March 2011 - Fractint - mailman.xmission.com

FOTD 18-03-11 (Chunky Peanut Butter [6])
by Jim Muth 18 Mar '11

18 Mar '11

FOTD -- March 18, 2011 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us on a quick trip rather deep into the west side of Scepter Valley of the Mandelbrot set, which is the valley at -1.25 on the X-axis. In this area we find the tiny things I call 'peanut holes'. These holes appear to be far more plentiful than minibrots, though with an infinity of both, this is not mathematically true. Anyone who has ever enjoyed a bag of fresh roasted peanuts in the shell knows that most peanuts have two 'nuts' in a shell, but some freaky ones have only one nut in a shell, while others have three and rarely four nuts in a single shell. The peanuts in today's image are the 'three-in-a-shell' kind, and they surround the minibrot, growing ever smaller and more numerous the closer to the minibrot we look. Actually, these peanuts are not really trapped points at all, since they fill-in when the maxiter is raised. When rendered in the normal manner, today's image falls kind of flat, so to add some life, I calculated the image with the outside set to 'real'. The result turned out to be too busy and disorganized for a rating higher than a 6, but with a calcula- tion time of only 1-2/3 minutes, not much effort will have been wasted if the result proves disappointing. The name "Chunky Peanut Butter" seemed appropriate when I noticed the number of tiny peanut holes filling the screen. The task of calculation may be avoided by viewing the finished image on the FOTD 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/> Pleasant conditions prevailed here at Fractal Central on Thurs- day as the sun shone brilliantly and the temperature reached 61F 16C. The sun is now climbing high enough during the midday hours that it misses the back edge of the fractal cats' window shelf, so they spent the afternoon on the front part of their shelf, watching for stray cats to wander by. With the spring jobs coming in, my day was rather busy, but I still found time to find a fractal. The next FOTD will be posted in two days, more or less. Until then, take care, and be wary of e-mails that want you to stand in as the heir to an abandoned sum of 26-million U.S. dollars. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= ChunkyPeanutButter { ; time=0:01:46.73-SF5 on P4-2000 reset=2004 type=mandel passes=1 float=y center-mag=-1.250000626757216/+0.0003126618705661/\ 1.95e+011/1/11/0 params=0/0 maxiter=150000 bailout=16 inside=0 outside=real periodicity=6 colors=000U91T81S80R80P70P70S70R60P60P50N50M50K40K\ 40I40L30L30K30J20I20I20C10B10C00B10B20B20130B40B40\ B50L60L60L70L80L80L90LA0LA0LC1LE1KF2KH3KK3KL4KN4KP\ 5KQ5KQ6KQ6KO7KO7KO8KN8KO9KP9KOAKPAJPBJPCJPCJQDJQDJ\ REJSEJSFJTFJUGJUGJVHJWHJWIJXIJYJJYJJZKI_LI_LI`MIaM\ IaNIbNIcOIcOIdPIePIeQIfQIgRIgRIhSIiSIiTHjUHkUHkVHl\ VHmWHmWHoXRqXRsYRuY`vZ`wZjx_jx_ty`ty`tzatzatt`ts`j\ s`jr_jr_jq_jqZ`pZ`pZ`oY`oY`nYKnXKmXKlXLlWLkWLkWLjV\ LjVMiVMiUMhUMhUMgTNgTNfTNeTNeSNdSOdSOcROcRObRObQPa\ QPaQP`PP`PP_PQZOQZOQYOQYNQXNRXNRWMRWMRVMRVLSULSULS\ TLSSKSSKTRKTRJTQJTQJTPIUPIUOIUOHUNHUNHVMGVLGVLGVKF\ VKFWJFWJEWIEWIEWHDXHDXGDXGCXFCXECYECYDBYDBYCBYCAZB\ AZBAZA9ZA9Z99_98_88_78_77_67`67`56`56`46`45a35a35a\ 24a24a14`02a13a14a24b25b26b36tU7tU8tU8tU9tUAtUAtUB\ tUCtUCtUDzUEzUEzUFzUFzUGz9Ht9HtAItAJtAJtD5tD5tC5tC\ 4tC4tB4tB3tA3tA2tA2t92t91 } END PARAMETER FILE=========================================

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FOTD 16-03-11 (Back to the Past [5.5])
by Jim Muth 16 Mar '11

16 Mar '11

FOTD -- March 16, 2011 (Rating 5.5) Fractal visionaries and enthusiasts: My web site is progressing, but I had no idea how much progress was needed. Accurate time forecasts are futile, so all I can say is that the time is not too far off, and the wait will be worth the impatience. Today's image is another return to the world of 12 years ago. I brought up the Mandnewt07 formula and set it loose to find today's image. I have no idea what this series of formulas was originally intended to do, but they certainly do make some interesting images, as today's rather disorganized image demonstrates. With more time I might have done a better coloring job. As it is, I could rate the finished product no higher than a 5-1/2, which is just a tiny bit above average. The name "Back to the Past" refers to the age of the generating formula. The calculation time of 1-3/4 minutes means little effort will be needed to run the parameter file. The image may also be seen on the FOTD 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/> My own web site will soon be coming at: <address to be revealed> Tuesday here at Fractal Central featured morning sun, afternoon clouds, and light rain in the evening. The fractal cats kept themselves busy chasing each other up and down the hallway. My day was about average. The next FOTD, likely an improved one, is scheduled to be posted in 48 hours. If nothing goes wrong, it might appear on time. Until whenever, take care, and I hear the duck has lost his job. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Back_to_the_Past { ; time=0:01:44.20-SF5 on P4-2000 reset=2004 type=formula formulafile=mandnewt.frm formulaname=MandNewt07 passes=1 periodicity=0 center-mag=-6.78166/-12.3172/0.07303401/1/-92.5/0 params=2/3/3/1/1/-1 float=y maxiter=255 inside=atan colors=00005W15Q35K45E65D75D95CA5CC5CD5DF5DG5EI5EJ\ 5FLAFMFGOHGPJHRLISNIUPJVRJXTKYUK_VL`WLbXMcYMeZNf_O\ h_Pi`QkaRlaSnbTobUpcVpdWpdXpeYpfZpf_qg`qhaqhbqicqj\ dqjeqkfrlgrlhrmirnjrnkrolspmspnsqosrpsrqssrststttt\ uutvutvutwutxuuxuuyuuzuuzuuzuuzuuzutzttxstvrstqssp\ sqoronrmmrklqjkqhjqfiqdhpbgpafp_eoYdoWcoVbnTanR`nP\ _nNZmMYmKXmIWlGVlEUlDTkBSk9Rk7Qk6Pj7Oi7Ni7Mh8Lg8Lg\ 8Lf9Le9Le9LdALcAKcAKbBKaBKaBK`BK_CK_CKZCKYDKYDKXDJ\ WEJWEJVEJUFJPFJKGJFHHAIF8ID6JB4J92K70L50L41L43L45K\ 46K48K49K4BJ4DJ4EJ4GJ4HJ4JI4LI4MI4OI4QH4RH4TH4UH4W\ H4YG4ZG4`G4aG4cF4eF4fF4hF4oH0iF4dE8_DCVCFPBJKANF9R\ 86V97UA8UB8TB9TC9TDASDASEBSFBRFCRGCRHDQHEQIEQJFPJF\ PKGOLGOMHOMHNNINOINOJMPJMQKMQLLRLLSMLSMKTNKUNKUOJV\ OJWPIXPIXQIYRHZRHZSH_SG`TG`TGaUFbUFbVFcUFdTFcRFbPF\ aNF`LFZJFWHHUCJQ6LM7NL8PK9PJAPJBPKCPaWJZUIWTHSSGPR\ FLPEIODFNCBMB8KA4J91I80H7 } frm:MandNewt07 {; Jim Muth z=c=(pixel*p1): a=z^3+(c-p2)*z-c b=3*z^2+c-1 z=z-p3*a/b 0.000000000000000000000000000001 <= |a| } END PARAMETER FILE=========================================

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FOTD 14-03-11 (Shadow Dance [6])
by Jim Muth 13 Mar '11

13 Mar '11

FOTD -- March 14, 2011 (Rating 6) Fractal visionaries and enthusiasts: Things have been very wet here at Fractal Central these past few days, wet enough in fact to flood the FC basement 10cm deep. But by Sunday the water had subsided, and things were getting back to normal. In the fractal department, I have returned to an old formula for today's image -- the Mystic2 formula, which is at least 12 years old. When the inside is set to a flat color, this formula draws nothing but empty circles, but when an active coloring such as the 'bof61 is applied to the inside, strange things begin happen- ing. Today's image shows some of these strange things. The image consists entirely of inside stuff made visible by the 'bof61' inside fill. It is very sensitive to changes in the inside fill, the function and the p3 parameter. The p1 and p2 parameters have a far lesser effect. The name "Shadow Dance" sounds kind of Native Americanish, but it has little to do with the appearance of the image. Due to the lack of organized colors, I could rate it no higher than a 6. The finished image soon will be available on the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The original FOTD web site may be found at: <http://www.Nahee.com/FOTD/> My own FOTD web site will soon be up and running, though due to problems dealing with the flooded basement, it has made no progress since the last report. Sunday brought clouds and a temperature of 43F +6C to Fractal Central. The fractal cats took it all in stride. They were more interested in being fed. My day was spent recuperating from the flooded basement and watching far greater disasters on TV. The next FOTD will be posted in a couple days. Until then, take care, and no matter how bad things seem, they are never so bad that they could not get worse. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Shadow_Dance { ; time=0:01:31.62-SF5 on P4-2000 reset=2004 type=formula formulafile=jim.frm formulaname=Mystic2 function=cotan passes=1 center-mag=0/0/31 params=1/-3/3/4/3/5.899 float=y maxiter=255 inside=bof61 periodicity=6 colors=000TETTFRTHPTIMTJKTLIoMGTNETOCPQFzZ0jALHSJG\ eHFQGDOECNDBMB9LA8J87I7zH54G43E21D10C00H01C3C003DB\ ztF5Fm6EO7Fm8FW9G`AGdBHhCHlEIeGIZIJSKJLLJEOICRHAUG\ 8XF6_E4bD2dD0cE4bE7aEB`FE`FH_FLZGOYGSYGVXHYWHaVHdV\ HgYEb_BYa8Uc5Pe2Kg0GX9IMIKBRM1_O4ZM7YK9XICWGEVEHUC\ JTAMS8OR6RQ4TP2WO0YN0`M0bM0aL2`K9_JGZIOYHVXGaXFhPD\ THBD9A0II5RPB_XIgcOddMbeL`fKYgIWhHUiGSjFLaOFUW9Mc3\ EkBFZJGMRH9ZI0QT0Ic0`RKEhUJYSNNQRCPV1NZ0MY0OX1PW6R\ WASVFUUKVTPWTTYSYZRb`QgaQkbSgaTcaV`aWXaXUaZQa_Na`J\ abGacCad9a`6YX3VU1SQ0OM0LJ0ILIKNfMGcWA`eAacAaaAb_A\ bZAcXAcVAcUD_SGWRISPLOOOKNQGLTCKV9JXAHYBFZBD_CB`D9\ aD8bE6cF4dF2eG0fG0UN0HT05Z08W0AU0DR1FP1IM2KK3MI3PF\ 4RD5UA6W86Z57`38b18U49M79E995C90F90H90G80G80F70F73\ E66E69E6BD5ED5HC4KC4MC4LC4JC3HC3GD2ED1CD1BD09D07D0\ 6E04E02E01E00E00E00D01D22D43D74DA5DC6DF7DH8DK9DNAD\ PBDSCDUBBQB9MA7IA5F94B927 } frm:Mystic2 {; Jim Muth a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3), g=pixel, z=(pixel)^a+(b*(pixel))^c: z=(fn1(z)+(d*(g)))^k+(f*(cos(g))) g=sqr(g), LastSqr <= 100 } END PARAMETER FILE=========================================

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Astroid Out
by Mike Frazier 10 Mar '11

10 Mar '11

Here is a link to a web page with an image: http://www.fracton.org/fmlposts/astroid_out.html The formula for this fractal is called True_Astroid and is based on the original Astroid_Mset by Paul Carlson. The original draws an "inside out" astroid curve while this one draws it in true form. The orbit trap formula is modified to use the polar form instead of the parametric form. The changes to the formula were suggested by Gerald Dobiasovsky. The parameter file used to make this image is below: Astroid_Out { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=True_Astroid passes=1 float=y center-mag=-1.265578607178311/0.1218562499999997/2\ 22.222225/1/0/0 params=0.01/0.59/8/30/0/0/0/0/0/0 maxiter=500 inside=255 outside=summ colors=000fOz<28>I0Kz0f<28>O08z88<28>O00zW0<28>c40\ zz0<28>aG00zR<28>0C40zz<28>0CCGGz<28>00O000<12>000\ z88 } frm:True_Astroid { ; Based on ; Astroid_Mset copyright (c) Paul W. Carlson, 1997 ; Modified for compatibility with Fractint 20.04 and ; Fracton by Mike Frazier, 2011 ; Additional improvements by Gerald Dobiasovsky ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; real(p1) = a factor controlling the width of the curves ; imag(p1) = radius of the astroid ; real(p2) = number of color ranges ; imag(p2) = number of colors in each color range ; ; Note that the equation variable is w, not z. ; Initialize cindex to the index of the background color ; Formula modified to avoid color index 0 which can not ; be used with outside=summ in FractInt v20.04 ;**************************************************** w=0, c=pixel, z=0, cindex=254,; Background color 254 bailout=0, iter=0, range_num=0, i=(0,1), r=imag(p1), ;**************************************************** ; In the accompanying par file, ; we have 8 color ranges with 30 colors in each range ; for a total of 240 colors. The first range starts at ; color 1. Pixels will use color 254 when |w| > 1000. ; Other values can be used here as long as the product ; of num_ranges times colors_in_range is less than 255. ; Color 254 is reserved for the background color and ; color 255 can be used for the inside color. ;**************************************************** num_ranges=real(p2), colors_in_range=imag(p2), ;**************************************************** ; Real(p1) controls the width of the curves. ; These values will usually be in the range 0.001 to 0.1 ;**************************************************** width=real(p1), index_factor=(colors_in_range-1)/width: ;**************************************************** ; The equation being iterated. Almost any equation ; that can be expressed in terms of a complex variable ; and a complex constant will work with this method. ; This example uses the standard Mandelbrot set equation. ;**************************************************** w=w*w+c, ;**************************************************** ; The orbit trap curve. This example uses an "astroid" ; curve (which has absolutely nothing to do with huge ; rocks in outer space). Any two-dimensional curve can ; be used which can be expressed in parametric form in ; terms of the angle from the origin. ;**************************************************** ; ang is really tan(ang) here ang=imag(w)/real(w), astroid=r*sqrt((ang^2+1)/(|ang|^(1/3)+1)^3), ;**************************************************** ; If the orbit point is within some distance of the curve, ; set z to the index into the colormap and set the bailout ; flag. ;**************************************************** distance=abs(|w|-|astroid|), if(distance<width&&iter>1), cindex=index_factor*distance+range_num*colors_in_range+1, bailout=1, endif, ;**************************************************** ; Cycle through the range numbers (0 thru num_ranges - 1) ; With two color ranges, even iterations use color ; range 0, odd iterations use color range 1. ;**************************************************** range_num=range_num+1, if(range_num==num_ranges), range_num=0, endif, ;**************************************************** ; Since we are using outside=summ, we have to subtract ; the number of iterations from z. ;**************************************************** iter=iter+1, z=cindex-iter, ;**************************************************** ; Finally, we test for bailout ;**************************************************** bailout==0&&|w|<1000 } -- Mike Frazier www.fracton.org

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FOTD 10-03-11 (Forevermore Fractal [7])
by Jim Muth 10 Mar '11

10 Mar '11

FOTD -- March 10, 2011 (Rating 7) Fractal visionaries and enthusiasts: The FOTD web site is just about ready to upload. (Annoying little problems keep popping up and delaying things.) My original plans were to start with the earliest FOTD's and keep going until I got caught up to date. But a little math shows that it would be over a year before I reached the point where I would start posting the new FOTD images as I find them. So I will slow down on the old stuff and begin posting the new stuff the same day as I find it. That way, the old stuff will not be advancing toward an ever receding finish line. The last images to be posted to the web site will be those of February 2011. Then it will be back to an all-new FOTD most every day. Today's image lies in the same parent fractal that held the image of March 08. But instead of lying inside the fan, it lies on the bay side of the valley separating the fan from a large bay just to its south. The name "Forevermore Fractal" implies that fractals go on forever, which most of them do. The rating of a 7 indicates that I consider the image to be worth at least a quick glance. That glance may be enjoyed by running the attached parameter file or by visiting the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> The old original web site is posted at: <http://www.Nahee.com/FOTD/> but it is far from being up to date. The clouds increased here at Fractal Central on Wednesday as the forecasted torrential rain approached. The fractal cats enjoyed a day by the heat since the outside temperature never rose above 39F +4C. The forecast calls for major flooding by Friday, so we will see how it goes. The forerunner light rain arrived at 6pm, mixed with a few half-melted flakes of snow. Meanwhile, both FL and I had a very busy day, both with commercial work and getting the web site up and running. The next FOTD will be posted in a couple days. Until then, take care, and let's hear it for technology. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= ForevermoreFractal { ; time=0:0X:XX.XX-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+0.6626183470281375/-2.030395519434738/\ 3.192119e+008/1/-155/0 params=-4/-1.3/-0.8/-5.3/0/\ 0/0/0 float=y maxiter=3500 inside=0 logmap=605 periodicity=6 colors=000YOKXOKXPKWPJWQJVQJVQJURITRITSISSISSHRTHR\ THQUHQUGPUGPVGOVGOWFOVGOUGOTGOTGOSGORGOQGOQGOPGOOG\ OOGONGOMGOLGOLGOKGOJHOJHOIHOHHOGHOGHOFHOEHOEHODHOC\ HOBHOBHOAHO9HL6IM7HN8HN8HO9HO9HPAHQBHQBHRCGRCGSDGT\ EGTEGUFGUFGVGGWHFWHFXIFXIFYJFZKFZKF_LF_LE`MEaNEaNE\ bOEbOEcPEeQFdPEcPEbODbODaOD`NC`NC_MCZMBZMBYLBXLAXL\ AWKAVK9VJ9UJ9TJ8TI8SI7RI7RH7QH6PG6PG6OG5NF5NF5MF4L\ E4LE4KD3JD3JD3IC2HC2HC2ID3JD4KE5KE6LE7MF8NF9NG9OGA\ PGBPHCQHDRIESIFSIFTJGUJHUKIVKJWKKXLLXLLYMMZMNZMO_N\ P`NQaORaORbOScPTdPUdQVeQWfQXfRXgRYhSZiS_iS`jTakTbk\ UblUcmUdnVenVfoWgpWhpWhqWdqW`rWXrWTrWPsWLsWHtWDtW9\ tW5uY7uZ9u`AuaCucEvdFvfHvgJviKvjMyjKxkLwkMwkMvkNvk\ NukOukOtkPtkPslQslQrlRrlRqlSplTplcolcolcnmcnmcmmcm\ mclmclmmkmmkmmjmmknmjmmimmilmhlzhkzgkzgjzfjzfizeiz\ eizdhzchzcgzbgzbfzafzaez`ez`dz_dz_dzZczYczYbzXbzXa\ zWazW`zV`zV_zU_zU_zTZzSZz } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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<David>, Friends-Fractint's evolver on Mar 4, 2011 FOYD(Emerald)
by Hal Lane 09 Mar '11

09 Mar '11

David, Friends, I used Fractint's evolver on Jim's March 4th, 2011 FOYD (Emerald) and created 81 thumbnail-sized variations on his fractal. It's on the FOTD site named E110304A.gif in the "Hal's Variations..." (far right column) of the March 2011 FOYD web page at: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html This fractal has a lot more parameter space left to explore... While we're on "interesting things to try," try putting these two images in adjacent tabs in your browser: http://www.emarketingiseasy.com/TESTS/FOTD/F110308U.gif and http://www.emarketingiseasy.com/TESTS/FOTD/F110308T.jpg (make sure you maximize both of them by clicking each image once!), then move the focus between the two tabs with: <ctrl><pg-up> and <ctrl><pd-down> to see the effect of anti-aliasing and sharpening on this variation on Jim's March 8, 2011 FOTD. - Hal Lane ######################### # hallane(a)earthlink.net # #########################

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FOTD 08-03-11 (Taking a Break [5])
by Jim Muth 08 Mar '11

08 Mar '11

FOTD -- March 08, 2011 (Rating 5) Fractal visionaries and enthusiasts: Things turned quite busy here at FC on Monday, with lots of snow to clear away and plenty of other work to clear up also. When things turned too hectic, I decided I needed a break from the routine of getting the early FOTD images and parameter files ready to be posted to my FOTD web site, which involves boring and repetitious things such as taking out the carriage returns in the discussions. (Recoloring the old images is a lot more fun.) Unless we get flooded or something else happens, the web site should appear late this week. What better way to take a break than to find an all-new fractal? I named it "Taking a Break" because that's what I was doing when I found it. It's not much of an image, rating only only a hum- drum 5, but it's all new, and that's what counts. The image lies near a larger minibrot in the 'fan' of the frac- tal that results when 4 negative parts of Z^(-1.3) are combined with 0.8 negative part of Z^(-5.3) and (1/C) is added on each iteration. The calculation time of only 36 seconds is blessedly brief. Another way to see the image is to visit Hal's FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> where the finished image is posted. Paul's web site is still located at: <http://www.Nahee.com/FOTD/> but it is far from up to date. Rain fell all day Sunday here at Fractal Central. At nightfall it changed to heavy snow, which fell all night. Monday dawned with a clearing sky and 13 inches, (32cm) of fresh snow on the ground, with drifts over one meter high. Luckily, the rest of Monday turned quite mild. The temperature of 43F +6C and strong sun did away with much of the snow. The fractal cats were puz- zled by the changed appearance of the outside world, but fully enjoyed the sun on their window shelf. My day was hectic; FL's was pretty much the same. The next new FOTD will be posted whenever I again need a break from setting up the web site. I will continue to post the old FOYD's every couple days while working on the site. Until whenever, take care, and if science is wrong, then what is right? Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Taking_a_Break { ; time=0:00:36.14-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip center-mag=+2.09990941577677900/-1.443549276860739\ 00/2.165757e+009/1/-82.4995882901815349/0.00083256\ 2149663956808 params=-4/-1.3/-0.8/-5.3/0/0/0/0 float=y maxiter=1500 inside=0 logmap=144 symmetry=none periodicity=6 cyclerange=12/255 sound=off mathtolerance=0.05/1 colors=00029f4Af6Be8CiADmCEqEFuGGyGHzGIzGJzhEVfDTW\ DQTCNJCLLBI6BG7GE8KD8OC9TA9X9A`8Ad7CeADeDFeGGeJHfM\ JfPKfSLfUReSXeQbdPhdNncLscKrgPqkUpnZorcouglpYikOff\ Eca5UX9KSDANH0JL8MNFOPNQRUST`VVhXXoZZv`_ZSdCKhsNko\ RikUhhXfd_eabcYebVhaWicXjdYkfYkgWkaUkXSkSRkMPkHNkC\ Mk7WrEdyLhsPkmSZ_cMNoAAz7Mg4YQ1i85bB9WEDQHHJKLDNP6\ QS0SQ8XOF`MMeLUiJ`nHgrGnvvXbmUYeRUYOPQMLTZZWkkYwx`\ uvctufrtiqslpqonprmoulndfQVeRMeRDdS4dSFb_Qag`_ojZw\ lbrnemphhrlctoZurVcwofxfhxYkyPmyGKGSNKWPNZRRbTUeWY\ iY`l_dpags`ap_WnZRlYQiXQfWPcVP`UOYUOWfTTrXRgcNYiJO\ oGOlIOiKOgMOdOObQO_SOYUCka0yh2og4ef6Xf8Ne9EeEN_IVU\ NbORjIWrC_z6UmCO`HIOMCCRADN9EJ8FF6GB5H74H42zX4zS6z\ O8zKAzGzzCzz8zz4zz6zz8zzAzzHzzNCzzEzzGzzIzzKzzLzzF\ zzDzzzzzzzzzzzzzzzzzzzzzzzzzzzzLzzQzzVzz_zzdzzizzn\ zzgzzazzVzzPzzIzzCzzIzzNzzSzzYzzbzzgzzjzzmzzpzzqzz\ rzzrzzszzszzuzzvzzWzz`zzY } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================

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FOTD 06-03-11 (Europa)
by Jim Muth 06 Mar '11

06 Mar '11

FOYD -- March 06, 2011 (Rating 9*) Fractal visionaries and enthusiasts: Today's blast from the past is a fractalized imaginary scene on Europa, the ice-covered moon of Jupiter. It first appeared in June of 1997. It appears again today in an updated version, which will likely be worked on a bit more before making it to the new FOTD web site. The name "Europa" says it all. Since the image is a repeat, I could give it no rating, though if I had rated it, a rating of 9 would have been justified. The effect of a distant sun reflect- ing off a surface of rough ice is remarkably convincing, though I doubt that the wispy clouds could exist in such a scene, since Europa has no atmosphere. The formula is a test that I discarded long ago, but it had a few good images in it, so here it is in all its unglory. The image may be seen by running the included parameter file or by visiting the current FOTD web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> BTW, plans are to have the first page of my FOTD web site up and hopefully running sometime this week. We'll see how it goes. Stay tuned for imminent excitement. Saturday brought lots of clouds to Fractal Central, but it also brought a temperature of 59F 15C, which kept the fractal cats satisfied. The rest of the day went along routinely. Sunday brought a chilly rain, with a steadily dropping temperature. The next FOYD will be posted in a few days. Until whenever, take care, and balance that budgie. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Europa { ; time=0:01:36.72-SF5 on P4-2000 reset=1960 type=formula formulafile=jim.frm formulaname=man-yz-xz passes=1 center-mag=-0.00000686598512544/-1.845082873438826\ /8.246947e+010/-5.121e-005/359.999056918636597/\ -89.9990597420641762 params=0/0/1/0 float=y maxiter=5000 inside=255 logmap=yes periodicity=10 colors=0007Ry7Rx8Qw8Qv9Qt9PsAPrAPqBOpBOoCNnCNmDNkD\ MjDMiEMhELgFLfFLeGKcGKbHKaHJ`IJ_IJZIIYJIWJIVKHUKHT\ LGSLGRMGQMFPNFNNFMOELOEKOEJNEJNEJMEJMEJLDJLDJLDJKD\ JKDJKDJJDJJCJICJICJICJHCKHCKGCKGBKGBKFBKFBKFBKEBKE\ BKDAKDAKDAKCAKCAKBAKBAKBAKA9KA9K99K99K99K89K89K88K\ 78K78K68L68L68L58L57L47L47L47L37L37L37L26L26L16L16\ L16L27M27N38N38O49O49P4AQ5AQ5AR6BR6BS6CS7CT7CU8DU8\ DV8EV90W90XA0XA1YA2YB3ZB4ZC5_C6`C7`D8aD9aDAbEBcECc\ FDdFEdFFeGGeGHfHIgHJgHKhILhIIiJNjJOjJPkKKkKQlLRlLR\ mLRnMRoNKpNSpNTqNVzJazJezKhzUhzOfzGdzGbzK`zMZzSPvS\ SwTYxTYyTYyTZzU_z0czV`zV`zV`zWazWazWazXbzXbzYczYcz\ YczZdzZdz_ez_ez_ezZdzZdzZdzYdzYdzYczYcztzzvzzxzzzz\ zzzzzzzWbzWbzVbzVbzVazVazUazUazUazUazTazT`zT`zT`zS\ `zS`zS`zS`zR_zR_zR_zR_zQ_zQ_zQ_zQZzPZzPZzPZzPZzOZz\ OYzOYzOYzNYzNYzNYzNYzMXzMXzMXzMXzLXzLXzLXzLWzKWzKW\ zKWzKWzJWzJWzJVzJ`zJazJaz } frm:Man-YZ-XZ {; Jim Muth, Thanks to Benno ; p2 = 0 = Julibrot YZ plane ; p2 = 1 = Julibrot XZ plane ; p2 = >0 <1 = Oblique planes z=real(pixel)+flip(real(p1)), c=imag(pixel)+flip(imag(p1)), a=p2, b=flip(cos(asin(p2))): z=sqr(z)+((a+b)*c), |z| <= 25 } END PARAMETER FILE=========================================

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Folium
by Mike Frazier 04 Mar '11

04 Mar '11

Here is a link to a web page with an image: http://www.fracton.org/fmlposts/folium.html The formula for this fractal is called Folium_Curve and is based on the formula Astroid_Mset by Paul Carlson. It generates a Folium Of Descartes curve which looks like a line with a loop in it. This curve was picked to demonstrate that it is possible to generate curves with loops using the cartesian form as suggested by Gerald Dobiasovsky. The image looks best drawn large and anti-aliased. The parameter file used to make this image is below: Folium { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=Folium_Curve passes=1 float=y center-mag=-0.5721775288599359/0.6474535253927753/\ 17.777778/1/-5/0 params=1e-05/1/5/30/0.375/0/0/0/0/0 maxiter=500 inside=255 outside=summ colors=000fOz<22>N5TM4RL3Q<3>I0Kz0f<22>W0FV0ET0D<3\ >O08z88<22>W22V11T11<3>O00zW0<22>hA0g90f80<3>c40zz\ 0<22>fQ0eO0dM0<3>aG00zR<22>0N90L80J7<3>0C40zz<22>0\ NN0LL0JJ<3>0CCGGz<22>33W33V22T<3>00O000<7>000<4>00\ 0z88 } frm:Folium_Curve { ; Folium of Descartes example by Mike Frazier based on ; Astroid_Mset copyright (c) Paul W. Carlson, 1997 ; Additional improvements by Gerald Dobiasovsky ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; real(p1) = a factor controlling the width of the curves ; imag(p1) = radius of the curve ; real(p2) = number of color ranges ; imag(p2) = number of colors in each color range ; real(p3) = folium constant ; ; Note that the equation variable is w, not z. ; Initialize cindex to the index of the background color ; Formula modified to avoid color index 0 which can not ; be used with outside=summ in FractInt v20.04 ;**************************************************** w=0, c=pixel, z=0, cindex=254,; Background color bailout=0, iter=0, range_num=0, i=(0,1), r=imag(p1), ;**************************************************** ; In the accompanying par file, ; we have 8 color ranges with 30 colors in each range ; for a total of 240 colors. The first range starts at ; color 1. Pixels will use color 254 when |w| > 1000. ; Other values can be used here as long as the product ; of num_ranges times colors_in_range is less than 255. ; Color 254 is reserved for the background color and ; color 255 can be used for the inside color. ;**************************************************** num_ranges=real(p2), colors_in_range=imag(p2), ;**************************************************** ; Real(p1) controls the width of the curves. ; These values will usually be in the range 0.001 to 0.1 ;**************************************************** width=real(p1), index_factor=(colors_in_range-1)/width: ;**************************************************** ; The equation being iterated. Almost any equation ; that can be expressed in terms of a complex variable ; and a complex constant will work with this method. ; This example uses the standard Mandelbrot set equation. ;**************************************************** w=w*w+c, ;**************************************************** ; The orbit trap curve is an epicycloid. ; Any two-dimensional curve can ; be used which can be expressed in parametric form in ; terms of the angle from the origin. ;**************************************************** xx=r*real(w),yy=r*imag(w), a=real(p3), ;**************************************************** ; If the orbit point is within some distance of the curve, ; set cindex to the index into the colormap and set the bailout ; flag. Note: the way we use the "distance" here has ; the effect of turning the curves inside-out in the image. ;**************************************************** distance=|xx^3+yy^3-3*a*xx*yy|, if(distance<width&&iter>1), cindex=index_factor*distance+range_num*colors_in_range+1, bailout=1, endif, ;**************************************************** ; Cycle through the range numbers (0 thru num_ranges - 1) ; With two color ranges, even iterations use color ; range 0, odd iterations use color range 1. ;**************************************************** range_num=range_num+1, if(range_num==num_ranges), range_num=0, endif, ;**************************************************** ; Since we are using outside=summ, we have to subtract ; the number of iterations from z. ;**************************************************** iter=iter+1, z=cindex-iter, ;**************************************************** ; Finally, we test for bailout ;**************************************************** bailout==0&&|w|<1000 } -- Mike Frazier www.fracton.org

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FOTD 04-03-11 (Emerald)
by Jim Muth 04 Mar '11

04 Mar '11

FOYD -- March 04, 2011 Fractal visionaries and enthusiasts: Today's blast from the past is from way back -- May 06, 1997. But the image we see today is far different than the old one I posted almost 14 years ago. I have reworked it to bring out the effect of translucency at the edges. The formula behind the action is the MandNewt10, one in a series of formulas that I wrote many years ago and have since almost forgotten about. I never did figure out exactly what they do. I have dropped the rating system for the FOYD's. It's hard to give proper ratings to images that are mere tweakings of earlier scenes. The name "Emerald" is obviously based on the color scheme. The calculation time of all these old images is quite brief. After all, when I began the FOTD I was using a 100mhz-80486 machine. To see the image without the need for calculation, check Hal's web site at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> Paul's site still has the old version of the image posted. My own FOTD web site is moving along. The design is pretty well worked out. In fact, the first month is almost ready. We will upload it in a couple days and see how it flies. I'll post the address as soon as the first month is online and we see that it's working. If nothing goes wrong, there will be only 166+ more months to get posted! Thursday was quite chilly but sunny here at Fractal Central. The temperature rose from a morning low of 14F -10C to an after- noon high of only freezing. The fractal cats fully enjoyed the warm sun, but they would have preferred a bit less draft from the window. The next FOYD will be posted in a couple days. Until next time, take care, and I hear that the world is due to end on May 21. Jim Muth jamth(a)mindspring.com START PARAMETER FILE======================================= Emerald { ; time=0:00:57.26-SF5 on P4-2000 reset=1950 type=formula formulafile=basicer.frm formulaname=MandNewt10 center-mag=-0.106416/0/2.38\ /1/90/0 params=5/-1/1/0.5/1/5e-031 float=y passes=1 maxiter=430 inside=255 logmap=yes periodicity=0 colors=0008H78H78H78H78H77I67I67J67J6A66A86AA6AC6A\ E6AG6AI6AJ6AK5AL5AM5AN5AO5AP5AQ5AR59S58T57U56U56U5\ 6U56U56U56U56U55U45U45U45U45U45U45U45U45U45U45U45U\ 45U45V45W45X45Y45Z44_34_34`34`34a34a34a34b34b34c34\ c34c34d34d34d34e34e35f36f27f28g29g2Ag2Bh2Ch2Di2Ei2\ Gi2Ij3Kk3Mk3Ol4Qm4Sn4Un4Wo4Yp4_q5aq5cr5es5gs5it6ku\ 6mv6ov6qw6tx6wy7zz7wz7tz7qy8oy8my8ly9ky9jy9ix9hx9g\ xAfxAexAdxAcxAbxBaxB`xB_wBZwCYwCXwCWwCVwCUwDUwDUwD\ UwDUvDUvEUvETvETvETvETvFTvFTvFTvFTvFSuGSuGSuGSuGSu\ GSuHSuHSuHRuHRuIRtIRtIRtIRtIRtJRtJQtJQtJQtJQtKQsKQ\ sKQsKQsKPsLPsLPsLPsLPsLPsMPsMPrMOrMOrMOrNOrNOrNOrN\ OrOOrONrONqONqONqPNqPNqPNqPNqPMqQMqQMqQMqQMpQMpRMp\ RMpRLpRLpRLpSLpSLpSLpSLoSLoTKoTKoTKoTKoUKoUKoUKoUK\ oUJnVJnVJnVJnVJnVJnWJnWJnWInWInWInXImXImXImXImXImY\ HmYHmYHmYHmYHmZHlZHlZHlZGl_Gl_Gl_Gl_Gl_Gl`GlbGleFl\ hFmkFmnFnqFntFowFozFpzFpz } frm:MandNewt10 {; Jim Muth z=g=pixel, a=real(p1), b=imag(p1), c=real(p2), d=imag(p2), k=real(p3), f=imag(p3): h=z^a+(g-b)*z-g j=c*z^d+g z=z-k*h/j, f <= |h| } END PARAMETER FILE=========================================

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