February 2014 - Fractint - mailman.xmission.com

FOTD 21-02-14 (Slowly I Turned [A-8,M-5])
by Jim Muth 23 Feb '14

23 Feb '14

FOTD -- February 21, 2014 (Rating A-8,M-5) Fractal visionaries and enthusiasts: Today's image lies deep in the February 19 image, which calculated in a few seconds. Today's image however takes a full 1-1/4 hours to calculate, a difference due almost entirely to the much slower arbitrary precision math routine. The name "Slowly I Turned" is a phrase I remember from an old comedy movie. The art rating of an 8 is due to the coloring, which took near an hour to get right. The math rating of a 5 is the Mandelbrot average. Only the most patient will choose to start the parameter file and begin waiting. But luckily, it is not necessary to run the parameter file. The finished image can be seen on the FOTD web sites. Save an hour and avoid impatience by checking 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> The morning brought heavy clouds and rain to Fractal Central, but the clouds broke in the afternoon, leading to a sunny end of the day with a temperature of 46F +8C. The fractal cats slept through the sunny periods, while the fractal humans made it through another day with nothing out of the ordinary to report. The next FOTD will be posted two days from today. Until then, take care, and if it turns out that the world is not real, would it make any difference? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= Slowly_I_Turned { ; time=1:15:00.00 SF5 at 2000MHZ reset=2004 type=mandel passes=1 center-mag=-1.7864\ 3991622914440196793/1.20725951235732689e-007/4.988\ 564e+018/1/-141/0 params=0/0 float=y maxiter=14500 bailout=16 inside=0 logmap=-3129 periodicity=6 colors=33300I00I00I00I00I00I00I00I00I00I00I00I00I0\ 0I00I00J00J00J00K00K00K00L00L00L00M00M00M00N01N02N\ 03O14O25P36P47Q58Q69R79R8AS9ASABTBBTCDUEFUGHUIJUKL\ UMMW666888AAACCCEEEGGGIIIKKKMMMOOOQQQTTTVWV_a_ilrz\ tzppweeeZZZOOOFFFCBJAAAE6NK6NUJWcYclllwwwwjnFFNN6D\ c9JwCPwNUwbbwmfwwwwwwwwwwwwwwwccvwUuoUwiKwfBwwUwuc\ wscuzmpnmneaz_czT_zNXzJVzEZz9bz9hzAfzIczQdzZTgfWki\ VnnTpwXqwXnwZlwciwmfwo`wtWwmRwiNwcIwcEwhEwhKwmQcmK\ NmHGmGFmGImHJmGMmGQmHSmGWmHYmH`mGcmGgmHczJ`zL_mMZm\ PYmSYmUYmXYmYVmYUmZSm_Qm`NmbMmcLmgKmizcczcZzcWzcTz\ cOzcLzcHzcFzmCzmDzmEzmGzmGzmGzmIzmIzmJzmKzmLzmLzmM\ zmNzmNzmJzzzzzzzszzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================

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path through iterated map
by sciwise＠ihug.co.nz 22 Feb '14

22 Feb '14

Upon generating a map of an iterated function, is it then possible to read out values from that map for values of c from another function , along a unique path . 1. Generate F(z)

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Fwd: <Mike> Re: Post 20140219
by Mike Frazier 20 Feb '14

20 Feb '14

Thanks for the comments. I like these formulas because they generate fractals with a lot of variety and they aren't fussy about generating an image. Pretty much anything goes with the two (or more) terms. You can use different terms or the same one repeated and get good results. I have tried lots of combinations of terms and I like the ones with a trigonometric term mixed with a z term the best. Using a trigonometric term generates fractals that have much more intricate features. I forgot part of the equation I posted and the actual equation has an offset constant added to the pixel constant (see PAR file below). The offsets move the origin of each term so they overlap but don't sit right on top of each other. To find this fractal, I was exploring zooming into an area with the "wrong" symmetry. This fractal has z^3 as its dominant term so zooming into 3 way symmetry will always end in a z^3 minibrot. Over the past few years I have been exploring deep zooms into areas with other than the dominant symmetry. For this fractal, I zoomed into an area with two way symmetry to see what was there. In the past, I have found lots of interesting stuff when doing that and this fractal continued the pattern. You would be right if you guessed that there cannot be a minibrot at the center of the two way symmetry. In most of the cases I have looked at the fractal died out but not until you zoom far in. Once the area died out I picked an area of 3 way symmetry off to the side and zoomed into that. All of the good detail along the way was "copied" into the zoom of the 3 way symmetry. The fractal I posted was one of the nice areas along the way. I originally didn't post the PAR file because the image is a deep zoom and needs arbitrary precision math for a formula type that is not available in FractInt. Zooming out until the depth is compatible with double precision allows FractInt to be able to generate the fractal. Here is an image of the two way feature I zoomed into and a FractInt compatible PAR file with the exact equation. You can zoom out more if you want to see the parent fractal. Here is a link to an image: http://dl.dropboxusercontent.com/u/33642054/image/post_20140219_zout.jpg The Fractint compatible PAR file for the image is: 20140219_zout { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20140220_0805 passes=1 float=y center-mag=-0.1900505137602805/-1e-51/44246396.029\ 66739/1/0/0 params=-1/1/0/3/-1/0/1/0/0/0 maxiter=2000 inside=0 periodicity=6 colors=0000000000000000000000000000000000000000000\ 000000000000000000900J20V40d40n6cze0q70g60W30M30C2\ 00007D0FR0Of8at4_s0Nc0FQ06C302F0BT0Nf0YtCls6ie0ZS0\ ME0C00007D0FR0Of8at4_s0Nc0FQ06C302F0BT0Nf0YtCls6ie\ 0ZS0ME0C00007D0FR0Of8at4_s0Nc0FQ06C302F0BT0Nf0YtCl\ s6ie0ZS0ME0C00000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 00000000000000000000000000000000000000000000000000\ 0000000000000000000000000 } frm:F_20140220_0805 { ; Similar to the parallel resistance formula a=real(p1),b=real(p2),d=imag(p1),f=imag(p2), z=0,c1=pixel-p3,c2=pixel-p4: z=1/(1/(a*z*(cos(z)-1)+c1)+1/(d*(z^f)+c2)), |z|<100 } -- Mike Frazier www.fracton.org

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FOTD 20-02-14 (A New Orientation [A-5,M-7])
by Jim Muth 20 Feb '14

20 Feb '14

FOTD -- February 20, 2014 (Rating A-5,M-7) Fractal visionaries and enthusiasts: Today's image shows the same scene and uses the same color palette as yesterday's image, yet it appears totally different. The reason is that today's image is sliced through the Julibrot at a different angle. And while yesterday's image calculated in 10 seconds, today's takes 5-1/4 minutes to finish. This time difference is a result of the high speed of the mandel formula hard-coded in Fractint. As is usually the case with images sliced at such odd angles, I needed to stretch and skew the image to bring it to reasonable proportions. I re-used the same color palette to keep track of the elements common to both images. The artistic aspect rates only a 5. The stretched and tortured features are really not all that attractive. The math aspect however is worth a 7, up four points from yesterday's lowly 3. The four dimensional nature of the Julibrot plays a great part in the math rating of today's image. The calculation time of 5-1/4 minutes is slow by any standards, but visiting the web sites will eliminate the calculation wait. The finished image is or soon will be 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 mix of sun and clouds with a high temperature of 48F +9C made today feel like spring despite the huge piles of snow still lying around. The fractal cats took advantage of the sun when it was shining, then got into a tussle that grew a bit too heated. The fractal humans watched the olympic ice skating, but became only mildly disappointed when the U.S. (in the opinion of many, the greatest nation on earth), failed to win a medal. Unless something unexpected happens, the next FOTD, which is already in the bag, will be posted in 24 hours . Until next time, take care, and is there such a thing as a real illusion? Jim Muth jimmuth(a)earthlink.net START PARAMETER FILE======================================= A_New_Orientation { ; time=0:05:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 center-mag=-0.000000000\ 00429617/+0.00000000000046497/1.427789e+012/\ 0.02601/6.40410471357221045/70.6951562808555707 params=-105.18/-176.87/37.25/8.91/-1.7864399162298\ 41/1.20723576e-007/-1.786439916229841/1.20723576e-\ 007/2/0 float=y maxiter=6400 inside=0 logmap=-893 periodicity=0 mathtolerance=0.05/1 colors=00000C00C00D00D00E00F00G10H20I30J40K50L60M7\ 0O81Q92SA3TB4UC5VE6WF7YG8_H9aICcNFeTHgZKicNmiQroTv\ tVzKHePIaUJYZKUcLRhLNmPJrUGvZCzc8zh5z0Dc6KP8DDA70C\ 14G58K8BOCFRFJVIMZMQbPTeSWbOY`K_YHaWDcUAVP9NL8FH77\ D66A960C6AF5FI5KK5PN4UQ4ZT4cV5eY6g`7hb8je9lhAmjBom\ CrpCwrLzzHcxDUv9Kt5Cs8FqAHpCJnFLmHNlJQjMSiOUhQWfTY\ eV`cXbb_daaffchmejzbhm`ffZd`WbaU`aSZbPXcNVdLTdIReG\ PfENgCMgELeGLdIKcJKaLK`NJ_OJYQIXSIWTIUVHTXHSYHRVOS\ SVSQ`TNgTLmUItUGzUHxVHwVHuVItVIsVIqVJpVJnWJmWKlWKj\ WKiWLgWLfWLeWTc1WcBYcK_cTbcbdckfctgcthcsictjcukcvm\ cwncxocypczqczrczscztczuczvczwczxczzczzczzczzczzcz\ zczzczzczzczzczzczzczzczzczzczzczymzzmzzmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================

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MOTD 200214 Triple Unty
by Albrechtx 20 Feb '14

20 Feb '14

HI, ; The frm I use most is the ManyMods. One of the reasons is the versatility. In an almost intelligent way it adapts to different settings and other frms. Only 2 examples Space Station 160214 and Two Kinds of structures 180214 and many more. It came to life in a collaboration between Sylvie Gallet and Linda Allison. In today´s MOTD it adapts to the Newton frm in an also intelligent way; There are 3 different images which only change the number of elements for a half circle, 3, 7, 32. The images look entirely different although the basic shape is the same. For 7531_b1 there is an alternative coloring which can make you shiver. ; https://www.dropbox.com/sh/ti0cbisn08yg9ix/sndHfvqKqZ ; Cheers, Albrecht

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Re: [Fractint] Two Worlds
by Albrechtx 20 Feb '14

20 Feb '14

Am 20.02.2014 08:21, schrieb Hal Lane: > Each of the very different areas of the images appeared > to be constrained to have colors from different halves > of the color map (with minor exceptions)! In fact, it > would almost appear that many of the minor exceptions > of pixels coming from the "wrong" half of the color map > in 26054-04.GIF have had their color "hand adjusted" in > the color map to black in 26054-14.GIF, to more clearly > separate the two different-looking areas of the image. > > > Am I correct in this analysis, Albrecht? <---<< > yes, of course I do no "handadjusting" of colormaps, it maybe due to the soft transitions of this colormap. 20654-14 was added later and had different settings. The colormap is sgg008, one of Sylvie?s masterpieces I think. ; Also, when you said: >> >...hardcoding of the borders... > are you referring to: > - changing statements or values in the formula code, or to > - adjusting parameter values read in by the formula, or to > - changing color map values to more carefully separate > the two different type of areas in the image? <---<< I?m referring to my border system - a third way to terminate a part of the image besides bailout and maxiter. As there were no reactions to my explanation of the warp system I dont think it makes sense to explain it here. ; Albrecht

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Re: [Fractint] MOTD 1130214 Two Worlds
by Hal Lane 20 Feb '14

20 Feb '14

Albrecht, In your post (below) when you say: > ...To have the outside and the inside of a mandel > completely and clearly in different colors:... do you mean that each of the very different areas of the images 26054-14.GIF and 26054-04.GIF (at your DropBox link below) are constrained to use a different (separate) portion of their color maps? Hmmm. I may have just answered my own question... I "R"estored 26054-14.GIF and 26054-04.GIF in Fractint and invoked the color "E"ditor and looked at the colors in the images. Each of the very different areas of the images appeared to be constrained to have colors from different halves of the color map (with minor exceptions)! In fact, it would almost appear that many of the minor exceptions of pixels coming from the "wrong" half of the color map in 26054-04.GIF have had their color "hand adjusted" in the color map to black in 26054-14.GIF, to more clearly separate the two different-looking areas of the image. Am I correct in this analysis, Albrecht? <---<< Also, when you said: > ...hardcoding of the borders... are you referring to: - changing statements or values in the formula code, or to - adjusting parameter values read in by the formula, or to - changing color map values to more carefully separate the two different type of areas in the image? <---<< - Hal Lane ######################## # hallane(a)earthlink.net ######################## -------------------------------------------------------- Author: Albrechtx Date: 2014-02-13 13:47 -500 To: Fractint and General Fractals Discussion Subject: [Fractint] MOTD 1130214 Two Worlds HI, ; before I started I knew that it would be a difficult task.: To have the outside and the inside of a mandel completely and clearly separated and in different colors: Two different worlds! This involves hardcoding of the borders, - the contour of the mandel - which is more or less a matter of try and error. ; But as you can see I succeeded and it has become a beautiful image! ; https://www.dropbox.com/sh/8mew4zq3u8904u7/XW4A5snwYP ; Cheers, Albrecht ----------------------- --- This email is free from viruses and malware because avast! Antivirus protection is active. http://www.avast.com

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Re: [Fractint] 2914929
by Albrechtx 20 Feb '14

20 Feb '14

HI, ; I like this formula, it looks similar to ManyMods I´m using for my software but it has more deep zooming power and better details. Mike, sorry if I have not quoted the name correctly in the parfile. The link replaces the link in my reply to Hal. ; https://www.dropbox.com/sh/vctktfz0d72sr0t/GWJDJr8Aqe ; Cheers, Albrecht

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Invitation to connect on LinkedIn
by John Wilson 20 Feb '14

20 Feb '14

LinkedIn ------------ Fractint, I'd like to add you to my professional network on LinkedIn. - John John Wilson Retiree Vancouver, Canada Area Confirm that you know John Wilson: https://www.linkedin.com/e/-yo2s9j-hrtypex0-56/isd/20219167706/W0HE--e-/?hs… -- You are receiving Invitation to Connect emails. Click to unsubscribe: http://www.linkedin.com/e/-yo2s9j-hrtypex0-56/d6Kc1otLyJrh4CMMwYyQJN8GeK03x… (c) 2012 LinkedIn Corporation. 2029 Stierlin Ct, Mountain View, CA 94043, USA.

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<Mike> Re: Post 20140219
by Hal Lane 20 Feb '14

20 Feb '14

Mike, > ...this image has a very prominent 6 way symmetry... > [which] ...eventually breaks down and returns to 3 way... There are some blue 3-sided figures in each of the 6 blue "arms" of the large 6-sided snow crystal-like figure, too. There are also 6 small, dark "heads" between each of the 6 blue "arms" that look a bit like the head of the figure in the painting "The Scream". A very nice winter fractal... What does the parent fractal look like? <---<< - Hal Lane ######################## # hallane(a)earthlink.net ######################## ---------------------------------------------------- Author: Mike Frazier Date: 2014-02-19 18:16 -500 To: Fractint and General Fractals Discussion Subject: [Fractint] Post 20140219 This fractal is a parallel resistor formula of the following equation: z = 1 / (1 / (z * (cos(z) - 1) - pixel) + 1 / (z ^ 3 + pixel)) The dominant z term is z^3 so it should have 3 way symmetry but this image has a very prominent 6 way symmetry. I zoomed into the center and the 6 way symmetry eventually breaks down and returns to 3 way and ends in a normal z^3 minibrot. The fractal is a deep zoom at a magnification of about 1e21 so I won't post the PAR file. Here is a link to an image: http://dl.dropboxusercontent.com/u/33642054/image/post_20140219_640_5.jpg -- Mike Frazier www.fracton.org ---------------------------------------------------- --- This email is free from viruses and malware because avast! Antivirus protection is active. http://www.avast.com

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