2 min 21 sec runtime, 40Meg download. .

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FOTD 06-09-13 (The Other Half [A-6,M-7])
by Jim Muth 06 Sep '13

06 Sep '13

FOTD -- September 06, 2013 (Rating A-6,M-7) Fractal visionaries and enthusiasts: Today's fractal was created with the same iterated expression as yesterday's, but it is found in an entirely different parent fractal. This is because today's parent fractal was initialized to a different critical point, which appears as the value of the real(p5) parameter. I used the Fractint program to plot a second critical point graphically. (Fractint can draw basic graphs in which critical points can be tracked down and measured.) I do not do this very often because the process is tedious, but in today's case the result was satisfying. I found a new fractal, resembling yesterday's parent in some aspects but differing in other ways. I named today's image "The Other Half" because it is a scene in a parent fractal that is the second critical slice of yesterday's Julibrot. Once again, the artistic value of 6 lags behind the math value of 7, which makes the 13-minute calculation time not much of a bargain. But the web sites are always there to save time and frustration. Be rational and unfrustrated. Check the finished images 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> With its totally cloudless skies, today would have been absolutely perfect if it had been just a few degrees warmer here at Fractal Central. As it was, the morning low of 43F +6C and afternoon high of 70F 21C were a little too chilly for relaxing in the outdoor shade. The fractal cat relaxed under a chair cover, where he spent the afternoon as little more than a lump. The fractal humans, who are anything but normal, had a normal day. The next FOTD will be posted when I get in the mood to do it. Long experience says that the time will be either 24 or 48 hours. To be sure when, check back at these times. Until whenever, take care, and when bad guys use guns to kill innocent people, the liberals say we should solve the problem by passing laws that will affect only the good guys who have guns. (Criminals don't obey laws.) This is crazy enough, but then the conservatives say we should solve the problem by increasing the number of guns in circulation, so we will be ready to protect ourselves from the bad guys. Would the rational side please stand up. Jim (reason prevails but no one wants to hear it) Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= The_Other_Half { ; time=0:13:30.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotMix3a function=ident passes=t center-mag=+0.04948459960925363/+0.000012428074251\ 36/2.714126e+010/1/-50/0 params=4/2/3/4/2/3/-100/5\ /0.2765676348110211/0 float=y maxiter=4250 inside=0 periodicity=6 colors=000ZGGYDHYAJX7KX4L_EHaODgOFmJKlMIlOGlQElSCl\ UAlW8nMAlY6jh3il4hn0coKZoRVoQPoDKlCFgCAcCAZC9UC9QC\ 9TC9YF5gJ2sPBrSJkUSdW_ZZhS`pLbxFdjIPXK9WK8VJ8TI8SH\ 7QG7PF6NE6MD6LD5JC5IB5GA4F94E83C73B639628527415311\ 00421210100xjRviQuhPtgPrfOqeOpdNncMmbMlaLk`Li_KhZK\ gYJeXIdWIcVHaUH`TG_SGZRFXQEWPEVODTNDSMCRLCPKBOJANI\ AMH9KG9YWhTZsQWkOTdMRXKOQILIGJBQRAZZAgfApnAcdMSWYD\ UoFQlGNiHJfJGcKC`L7XN2TL9YKGbJMgITlMZvJZsHZpFZnDZk\ BZh9Zf7Zc5Za6Wd6UgbUEWaEPhFLpDIoFGnGEnIBmJ9lL8lL7l\ MDjPIiROhUTfW_dYcb`daac`Za_RW`LMdPUhS`mVhqYop`vobh\ nVfWIlA7eE6_I5TM5NQ4HU4JPELKNNGWPBdR6mT2vTPgTkUXcZ\ `WcdOhhGml8rp1vi5tc8rYCpSFnMJlGMjAQh4Tg7Xf9`fBdeDh\ e2zmFleRZZbLS_MOYMLVMITMFQIBRMCSPDTTEUWFVZGWbHXeIq\ f_YhIWgJVfKTeLSdMQcNPbOHRVOaOPtCVkI`cNfWSlOYrGbz3h\ w8gtCfrHeoLdlQcjUbgZagZbebaceaaia_laYpaWsaUvaF5_J9\ WMCSQFOTJKXMG`TA_PC_MDZJF } 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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