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Long lines in the Fractint parm file in my last post wrapped.
by Hal Lane 19 Nov '15

19 Nov '15

I noticed that some long lines in the Fractint par file in my last post wrapped while being emailed/posted. They make Fractint unhappy trying to read them if you just grab them & paste them into a file. I shortened the lines below and they test as correct. For correct "final" images, be sure to use periodicity set to zero on the Passes Options screen -- type: <P> to set periodicity. (And set passes=1, too.) I added "periodicity=6" to the parms since I found I was getting Fractint's default periodicity=1 and an *inaccurate* image -- all too easily. - Hal ----- Corrected info & parm files -------------------------- Using: - Sciwise's corrected formula code (with his initialization mod above), - the same parm values as in the original 1993 post, - centered at (0, 0) with magnification 1.0, - with //periodicity set to zero// (to guarantee an accurate image -- at the expense of speed), produces this (anti-aliased) image: http://www.emarketingiseasy.com/TESTS/Fractals/VHeunS00.jpg (Click image to defeat browser resampling if needed.) And with a Paul Carlsonesque color map (taken from one of Albrect's parm files, I believe) the same image looks like this: http://www.emarketingiseasy.com/TESTS/Fractals/VHeunS01.jpg This is the par file and formula used for the above VHeunS00.jpg image: --- Start of PAR file --------------------------------------------- VHeunS00 { ; sciwise's Volterra Lotka formula ; (with modified initialization) ; and bailout repair used. ; p, h variable. ; ; pars - taken from post with the 1993 V-Heun formula. ; frm - sciwise's modified ver of 1993 V-Heun formula: ; "V-HeunPH", repaired. ; reset=2004 type=formula formulafile=fractint.frm formulaname=V-HeunPH center-mag=0.0/0.0/1.0 periodicity=6 params=0.73899999999999999/0.73899999999999999/64/0 float=y maxiter=2048 inside=bof60 logmap=yes colors=(a)blues.map } frm:V-HeunPH { ; Sciwise's FRM REPAIRED BY RESTORING BAILOUT TEST -HHL ; Also parameterized on initialization and bailout values. -HHL x=real(p1) y=imag(p1) p=real(pixel) h=imag(pixel): u=x-x*y w=-y+x*y a=x+p*u b=y+p*w c=x+h*(u+(a-a*b)) d=y+h*(w+(-b+a*b)) x=c y=d z=x+flip(y) |z|<=p2 } ----- End of PAR file ------------------------------------- Here's my parms with a Paul Carlson-esque color map: This is the par file and formula used for the VHeunS01.jpg image: http://www.emarketingiseasy.com/TESTS/Fractals/VHeunS01.jpg --- Start of PAR file --------------------------------------------- VltLotk1 { ; My parms w Carlsonesque color map reset=2004 type=formula formulafile=mfr_14.frm formulaname=V-HeunPH passes=1 center-mag=0.0/0.0/1.0 periodicity=6 params=0.8/0.8 float=y maxiter=512 inside=zmag periodicity=0 sound=off colors=000<2>110110000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0\ F<3>z0K<6>Z0EV0DR0C<3>A08004000<26>000<4>000<7>Q0UU0YX0a_0dc0hf0l<2>p0w<\ 4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<10>2WI2TG2RE<3>4G54D36F5<16\ >kkammcpoe<3>zwm<3>mhZjdVfaS<3>VMCRI8OE4KA0000<43>000<4>000330<12>110 } frm:V-HeunPH { ; Sciwise's FRM REPAIRED BY RESTORING BAILOUT TEST -HHL ; Also parameterized on initialization and bailout values. -HHL x=real(p1) y=imag(p1) p=real(pixel) h=imag(pixel): u=x-x*y w=-y+x*y a=x+p*u b=y+p*w c=x+h*(u+(a-a*b)) d=y+h*(w+(-b+a*b)) x=c y=d z=x+flip(y) |z|<=p2 } ----- End of PAR file ------------------------------------- - Hal Lane ######################## # hallane(a)earthlink.net ######################## --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus

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String World
by Albrecht Niekamp 19 Nov '15

19 Nov '15

Some time ago I presented the Bubble Universe, now here is the String World. 3 images using the manipulating features of MFR14. Images Nr. 23-25 https://www.cubbyusercontent.com/pl/MultifracArchive/_67536d81761949e592b93… ; Albrecht ; --------------------------start Par--------------------------------------------------- 21547-26 { ; String World 1 ; Mandel-Secant-ManyMods-Manowar-Newton ; Time 0.10.00.10 Reso 1280/1024 Bootstick ; Colors SG reset=2004 type=formula formulafile=mfr14.frm formulaname=mfr_14_1 function=zero/ident/ident/ident passes=t center-mag=-0.50000020517775400/+0.62012988982442040/1.629366e+012/1/-52\ .4965746794954669/-0.000239043566757760062 params=-0.05825983458967864/0.3785210730307932/21547.6459571202/14523.49\ 11030602/152048.0404808041/384.16048940221/384.00482000595/128.100768300\ 1/256.1007683001/384.1007683001 float=y maxiter=3071 inside=maxiter periodicity=0 rseed=-2436 sound=off colors=0002pVjwbkuQVYXAvg1BcvaXAlWvkl0YmIcAJeKbAVXmJ10t2UFstUkp4bKzIUCrD\ E98SSzeNOlwwGlD9N7X0bcmNB0jQMoq1Ofw`ZSL6Nf7gE_FMuciyBgoNtOpiQ4Tf_`boRYad\ zBq5KaOmfCDYqZxwo3P6uttXig07PCEqKAGoJoAeLUbD541RcXyjVjcylFw4cXZ61KtxAqM7\ feWKB7YeVJY19kDWjlK54oeFOHioHrvLVJPsKjf5Ccbb6lSYnFoQWQSeC_9wOi2_gHphRDKZ\ 8i5WxAQX65AxcpKJr`8ASx2zKtDRJo9UEkIsj1Iyv04RrmX_RaxapfYqPvuMa4Qoyc6Dc5VO\ f98NT30MOqS_IeIS2QN_ja70_GkHFefDj7twbZKCrMrijNGzYpm3yB2yaRy3Yje4bmwDCToz\ d5syZnfm97SNWfZGLlz010PRU3gfkEagMPyLVvCYfZQNXpZQvOowdRjsg8i1hZWs0lQkTv0_\ QDTs_lxPIN4MjBHg5jnU_XP2lKoVx8KeDmsoDRh_crkXEQ6JOIAO0FUpGrU_1H92NnoXYXax\ y`eVL8n711EbDQiPFTIK_Evn4bU7HKTBU_GNNQDXEv`roR5DuYlKbp_47UDKbcqHe8fYXVcp\ 3ruY47RJbt3GF4Gu8Na`HxKeJvbc6amLC`1dhwQAxa24Q2cJ_9G8RGHKQ2UOQ4gHDYwyu0ec\ u25uCniCZZxnt61bGgIljLomQ6l1Sri6b0K6f_vZ01j9sghPSah2Pt5 } 21547-28 { ; String World 2 ; Mandel-Secant-ManyMods-Manowar-Newton ; Time 0.10.19.00 Reso 1280/1024 Bootstick ; Colors SG reset=2004 type=formula formulafile=mfr14.frm formulaname=mfr_14_1 function=zero/ident/ident/ident passes=t center-mag=-0.50000020517818930/+0.62012988982377440/1.512454e+013/0.999\ 9/-62.5153264683909953/-0.0375564993000660971 params=-0.05825983458967864/0.3785210730307932/21547.6459571202/14523.49\ 11030602/152048.0404808041/384.16048940221/384.00482000595/128.100768300\ 1/256.1007683001/384.1007683001 float=y maxiter=3071 inside=maxiter periodicity=0 rseed=-2436 sound=off colors=0002pVjwbkuQVYXAvg1BcvaXAlWvkl0YmIcAJeKbAVXmJ10t2UFstUkp4bKzIUCrD\ E98SSzeNOlwwGlD9N7X0bcmNB0jQMoq1Ofw`ZSL6Nf7gE_FMuciyBgoNtOpiQ4Tf_`boRYad\ zBq5KaOmfCDYqZxwo3P6uttXig07PCEqKAGoJoAeLUbD541RcXyjVjcylFw4cXZ61KtxAqM7\ feWKB7YeVJY19kDWjlK54oeFOHioHrvLVJPsKjf5Ccbb6lSYnFoQWQSeC_9wOi2_gHphRDKZ\ 8i5WxAQX65AxcpKJr`8ASx2zKtDRJo9UEkIsj1Iyv04RrmX_RaxapfYqPvuMa4Qoyc6Dc5VO\ f98NT30MOqS_IeIS2QN_ja70_GkHFefDj7twbZKCrMrijNGzYpm3yB2yaRy3Yje4bmwDCToz\ d5syZnfm97SNWfZGLlzni0PRU3gfkEagMPyLVvCYfZQNXpZQvOowdRjsg8i1hZWs0lQkTv0_\ QDTs_lxPIN4MjBHg5jnU_XP2lKoVx8KeDmsoDRh_crkXEQ6JOIAO0FUpGrU_1H92NnoXYXax\ y`eVL8n711EbDQiPFTIK_Evn4bU7HKTBU_GNNQDXEv`roR5DuYlKbp_47UDKbcqHe8fYXVcp\ 3ruY47RJbt3GF4Gu8Na`HxKeJvbc6amLC`1dhwQAxa24Q2cJ_9G8RGHKQ2UOQ4gHDYwyu0ec\ u25uCniCZZxnt61bGgIljLomQ6l1Sri6b0K6f_vZ01j9sghPSah2Pt5 } 21547-30 { ; String World 3 ; Mandel-Secant-ManyMods-Manowar-Newton ; Time 0.10.18.85 Reso 1280/1024 Bootstick ; Colors SG reset=2004 type=formula formulafile=mfr14.frm formulaname=mfr_14_1 function=zero/ident/ident/ident passes=t center-mag=-0.50000020517821460/+0.62012988982378010/1.400421e+013/1.000\ 5/-62.5979189790724107/0.099222572141416332 params=-0.05825983458967864/0.3785210730307932/21547.6459571202/14523.49\ 11030602/152048.0404808041/384.16048940221/384.00482000595/128.100768300\ 1/256.1007683001/384.1007683001 float=y maxiter=3071 inside=maxiter periodicity=0 rseed=-2436 sound=off colors=000cU7IKTCU_HNNRDXFv`soR6DuZlKcp_57UEKbdqHf8fZXVdp3suY57RKbt4GF5G\ u9NaaHxLeJwbc7amMC`2dhxQAya25Q2dJ_AG8SGHLQ2VOQ5gHEYwzu0fcu35uDniDZZynt71\ bHgImjLpmQ7l1Tri7b0L6f`vZ01jAsgiPSbh2Qt53pVkwbluQWYXBvg2BcwaXBlWwkl1YmJc\ AKeKcAVYmJ20t3UFttUlp4cKzJUCsDEA8STzeOOlxwGmD9O7X1bcnNB1jQNoq2Ofx`ZTL6Of\ 7hE_GMudiyCgoOtOqiQ5Tf``bpRYbdzCq5LaOnfCEYq_xwp3P7utuXih07QCErKAHoJpAeMU\ bE542RcYyjWjczlFx4cYZ62KtyAqN7ffWKC7YfVJZ19lDWklK64ofFOIioIrvMVJQsKkf5Dc\ bc6lTYnGoQXQSfC_AwOj2_hHpiRDLZ8j5WyAQY65BxcqKJs`8BSx3zKuDRKo9VEkJsj2Iyw0\ 4SrmY_RbxaqfYrPvvMa5Qozc6Ec5WOfA8NU30NOqT_IfIS3QN`ja80_HkHGefEj7uwb_KCsM\ rjjNHzYqm3zB2zaRz3Yke4cmwECTpzd6sy_nfn97TNWgZGMlz010QRU4gflEahMPzLVwCYgZ\ QOXp_QvPoweRjtg8j1h_Ws0lQlTv1_QETs`lxQIN5MjCHg6jnV_XQ2lLoVy8KfDmtoDSh_dr\ kYEQ7JOJAO0FUqGrV_1I92OnoYYXbxyaeVM8n811FbDRiPGTIL_Ewn4 } ----------------------------------------------------End---------------------------------

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test
by sciwise＠ihug.co.nz 18 Nov '15

18 Nov '15

Some of my previous messages to the group appear to have gone astray. sciwise

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Re: [Fractint] Sciwise got me interested in his Volterra-Lotka fractals.
by Hal Lane 16 Nov '15

16 Nov '15

--- Mike Frazier said: ----- > Nice images Hal. Thanks. > Is the par file available? I got the formula from Sciwise in the Fractint list serve, and - copied a random parm file to get the formula started, - copied and pasted in a color map of Albrecht's, and - parameterized the formula. I set an initial parameter value of (0.8, 0.8) -- as did Sciwise. This creates Sciwise's 'parent' fractal: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk12.gif The described parm file is below. However, when I went to save additional parameter files -- of other images I had located in the parent -- I was unable to. I believe the problem is that I installed Richard's Fractint for Windows beta 5 (now renamed Iterated Dynamics) in too deep a folder, whose folder name overflowed a buffer when trying to save the zoomed in, stretched, rotated, etc. portion of the parent image -- when trying to save a new parm file. I need to reinstall Richard's program. I attempted to compensate for the lack of parm files in my Fractint post by trying to describe where I zoomed into a previous image. These descriptions are in my Fractint post of: Nov 12, 2015 at 4:03 am EST: http://tinyurl.com/Fractint-Post-2015-11-12-04-03 or: https://mailman.xmission.com/lurker/message/20151112.090325.42611adc.en.html I believe there's enough info in that post that you can reproduce my images by exploring yourself. Let me know if you have any problems, please. Sciwise also sent me additional descriptive info about his posts on Volterra Lotka fractals at freebasic.net -- but did not post it to the Fractint list. I could ask him if I can share his email to me with the Fractint list serve, if you want... He's working with Basic language programs that he's using to investigate Volterra Lotka fractals in ways that I don't fully understand currently. He said: >You might want to look at my recent uploads to freebasic.net >forum , project , fractal map , fracmap1.bas and >fracmap1a.bas. ### Start of Par file with SciWise's comments & frm: #### comment { Volterra Lotka , p , h variable. HHL: [Use: passes=1 maxiter=at least 512 I used: periodicity=0 I don't know if that's needed -- I just wanted to be safe while looking at a new fractal.] V-HeunPH.frm initial condition: [ x = 0.8 , y=0.8 ], this initial condition might be determined from the V-Heun map. [ p , h ] varied over plane. x' = x - x*y y' = -y + x*y This is the second part of the Volterra Lotka formulas , in this instance we are selecting an initial condition and varying the parameters p & h across the plane. There's now another FreeBASIC file to obtain the sequences from the map generated by V-HeunPH.frm . The coordinates I used were : Top left corner: -2.0, 1.5 Bottom right corner: 2, -1.5 } VltLotk1 { reset=2004 type=formula formulafile=mfr_14.frm formulaname=V-HeunPH passes=1 center-mag=0.0/0.0/1.0 params=0.8/0.8 float=y maxiter=512 inside=zmag periodicity=0 sound=off colors=000<2>110110000KA4<7>gcOjgRmjT<3>zzc<9>UOFRKDOGA<3>A00<9>f0Ci0Dl0\ F<3>z0K<6>Z0EV0DR0C<3>A08004000<26>000<4>000<7>Q0UU0YX0a_0dc0hf0l<2>p0w<\ 4>_0dX0aU0Y<2>K0NH0JG0NE1R<3>7UX6`Z4h_2oa0wc<10>2WI2TG2RE<3>4G54D36F5<16\ >kkammcpoe<3>zwm<3>mhZjdVfaS<3>VMCRI8OE4KA0000<43>000<4>000330<12>110 } frm:V-HeunPH { x=real(p1) y=imag(p1) p=real(pixel) h=imag(pixel): u=x-x*y w=-y+x*y a=x+p*u b=y+p*w c=x+h*(u+(a-a*b)) d=y+h*(w+(-b+a*b)) x=c y=d z=x+flip(y) |z| } ######### End of Par file ################### - Hal Lane ######################## # hallane(a)earthlink.net ######################## -----Original Message--------------------------------------------- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Mike Frazier Sent: Monday, November 16, 2015 9:21 AM To: Fractint and General Fractals Discussion <fractint(a)mailman.xmission.com> Subject: Re: [Fractint] Sciwise got me interested in his Volterra-Lotka fractals. Nice images Hal. Thanks for posting them. Is the par file available? -- Mike Frazier www.fracton.org _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus

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Re: [Fractint] Sciwise got me interested in his Volterra-Lotka fractals.
by Hal Lane 16 Nov '15

16 Nov '15

I've done a bit more investigating of sciwise's Volterra-Lotka fractal formula. I'm showing my "investigations" in addition to finalized art images. If you want only the final "artistic" images, I identified those. Look for: "[ART IMAGE]s", if you want to skip over the "investigation" images. If needed, click once on all of the 1200 x 900 pixel images -- and/or (maybe) make your browser full screen. I used two tabs in my browser for viewing these images so I could keep two images open which allowed me to see the relationships between the two, as I elaborate below. Here again is sciwise's parent Volterra-Lotka fractal initialized with the default (0.8, 0.8) stretched ~10X vertically: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk13.gif Parameters varied from (0.00010, 0.00010) to (0.99990, 0.99990) : http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk14.gif The upper right corner image (0.99990, 0.99990) of VltLtk14.gif looked like it might have interesting areas in it: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk15.gif The "knee" area of VltLtk15.gif, below & to the right of center: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk17.gif The boxed area in VltLtk17.gif enlarged turned out to not be very interesting: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk18.gif The top dozen or so pixels at the very tip of the vertical straight line above and to the left of center in VltLtk15.gif, when enlarged, has quite a variety of seemingly unrelated -- but potentially interesting -- features: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk19.gif The left "hook" at the bottom of VltLtk19.gif: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk20.gif I suspected the patterns in the chaotic-looking area in the "cup" of the "hook" to be Moire fringes, since they looked to be aligned to 0, 22.5, and 45 degree orientations. So, ever a glutton for punishment, I enlarged VltLtk20.gif 's "cup", which revealed the regular structure of the "cup" and showed Moire fringes at 0 and 45 degrees (near the upper left corner.) http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk21.gif But, for some reason, the fringes / interference patterns went wild on the right side of the cup, and made star-like patterns: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk24.jpg VltLtk21.gif above also reveals the color map. I believe I took the map from one of Albrecht's images: "Thanks, Albrecht!" http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk21.jpg Please view the following two images without browser resampling: Thanks! [ART IMAGE] Here's the top of the "roller coaster track" in VltLtk15.gif enlarged. I skewed the triangular areas to try to compose them into the image as best as I could. There's a lot of interesting stuff going on here: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk22.gif [ART IMAGE] This is the area where the "bite is taken out of" (or "cup" is indented into) the lower right corner of the left triangle of VltLtk22.gif : It's tricky to verify the relationship between the corresponding areas in the two images visually since I rotated the color map, which made many features look a bit different. http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk23.gif Comments welcome on the investigation process, and on the images. Thanks, - Hal Lane ######################## # hallane(a)earthlink.net ######################## --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus

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4k UHD Monitor
by Albrecht Niekamp 15 Nov '15

15 Nov '15

Hi, sorry I had to to close my archives for some days as I needed the cloud space for multimedia purposes.Now they are back online but the link has changed. ; https://www.cubbyusercontent.com/pl/MultifracArchive/_67536d81761949e592b93… ; Some news: I bought a new UHD (4K) TV, Panasonic TX-50CXW704 with extreme image quality.This has a special 1920/1080 HDMI computer modus which improves the image quality of your desktop by upsampling and further sharpening. In DOS mode supplied by my bootstick all Nvidia Vesa modes are available For 16/9 this means up to 1280/1024 but apparently with the double amount of details. The images are unbelievably sharp and the colors are different, a lot different and more interesting. Sadly this effect gets lost if I´m watching these images with a 32bit Image viewer like Irfan viewer or similar. Maybe a viewer with 4k capacity would make a difference.It would show only a quarter of the DOS image on the desktop. Do you Know any? The attached Demo image (Nr.21) therefore is not the same as in DOS mode, but maybe with a better viewer things change. Please tell me. Albrecht

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Re: [Fractint] Sciwise got me interested in his Volterra-Lotka fractals.
by Hal Lane 10 Nov '15

10 Nov '15

P.N.L., Thanks for your comments -- and a "shout out" to the silent majority -- the lurkers! > I like this one [ > http://www.emarketingiseasy.com/TESTS/Fractals/VltLtkF0.gif > ] as well. The "rainbow" of colors really makes this stand out. The color map is taken from a 1998 contest image. "Leather Gem - by Damascena Korwen": http://www.emarketingiseasy.com/TESTS/Fractals/LeatherGem.gif I think she really nailed the leather colors, don't you? It's a really nice fractal, too. I try and remember to give her credit for her color map when I use it, but I lose track of the spelling of her name and have to search for it... I made several versions of her map -- reversed, rotated, etc. I occasionally used her map when doing variations on Jim Muth's FOTD images. But I most often kept Jim's original choice of colors. > The stretching [of Sciwise's Volterra-Lotka parent fractal] is much > more interesting than the unstretched parent version. I learned to try stretching after seeing Jim do it in some of his images. It can sometimes make a nondescript thin feature turn into a garden or a palace, or... - Hal Lane ######################## # hallane(a)earthlink.net ######################## -----Original Message----- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Paul N. Lee Sent: Tuesday, November 10, 2015 2:31 AM To: fractint(a)mailman.xmission.com Subject: Re: [Fractint] Sciwise got me interested in his Volterra-Lotka fractals. Hal Lane wrote: > > This is the default *Fractint* Volterra- Lotka fractal (a very fast > fractal) with the Leather Gem color map: > http://www.emarketingiseasy.com/TESTS/Fractals/VltLtkF0.gif I like this one as well. The "rainbow" of colors really makes this stand out. :-) > > ...and the parent again, stretched *only* vertically (by a factor of > about 10): > http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk13.gif The stretching is much more interesting than the unstretched parent version. Sincerely, P.N.L. _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus

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Re: [Fractint] Sciwise got me interested in his Volterra-Lotka fractals.
by Hal Lane 10 Nov '15

10 Nov '15

Paul said: > Interesting final image. Thanks! And I thank Sciwise, too -- for the formula -- and a chance to get back to calculating fractals. > If you decide to do further explorations, please > share the results with us. Sure. See below. It was only after I had done the Evolver exploration that I noticed that the parameters I was evolving were the initial conditions. It appears from the Evolver images (that I put links up for before) that these equations are not dramatically sensitive to initial conditions... ...with the exception that the formula doesn't like initial conditions of real or imaginary values of *exactly* zero or one. I used 0.0001 and 0.9999 when I was evolving. I'm doing further evolving on the *parent* of Sciwise's Volterra-Lotka fractal as I type this -- it looks like there may be a bit more action with the parent... I forgot to mention that I did a small amount of vertical stretching of the images in my previous post, and used one of the recommended coloring methods, zmag. I should also try bof60 coloring, too -- but it seems to me that the coloring method wouldn't likely be too important for all the "confetti" areas... This is the default *Fractint* Volterra-Lotka fractal (a very fast fractal) with the Leather Gem color map: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtkF0.gif Again, be sure to not let your browser resample the images -- just click them once if they've been resized to fit. This is *Sciwise's* Volterra-Lotka parent fractal: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk12.gif and the parent again, stretched *only* vertically (by a factor of about 10) : http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk13.gif My fractals in my previous post were zoomed into the center of Sciwise's parent Volterra-Lotka fractal. - Hal Lane ######################## # hallane(a)earthlink.net ######################## -----Original Message----- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of Paul N. Lee Sent: Monday, November 9, 2015 3:11 PM To: fractint(a)mailman.xmission.com Subject: Re: [Fractint] Sciwise got me interested in his Volterra-Lotka fractals. Hal Lane wrote: > > ...found some variation as a function > of the two parameters. I then: > - selected a thumbnail image in the Evolver, > - exited the Evolver, > - set Single Pass, and > - raised maxiter from 512 to 2048 (I think it was), and got this > image: > http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk11.gif > Interesting final image. Could be some possibilities on what one may produce with this. If you decide to do further explorations, please share the results with us. ;-) Sincerely, P.N.L. _______________________________________________ Fractint mailing list Fractint(a)mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus

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Sciwise got me interested in his Volterra-Lotka fractals.
by Hal Lane 09 Nov '15

09 Nov '15

Sciwise got me interested in trying his formula for Volterra-Lotka fractals. First I made his 'x' and 'y' initialization constants into parameters and then had Fractint's Evolver vary them from (0,0) to (1,1) in a quick & dirty Solid Guessing mode: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtka7.gif I then zoomed into the parameter space nearer to the (0.0) [lower left corner.]: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtka9.gif and found some variation as a function of the two parameters. I then: - selected a thumbnail image in the Evolver, - exited the Evolver, - set Single Pass, and - raised maxiter from 512 to 2048 (I think it was), and got this image: http://www.emarketingiseasy.com/TESTS/Fractals/VltLtk11.gif Be sure to not let your browser resample the image -- just click on it once. Sciwise's use of the Volterra-Lotka equations gives quite a different image from Fractint's built in Volterra-Lotka fractal. I used Richard's Fractint for Windows beta 5 (now called Iterated Dynamics) http://tinyurl.com/FractInt-for-Win-beta5 or: https://legalizeadulthood.wordpress.com/2007/04/13/fractint-for-windows-beta -5/ running on Windows 8.1(!) for the first time to create these images. Sorry to not have the PAR file, but I overflowed a buffer in the code and crashed the program while trying to save the PAR file -- likely due to my having too long a directory name. - Hal Lane ######################## # hallane(a)earthlink.net ######################## -----------Original Message------------- Author: sciwise Date: 2015-11-07 23:49 -500 To: fractint Subject: [Fractint] Volterra Lotka PH This is the second part of the Volterra Lotka formulas , in this instance we are selecting an initial condition and varying the parameters p & h across the plane. There's now another FreeBASIC file to obtain the sequences from the map generated by V-HeunPH.frm . The coordinates I used were : Top left corner: -2.0 1.5 Bottom right corner: 2 -1.5 ---------------------------------------------------------------------------- ------- comment{ Volterra Lotka , p , h variable . V-HeunPH.frm initial condition [ x = 0.8 , y=0.8 ], this initial condition might be determined from the V-Heun map . [ p , h ] varied over plane . x' = x - x*y y' = -y + x*y } V-HeunPH { x=0.8 y=0.8 p=real(pixel) h=imag(pixel): u=x-x*y w=-y+x*y a=x+p*u b=y+p*w c=x+h*(u+(a-a*b)) d=y+h*(w+(-b+a*b)) x=c y=d z=x+flip(y) |z| } --- --- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus

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Volterra Lotka PH
by sciwise＠ihug.co.nz 07 Nov '15

07 Nov '15

This is the second part of the Volterra Lotka formulas , in this instance we are selecting an initial condition and varying the parameters p & h across the plane. There's now another FreeBASIC file to obtain the sequences from the map generated by V-HeunPH.frm . The coordinates I used were : Top left corner . -2.0 1.5 Bottom right corner . 2 -1.5 ----------------------------------------------------------------------------------- comment{Volterra Lotka , p , h variable . V-HeunPH.frm initial condition [ x = 0.8 , y=0.8 ], this initial condition might be determined from the V-Heun map . [ p , h ] varied over plane . x' = x - x*y y' = -y + x*y } V-HeunPH { x=0.8 y=0.8 p=real(pixel) h=imag(pixel): u=x-x*y w=-y+x*y a=x+p*u b=y+p*w c=x+h*(u+(a-a*b)) d=y+h*(w+(-b+a*b)) x=c y=d z=x+flip(y) |z|

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