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[Feactint] Exploding Colors
by Albrecht Niekamp 03 Nov '15

03 Nov '15

There is a new one today, a zoom into yesterday´s image, nr.20. Maybe you like That one. Rotate the colors! https://www.cubbyusercontent.com/pl/MultifracArchive/_bb8cd4b47ce347b8a0669… Albrecht

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Amusement Park
by Albrecht Niekamp 27 Oct '15

27 Oct '15

HI, after a long time of abstinence this is a new image - completely new and interesting enough for presentation. The combination of frms has never been used before and needed some time to generate. This is the link for the archive - ; https://www.cubbyusercontent.com/pl/MultifracArchive/_bb8cd4b47ce347b8a0669… ; select new-gif-newgif -nr.19 ; Albrecht ; ---------------------start par--------------------------------------------- 10863-09 { ; Amusement Park ; Time 0.11.31.46 Reso 1280/1024 ; Secant-Lambda-Phoenix-Bees reset=2004 type=formula formulafile=mfr_14.frm formulaname=mfr_14_2 function=ident/ident/cabs/ident passes=t center-mag=2.78599/0.768859/10.22138/1/2.50000000000003331/8.94423424213\ 641738e-014 params=-1.069911801507614/-0.3965514084292124/10863.32005750112/20341.05\ 06020602/152048.0404808025/0.160489402241/0.00482000595/0.1007683/512.10\ 00083000999/512.1000083000999 float=y maxiter=2048 inside=maxiter periodicity=0 rseed=-2436 sound=off colors=000MA1<3>C92<6>TXAV`BXcC<3>grI<3>TnXQm_MlcIkgEfp9az<3>OJoRFlVAiZ5\ fb0cd7_iFRnNIyb0yj0000yr0yz1yzC<2>yzz<3>iqdeo_alU<3>Lb8<3>KQ8JM8JJ8<2>H8\ 8G44F00<3>SA5VD6YF7`I8dLAgMBhODiQF<3>peBqiAsm9uq8wu7yz5yz4yz3<4>yj4yg4yc\ 4<3>yS5yP5yL6yI6yE6vE6sD6<6>uAIu9Ku9M<3>w7Sx7Ux6Wy6Yy5_<3>e5M`5IV4E<2>Z4\ H<3>O3DM2CJ2A<3>705F0BN0G<3>f0Uk0Xp0`u0d<2>x0fy0gx0h<3>t1ms1nr1oq2q<2>u2\ u<3>b5eY6`T6X<2>E9L9AG6FO3KW0Qc0Sc<3>5Zc6`c6aa6c_6eY<3>EcgGciIbl<3>R_v<3\ >bivelvhnvkqvntvrww<2>yzz<3>pwznvzgrw<3>Fch7_d7Xa<3>7JO7FL7CI<4>WCA`B9eB\ 7<3>yA0<14>PA1 } ---------------------end---------------------------------------------------

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Fwd: Reading Fractal Map
by sciwise＠ihug.co.nz 26 Oct '15

26 Oct '15

-------- Original Message -------- SUBJECT: Reading Fractal Map DATE: Mon, 26 Oct 2015 23:06:33 +1300 FROM: sciwise(a)ihug.co.nz TO: A BASIC program is available at FreeBASIC , Forums , Projects [Fractal Map] that reads the values for the Volterra-Lotka fractal generated by fractint. The technique might also be applied to other fractals. I've sorted through the wealth of past posts and there is the possibility that a similar ability of plotting the fractal series exist from fractint. Edward

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35187-4
by Albrechtx 26 Oct '15

26 Oct '15

HI, got some time waiting for my flight, so using it to present one more image which is to beautiful to be kept a secret. ; https://www.dropbox.com/s/838eadbt0iq3qdl/35187-4.GIF Albrecht

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FW: Reading Fractal Map - Volterra-Lotka
by Hal Lane 26 Oct '15

26 Oct '15

> ...the possibility that a similar ability of plotting the > [Volterra-Lotka] fractal series exist from fractint. My FRADOC 20.4 says: (I hope this copy & paste doesn't "wrap" and wind up being hard to read...) ---------------------------------------------------------------------------- Fractint Version 20.04 Page 83 2.51 Volterra-Lotka Fractals (type=volterra-lotka) In The Beauty of Fractals, these images are offered as an example of "how an apparently innocent system of differential equations gives rise to unimaginably rich and complex behavior after discretization." The Volterra-Lotka equations are a refinement of attempts to model predator- prey systems. If x represents the prey population and y represents the predator population, their relationship can be expressed as: dx/dt = Ax - Bxy = f(x,y) dy/dt = -Cy + Dxy = g(x,y) According to Peitgen and Richter, "Hence, x grows at a constant rate in the absence of y, and y decays at a constant rate in the absence of x. The prey is consumed in proportion to y, and the predators expand in proportion to x." They proceed to "discretize" this system, by "mating" the Euler and Heun methods. For purposes of image computation, their formula (Equation 8.3 on page 125) can be interpreted as: x(new) = x + h/2 * [ f(x,y) + f[x + pf(x,y), y + pg(x,y)] ] y(new) = y + h/2 * [ g(x,y) + g[x + pf(x,y), y + pg(x,y)] ] [Note: I believe that "pf()" and "pg()" are "p*f()" and "p*g()" -Hal] This formula can be used to plot or connect single points, starting with arbitrary values of x(0) and y(0), to produce typical "strange attractor" images such as the ones commonly derived from the Henon or Lorenz formulae. But to produce an escape-time fractal, we iterate this formula for all (x, y) pairs that we can associate with pixels on our monitor screen. The standard window is: 0.0 < x < 6.0; 0.0 < y < 4.5. Since the "unimaginably rich and complex behavior" occurs with the points that do NOT escape, the inside coloring method assumes considerable importance. The parameters h and p can be selected between 0.0 and 1.0, and this determines the types of attractors that will result. Infinity and (1, 1) are predictable attractors. For certain combinations, an "invariant circle" (which is not strictly circular) and/or an orbit of period 9 also are attractive. The invariant circle and periodic orbit change with each (h, p) pair, and they must be determined empirically. That process would be thoroughly impractical to implement through any kind of fixed formula. This is especially true because even when these attractors are chosen, the threshold for determining when a point is "close enough" is quite arbitrary, and yet it affects the image considerably. The best compromise in the context of a generalized formula is to use either the "zmag" or "bof60" inside coloring options. See Inside=bof60|bof61|zmag|fmod|period|atan (p. 183) for details. This formula performs best with a relatively high bailout value; the default is set at 256, rather than the standard default of 4. Fractint Version 20.04 Page 84 Reference: Peitgen, H.-O. and Richter, P.H. The Beauty of Fractals, Springer-Verlag, 1986; Section 8, pp. 125-7. ------------------------------------------------ It strikes me that since there are only two parameters, h and p, that one might be able to use Fractint's Explorer/Evolver to vary them both and see the variety of "unimaginably rich and complex behavior" in a single screenfull of 'thumbnails.' See: FRADOC 20.4: pg 98: "3.12 Parameter Explorer/Evolver" or: http://www.nahee.com/spanky/www/fractint/findex.html I use <ctrl>-F in my browser to find my topic on this long table of contents page. I would try this, except I'm about to "Factory Restore" my Win8.1 machine. --------------------------------------------------- . . . " ...x represents the prey population . . . and y represents the predator population..." I once saw this relationship between predator and prey drawn in accelerated real time on the face of an oscilloscope by an analog computer. It drew this *Phase Space Plot* that shows the Number of Predators versus the Number of Prey (scroll down to the 2nd plot): http://tinyurl.com/Lotka-Volterra-equations or: https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations#A_simple_exam ple - Hal Lane ######################## # hallane(a)earthlink.net ######################## -----------Original Message------------- From: Fractint [mailto:fractint-bounces@mailman.xmission.com] On Behalf Of sciwise(a)ihug.co.nz Sent: Monday, October 26, 2015 6:07 AM To: fractint(a)mailman.xmission.com Subject: [Fractint] Reading Fractal Map A BASIC program is available at FreeBASIC , Forums , Projects [Fractal Map] that reads the values for the Volterra-Lotka fractal generated by fractint. The technique might also be applied to other fractals. I've sorted through the wealth of past posts and there is the possibility that a similar ability of plotting the fractal series exist from fractint. _______________________________________________ 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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Reading Fractal Map
by sciwise＠ihug.co.nz 26 Oct '15

26 Oct '15

A BASIC program is available at FreeBASIC , Forums , Projects [Fractal Map] that reads the values for the Volterra-Lotka fractal generated by fractint. The technique might also be applied to other fractals. I've sorted through the wealth of past posts and there is the possibility that a similar ability of plotting the fractal series exist from fractint.

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John W Cast it
by JackOfTradeZ＠comcast.net 23 Oct '15

23 Oct '15

. I'm not exactly sure of what you are doing, but you can use any of my viddies for your project(s) just give proper credit where due. A zip file should unzip and release the WMV video - I don't understand your issue. BTW - I HATE MicroShaft! The only good thing ever come out of Redmund was VB, and it looks like it's days are over {doing Python now anyway}. .

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Kaleidescope
by JackOfTradeZ＠comcast.net 22 Oct '15

22 Oct '15

. ok - got it. google chrome ran it ok. AWESOME! wish I could save it as a video file, flash sucks. look closely - it isn't a fractal [ie, mathematically rendered in the usual sense] I think this Romanian dude just gave his computer a good hit of acid. .

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Corrections and explanations
by John Wilson 21 Oct '15

21 Oct '15

http://inoyan.narod.ru/kaleidoskop.swf My apologies for screwing up my message regarding Kaleidoscop. Bad eyesight caused me to omit a period and misread an "f" for an "l". I'm intrigued by the thing, which looks to me like a Fractal viewed in a kaleidoscope with three, or possibly six, mirrors. It's initially fascinating, even hypnotic, but soon loses its novelty. Even though the "kaleidoscope" can be moved with the mouse to view different portions of the basic underlying fractal. Familiarity breeds contempt and this is not quite shaking the bits of colored shapes in a real kaleidoscope, to re-arrange them into a new pattern. After a little thought I think I have the answer, and his name is JackOfTradeZ. Now I'm using a Chromebook to Chromecast movies to my 42-inch T.V. and Kaleidoscop is quite spectacular when viewed in this fashion. I then speculated that a Fractint zoom by Lloyd Garrick could well form the right "shaker" for Kaleidoscop. I first had to check that I could cast of these zooms, and the last one I had downloaded was "The_Prophet." My Chromebook refused to cast it, as it was encoded as a Zipped .wmv file. (Because JackOfTradeZ just LOVES Microsoft). My Chromebook just spat and suggested that I had the file converted to a .webm format, and recommended http://Online-Convert.com . Online-Convert is a miraculous outfit, which seems to convert just about anything to anything else. It swallowed that Zipped .wmv file whole, digested it and returned me "The_Prophet.webm". This casts nicely. That was the hard part! Now all I must do is to ask permission to use one of those zooms and ask the author of Kaleidoscop jf he would be interested in such a project. My ex-wife #2 was born in the old USSR, and if I can enlist her help in contacting the author I'll be in business. As far as I'm concerned this part is not a do-it-yourself project. The final objective is for me to be able to sit at my coffee table in front of the T.V. watching marvels. Boccherini on the stereo system and a subtle incense in the air, plus a cheese board in front of me along with a glass of Madeira. Well, I can dream can't I? John W.

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Re: [Fractint] Fractint Digest, Vol 152, Issue 10
by Roger Kaufman 21 Oct '15

21 Oct '15

Hi J, Did you try to open it in a browser. I had to have Flash installed. Under Linux this is a little more complicated, but Adobe does have a standalone Flash player. It is a really cool Kaleidoscope you can control with your mouse. What I was trying to see is if the underlying image is a fractal image. I believe it is. Fractal images might make nice Kaleidoscopes in general. Roger On 10/21/2015 2:00 PM, fractint-request(a)mailman.xmission.com wrote: > http://inoyan.narod.ru/kaleidoskop.swf > > > > . > Opens in VLC player [Fedora 21] ; but it just flashes a brief image and exits.

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