From: owner-fractint-digest@lists.xmission.com (fractint-digest) To: fractint-digest@lists.xmission.com Subject: fractint-digest V1 #114 Reply-To: fractint-digest Sender: owner-fractint-digest@lists.xmission.com Errors-To: owner-fractint-digest@lists.xmission.com Precedence: bulk fractint-digest Saturday, February 21 1998 Volume 01 : Number 114 ---------------------------------------------------------------------- Date: Thu, 19 Feb 1998 17:56:24 -0600 (CST) From: pjcarlsn@ix.netcom.com (Paul and/or Joyce Carlson) Subject: (fractint) Petals_Mset Formula This formula is a combination of the Carlson Series formula and a variation of the rendering method in my Petals_Julia formula. The Petals_Julia formula used an orbit trap consisting of the areas of overlap of four circles that were tangent to each other (in pairs) at the origin. The present formula is similar except that the circles are moved away from the origin by an offset factor (parameter p2). This makes the petals method suitable for zooming in on little Mandys in Msets. The amount the circles are moved away from the origin is equal to p2 times p1. I can't really suggest a typical range of values for p1. I've used 0.18 in the pars here, but this could vary widely depending on the location. p2 will usually be quite small, say from 0.0001 to 0.2. The first par produces an image that looks a lot like a familiar Julia set. The other pars produce successive zooms into the image, producing images that are more and more symmetrical until they become almost circular. This is typical of the Carlson Series formula. Note to Fractint developers: this formula has a lot of computation in the initialization. It sure would be nice to have some "static" variables that could be initialized once per image intead of once per pixel. Paul Carlson Frm:Petals_Mset {; Copyright (c) Paul W. Carlson, 1998 ;**************************************************** ; Always use floating point math and outside=summ. ; ; Parameters: ; p1 = radius of the circles ; p2 = circle offset factor ; real(p3) = number of color ranges ; imag(p3) = number of colors in each color range ; ; Note that the equation variable is w, not z. Always ; initialize z to zero. ;**************************************************** w = 0 c = pixel r = p1 ro = r + r * p2 r2 = r * r f = 1 - 2 * p2 - p2 * p2 k = p2 * r + r * sqrt(f) ;abs val of petal center (k,k) plsqd = 2 * r2 * f ;petal length squared z = 0 num_ranges = real(p3) colors_in_range = imag(p3) range_num = 0 iter = 0: ;**************************************************** ; The Carlson Series (I had to name it something) :) ;**************************************************** w2 = w * w w4 = 0.01 * w2 * w2 w8 = w4 * w4 w12 = w4 * w8 w16 = w4 * w12 w = w2 - w4 - w8 - w12 - w16 + c ;**************************************************** ; Determine which pair of overlapping circles the ; orbit point falls in, if any. ;**************************************************** wr = real(w), wi = imag(w) c1 = (((wr-ro) * (wr-ro) + wi * wi) < r2) c2 = ((wr * wr + (wi+ro) * (wi+ro)) < r2) c3 = (((wr+ro) * (wr+ro) + wi * wi) < r2) c4 = ((wr * wr + (wi-ro) * (wi-ro)) < r2) IF (c1 && c4) d = (wr-k) * (wr-k) + (wi-k) * (wi-k) ELSEIF (c1 && c2) d = (wr-k) * (wr-k) + (wi+k) * (wi+k) ELSEIF (c2 && c3) d = (wr+k) * (wr+k) + (wi+k) * (wi+k) ELSEIF (c3 && c4) d = (wr+k) * (wr+k) + (wi-k) * (wi-k) ELSE d = 0 ENDIF ; IF (d > 0) ;************************************************ ; Set z equal to the index into the colormap. ;************************************************ index = colors_in_range * d / plsqd z = index + range_num * colors_in_range + 1 ENDIF ; range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF iter = iter + 1 z = z - iter d == 0 && |w| < 1000 } petlsm1 { ; Copyright (c) Paul W. Carlson, 1998 reset=1960 type=formula formulafile=petlsmnd.frm formulaname=Petals_Mset passes=t center-mag=-0.74667870138017570/+0.14517010627719700/4762\ 66.3/1/77.499 params=0.18/0/0.05/0/2/125 float=y maxiter=2000 inside=253 outside=summ colors=000aG0<60>zy0zz0zy0<60>aG0C0C<60>yVyzVzyVy<60>C0C00\ 0<3>000 } petlsm2 { ; Copyright (c) Paul W. Carlson, 1998 reset=1960 type=formula formulafile=petlsmnd.frm formulaname=Petals_Mset passes=t center-mag=-0.74667862934396400/+0.14516987843959050/1.9992\ 71e+008/1/77.498 params=0.18/0/0.05/0/2/125 float=y maxiter=2000 inside=253 outside=summ colors=000C0C<60>yVyzVzyVy<60>C0CaG0<60>zy0zz0zy0<60>aG00000\ 00zz0000000 } petlsm3 { ; Copyright (c) Paul W. Carlson, 1998 reset=1960 type=formula formulafile=petlsmnd.frm formulaname=Petals_Mset passes=t center-mag=-0.74667862932165550/+0.14516987859443410/3.51984\ 3e+009/1/105.999 params=0.18/0/0.05/0/2/125 float=y maxiter=3000 inside=253 outside=summ colors=000C0C<60>yVyzVzyVy<60>C0CaG0<60>zy0zz0zy0<60>aG000000\ 0zz0000000 } petlsm4 { ; Copyright (c) Paul W. Carlson, 1998 reset=1960 type=formula formulafile=petlsmnd.par formulaname=petals_mset passes=t center-mag=-0.74667862931571720/+0.14516987860055840/9.9995\ 6e+009/1/105.999 params=0.18/0/0.05/0/2/125 float=y maxiter=3000 inside=253 outside=summ colors=000C0C<60>yVyzVzyVy<60>C0CaG0<60>zy0zz0zy0<60>aG00000\ 00zz0000000 } - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 01:00:52 +0100 From: Guy Marson Subject: Re: (fractint) literary fractals At 18:56 19.02.1998 -0800, you wrote: >Hi >Does anyone know of any works of fiction in which fractals play a a part? The "Rolling Stones" were using animated fractals in there shows.. as back-ground.. but the "Stones" are still reality, no fiction.. >Off the top of my head, I know of The Ghost from the Grand Banks, Pier >Anthony's *Mode* Series. Also, they are tantalingly mentioned in passing in >Infinity's Shore. I am interested in references to fractals specifically, >not just to chaos in general. >Thank you. > > > > >- >------------------------------------------------------------ >Thanks for using Fractint, The Fractals and Fractint Discussion List >Post Message: fractint@xmission.com >Get Commands: majordomo@xmission.com "help" >Administrator: twegner@phoenix.net >Unsubscribe: majordomo@xmission.com "unsubscribe fractint" > PS: Sometimes a "REPLY" to me is bouncing! If this happened, please report as "NEW MESSAGE" to: guy.marson@mnhn.lu Thanks! - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Feb 1998 19:29:17 EST From: Nature102@aol.com Subject: Re: (fractint) literary fractals In a message dated 98-02-19 19:01:05 EST, pfjakub@earthlink.net writes: << Does anyone know of any works of fiction in which fractals play a a part? Off the top of my head, I know of The Ghost from the Grand Banks, Pier Anthony's *Mode* Series. Also, they are tantalingly mentioned in passing in Infinity's Shore. I am interested in references to fractals specifically, not just to chaos in general. >> ::Shrugs:: Jurassic Park had a lot of references to chaos in it, and I think a couple of references to fractals specifically. The chapter headings are stuff like "First Iteration," "Second Iteration," etc., and the pictures that go with them look suspiciously like L-systems. Also, this may be just fractal obsession, but I'm convinced that Robert Jordan's The Wheel of Time, Book 2, The Great Hunt has a reference to fractals or at least to chaos. "From Stone to Stone run the lines of 'if,' laid by those who knew the Numbers of Chaos." Sure sounds like fractals to me. :-P - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Feb 1998 19:13:33 -0600 From: "Damien M. Jones" Subject: Re: (fractint) literary fractals David Brin's "Glory Season" mentions fractals in passing as an entertainment for men while they're isolated from women. Damien M. Jones \\ dmj@fractalus.com \\ http://www.icd.com/tsd/ (temporary sanity designs) \\ http://www.fractalus.com/ (fractals are my hobby) - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Feb 1998 20:27:47 -0500 From: "Jason Hine" Subject: Re: (fractint) literary fractals ><< Does anyone know of any works of fiction in which fractals play a a part? Books, no. Movies... hmm. The starship Enterprise's main computer was protected by a fractal encryption technique in that latest movie, Star Trek: First Contact. Poems, well... I think that I shall never see A Poem lovely as a Fractal. - unknown God - the Father, God - the Son, God - the square root Of negative one? - Unknown Jason Hine - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Feb 1998 21:45:16 EST From: RNelson472@aol.com Subject: Re: (fractint) literary fractals The definition of Julia sets as z (n+1) = z^2 + c where c is a constant complex # and z is another seems to be wrong. Isn't it that initially z = 0? - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Thu, 19 Feb 1998 21:38:11 -0800 From: "Jay Hill" Subject: Re: (fractint) literary fractals Hi R - ---------- > From: RNelson472@aol.com > To: fractint@lists.xmission.com > Subject: Re: (fractint) literary fractals > Date: Thursday, February 19, 1998 6:45 PM > > The definition of Julia sets as z (n+1) = z^2 + c where c is a constant > complex # and z is another seems to be wrong. Isn't it that initially z = 0? > z=0 and c=pixel is the Mandelbrot set z=pixel and c=a constant for the picture is a Julia set Mandelbrot set is a map (c=pixel) of those Julia sets for which with z=0 the iterations do not diverge. The Mandelbrot set helps you find your way around in choosing which c and going to be interesting as Julia set parameters. Interesting meaning 'I like the MSet here next to or near this value of c' Jay - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 00:54:38 -0500 (EST) From: Jim Muth Subject: Re: (fractint) literary fractals At 06:56 PM 2/19/98 -0800, you wrote: >Hi >Does anyone know of any works of fiction in which fractals play a a part? >Off the top of my head, I know of The Ghost from the Grand Banks, Pier >Anthony's *Mode* Series. Also, they are tantalingly mentioned in passing in >Infinity's Shore. I am interested in references to fractals specifically, >not just to chaos in general. >Thank you. > One of the best novels I've read that has its basis in mathematics is "The Inverted World" by Christopher Priest. It was written in the early 1970's before the full richness of fractals was realized, but the idea is there, and it's well worth a read if you can find a copy. Jim Muth jamth@mindspring.com - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 19:17:59 +1300 From: "Morgan L. Owens" Subject: Re: (fractint) literary fractals At 18:56 19/02/98 -0800, Peter Jakubowicz wrote: >Hi >Does anyone know of any works of fiction in which fractals play a a part? >Thank you. > Among those works in which fractals actually "play a part" rather than just being mentioned 'cos it's trendy to do so... Greg Egan has a short story called "The Infinite Assassin" (originally in INTERZONE #48, Jan.91; also appears in his _Axiomatic_ anthology) in which the Cantor Dust plays a crucial role. Egan's a bloody good writer - about the only one I know who does modern mathematics justice. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 04:48:16 EST From: MAksoy@aol.com Subject: Re: (fractint) literary fractals In a message dated 98-02-19 19:01:05 EST, Peter Jakubowicz wrote: >>Hi >>Does anyone know of any works of fiction in which fractals play a a part? >> ...I am interested in references to fractals specifically, >>not just to chaos in general. >>Thank you. >> There is the play Arcadia by Tom Stoppard (1993) which deals extensively with fractals and chaos. Its main character is Thomasina, a Victorian child prodigy who constructs her own "Geometry of Irregular Forms" (shades of Mandelbrot!). Of course, she keeps her own mathematical journal ( "I, Thomasina Coverly, have found a truly wonderful method whereby all the forms of nature must give up their numerical secrets and draw themselves through number alone."). There is an entire website on this play and how it relates to fractal geometry: Chaos, Fractals and Arcadia at http://math.bu.edu/DYSYS/arcadia/index.html. Mark Aksoy http://members.aol.com/maksoy/vistfrac/vistfrac.htm - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 08:59:22 -0500 (EST) From: Ian Kaplan Subject: Re: (fractint) literary fractals MAksoy wrote: > > In a message dated 98-02-19 19:01:05 EST, Peter Jakubowicz wrote: > > >>Hi > >>Does anyone know of any works of fiction in which fractals play a a part? > >> ...I am interested in references to fractals specifically, > >>not just to chaos in general. > >>Thank you. > >> > > There is the play Arcadia by Tom Stoppard (1993) which deals extensively with > fractals and chaos. Its main character is Thomasina, a Victorian child > prodigy who constructs her own "Geometry of Irregular Forms" (shades of > Mandelbrot!). Of course, she keeps her own mathematical journal ( "I, > Thomasina Coverly, have found a truly wonderful method whereby all the forms > of nature must give up their numerical secrets and draw themselves through > number alone."). Just wanted to add that Arcadia is probably one of the best works for the stage in the last decade or so, a really gorgeous play, and in my opinion the best of Stoppard's considerable body of work... Most of the play is a kind of hands-on philosophical wrestling with the notion of chaos and how it fits into our old ways of thinking. Another of its main characters is a modern maths grad student, doing a Ph. D. in chaos. While it loses a lot by being read instead of seen, it's stlil well worth reading. If anyone cares, I'll post the publishing info when I get home today; I think it's from Ballard... - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 09:43:21 EST From: RENRAD1@aol.com Subject: Re: (fractint) literary fractals In a message dated 98-02-19 19:01:05 EST, pfjakub@earthlink.net writes: << Does anyone know of any works of fiction in which fractals play a a part? Fractals are also an element in Alan Dean Foster's book "Cyber Way" "Yes. Julia sets within a Mandelbrot Set, the likes of which nobody's ever seen before. All extrapolated from the yellow grains of the Kettrick painting. The radioactive yellow. " "The fact that the sand that was used happened to be radioactive has nothing to do with this." "Perhaps not, but it makes for an interesting coincidence, don't you think? |more... RENRAD1 - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 09:46:54 EST From: RNelson472@aol.com Subject: Re: (fractint) literary fractals Thanks for the explanations. I have concentrated on the Mandlebrot set and have not investigated the extensive Julia sets. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: 20 Feb 1998 22:10:41 +0100 From: Brederlow Subject: (fractint) Aproximating the M-Set with geometrical shapes The M-Set consists of the large Apple shaped part and many conbected circles (and many other smaller apples and circles and maybe other stuff). What I now wonder is, if anyone knows how to construct a good aproximation of the mset by gemoetrical shapes. I have a formula for the main apple part and the circle that lies in front of it (on the negative x axis). Are there formulas for other circles or is there a method to calculate them? The formulas don't have to be a perfect match for some part of the M-Set, but every point the formula claims to be in the M-Set MUST be in the M-Set. May the Source be with you. Mrvn - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 17:05:18 EST From: Nature102@aol.com Subject: Re: (fractint) literary fractals In a message dated 98-02-20 09:50:58 EST, RNelson472@aol.com writes: << Thanks for the explanations. I have concentrated on the Mandlebrot set and have not investigated the extensive Julia sets. >> Hey, the Mandelbrot's more than big enough to keep you occupied for a long time without bothering with Julias or anything else. :-P I was looking for QBasic programs the other day for no apparent reason, and I saw one that drew the "Mandelbroth" set. I found that incredibly funny for no apparent reason. :-P - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 15:17:31 -0700 From: Rich Thomson Subject: Re: (fractint) Aproximating the M-Set with geometrical shapes In article , Brederlow writes: > I have a formula for the main apple part and the circle that lies in > front of it (on the negative x axis). Are there formulas for other > circles or is there a method to calculate them? You can read "A Parameterization of the Period 3 Component of the Mandelbrot Set" . This gives the closed forms of the period 3 components and explains the general method you could use to derive higher period components, but this method quickly gets out of control fast in terms of the equations. You might be able to get something meaningful out of Mathematica for the higher orders. - -- Rich Thomson rthomson@ptc.com - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 16:19:02 -0600 From: "Paul N. Lee" Subject: Re: (fractint) literary fractals Peter Jakubowicz wrote: > > Does anyone know of any works of fiction in which fractals > play a a part? Off the top of my head, I know of The Ghost > from the Grand Banks, > "In principle the Mandelbrot Set could have been discovered as soon as men learned to count. But even if they never grew tired, and never made a mistake, all the human beings who have ever existed would not have sufficed to do the elementary arithmetic required to produce a Mandelbrot Set of quite modest magnification." - Arthur C. Clarke, The Ghost from the Grand Banks > > Pier Anthony's *Mode* Series. Also, they are tantalingly > mentioned in passing in Infinity's Shore. I am interested > in references to fractals specifically, not just to chaos > in general. > The science fiction story "To the Valley of the Sea Horses" in the book KEYS TO INFINITY published by Wiley. The following is taken from "Chapter 6. To the Valley of the Sea Horses": Near the corner stood a slightly soiled sign marked "Fractal Tours" in bright red. Beneath the sign was a PC on a long battered table usually used for city garage sales, and on its monitor was a beautiful image. A geometrical pattern of some kind, it mesmerized Herman. An excited young black man was talking about the pattern. Four other people sat on rusty, dented folding chairs listening to the lecture. Herman sat on an empty chair and began to listen. The young man pointed at the monitor. "That beautiful image, ladies and gentlemen, is a Mandelbrot set." Herman noticed that the man had said the last two words with a certain degree of reverence, almost awe. The young man went on to explain that the shape was called a fractal because of its geometric intricacy. Amazingly, it was produced by a very simple formula, z = z**2 + c. Also, (I not positive) but I thought Issac Asimov also mentioned fractals in one of his stories. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 15:14:17 -0800 From: "Jay Hill" Subject: Re: (fractint) Aproximating the M-Set with geometrical shapes Mrvn wrote: > The M-Set consists of the large Apple shaped part and many connected > circles (and many other smaller apples and circles and maybe other > stuff). > What I now wonder is, if anyone knows how to construct a good > approximation of the M-Set by geometrical shapes. > I have a formula for the main apple part and the circle that lies in > front of it (on the negative x axis). Are there formulas for other > circles or is there a method to calculate them? Yes, but it is not simple. There are exact formula for some components and approximate formula for the rest. Is this what you are trying to make? http://www.geocities.com/CapeCanaveral/Lab/3825/Hulahoop.gif > The formulas don't have to be a perfect match for some part of the > M-Set, but every point the formula claims to be in the M-Set MUST be > in the M-Set. Now this looks like your after a test of a point to determine what color it is, that is different and more difficult. Again, there are exact tests for some... ask Dr. J. http://home.san.rr.com/jayrhill/FotN/FotN51.html And approximate tests could be developed for the rest. Is this what you are trying to make? http://www.geocities.com/CapeCanaveral/Lab/3825/Mandelbr.gif > May the Source be with you. Sources not compile on my machine. May the Executable be with you. - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 16:23:29 -0700 From: Rich Thomson Subject: Re: (fractint) Aproximating the M-Set with geometrical shapes In article <882565B1.00784637.00@NOTESGW.NOSC.MIL> , "Jay Hill" writes: > and approximate formula for the rest. Is this what you are trying to make? > > http://www.geocities.com/CapeCanaveral/Lab/3825/Hulahoop.gif Interesting image Jay; what's its origin? - -- Rich Thomson rthomson@ptc.com - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 18:05:49 -0600 (CST) From: pjcarlsn@ix.netcom.com (Paul and/or Joyce Carlson) Subject: (fractint) Newton Mset Formula This formula is a Newton's Method solution of a 4th-order polynomial using my 3D Stalks rendering method. The image it produces is different from most Newton fractals and is quite pretty, I think. The reason for the convergence test for early exit is so that a background color can be used that is different from the "inside" color so the little Mandy can be seen. The colors in the par produce an image with a solid black background (which brings out the colors in the stalks), but if you would like to see which areas converge to which roots, change colors 244, 244, 246 and 247 in the colormap. The roots of this polynomial are: c, -c, sqrt(-1/(c*c)), -sqrt(-1/(c*c)) I've called this formula Newt2_Stalks_Mset because it's the second in a series of eight polynomials that I use for Newton Msets. I'll be posting the others from time to time. Paul Carlson frm:Newt2_Stalks_Mset {; Copyright (c) Paul W. Carlson, 1998 ;**************************************************** ; Newton's solution of (w*w-c*c)*(w*w+1/(c*c))=0 ; Always use floating point math and outside=summ. ; ; real(p1) = a factor controlling the size of the stalks ; imag(p1) not used ; real(p2) = number of color ranges ; imag(p2) = number of colors in a range ; real(p3) = value of |w| for bailout ; imag(p3) = iterations count for early exit ; ; Note that the equation variable is w, not z. Always ; initialize z to zero. ;**************************************************** c = pixel csqd = c * c icsqd = 1 / csqd sc = sqrt(-icsqd) cr1 = real(c), ci1 = imag(c) cr2 = real(sc), ci2 = imag(sc) a = csqd - icsqd w = sqrt(a / 6) ; value where F''(w) = 0 z = 0 bailout = 0 iter = 0 stalk_width = real(p1) range_num = 0 num_ranges = real(p2) colors_in_range = imag(p2) index_factor = (colors_in_range - 1) / stalk_width: ; w = (3 * (w^4) - a * (w^2) + 1) / (4 * (w^3) - 2 * a * w) ; wr = real(w), wi = imag(w) IF (abs(wr) <= abs(wi)) min_dist = abs(wr) ELSE min_dist = abs(wi) ENDIF ; IF (min_dist < stalk_width && iter > 0) z = index_factor * min_dist + range_num * colors_in_range + 1 bailout = 1 ENDIF ;**************************************************** ; If we're no longer looking for stalks, check if ; we've converged on a root. ;**************************************************** IF (iter > imag(p3)) IF (((wr-cr1) * (wr-cr1) + (wi-ci1) * (wi-ci1)) < 0.00001) z = 244 bailout = 1 ELSEIF (((wr+cr1) * (wr+cr1) + (wi+ci1) * (wi+ci1)) < 0.00001) z = 245 bailout = 1 ELSEIF (((wr+cr2) * (wr+cr2) + (wi+ci2) * (wi+ci2)) < 0.00001) z = 246 bailout = 1 ELSEIF (((wr-cr2) * (wr-cr2) + (wi-ci2) * (wi-ci2)) < 0.00001) z = 247 bailout = 1 ENDIF ENDIF ; range_num = range_num + 1 IF (range_num == num_ranges) range_num = 0 ENDIF ; iter = iter + 1 z = z - iter ; (bailout == 0) && |w| < real(p3) } n2smset1 {; Copyright (c) Paul W. Carlson, 1998 reset=1960 type=formula formulafile=n2stlks.frm formulaname=newt2_stalks_mset passes=1 center-mag=+0.53134409219500000/+0.84715435134499990/4508.94\ 1/1/122 params=0.1/0/8/30/10000/100 float=y maxiter=2000 inside=255 outside=summ colors=000z0f<28>O08z88<28>O00zW0<28>c40zz0<28>aG00zR<28>0C40z\ z<28>0CCGGz<28>00OfOz<28>I0K000<12>000zzz } - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Fri, 20 Feb 1998 17:12:04 -0800 From: "Jay Hill" Subject: Re: (fractint) Aproximating the M-Set with geometrical shapes Rich Thomson wrote: >In article <882565B1.00784637.00@NOTESGW.NOSC.MIL> , "Jay Hill" writes: >> and approximate formula for the rest. Is this what you are trying to make? >> >> http://www.geocities.com/CapeCanaveral/Lab/3825/Hulahoop.gif >Interesting image Jay; what's its origin? > Rich Thomson > rthomson@ptc.com It is a by-product of the 1993 evaluate the area of the Mandelbrot craze. I can display points on boundaries of all (but one*) midgets up to period 16 and buds on each to much higher period. The accuracy is better than 12 digits, usually more like 16. We are talking about 430809 components and some days of computing. >:-( Limits are basically the 80 bit floats on the Intel chips. The particular image ( Hulahoop.gif) does not display all of these. See my article, Area of Mandelbrot Set Components and Clusters. http://www.geocities.com/CapeCanaveral/Lab/3825/Period-Area-16.html * All but one means I found all but one midget. There is still one out there somewhere. If I find it, it may spell the doom of Dr. J ;-) so I leave well enough alone, for now. There is a cool story by Vernor Vinge titled True Names, 1976 (or so). In it folk are on the web in virtual reality suits. If ones true identity becomes known, then that person is at the mercy of others. Example, a cyber criminal's name is found and he is blackmailed in the real world. One of my favorite novelettes Or how about the Niven (I think he is the author) story called the 9 billion names of God. In this story, the monks of Tibet are writing down all the names of God. When they complete the task, the universe will end. The story has two IBM computer geeks install main frames at the temple which should dispose of the job in weeks. As the two geeks are returning to the valleys below the mountains the guy on the lead donkey looks back at his associate who is looking up. And... well, go read it. Jay - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 21 Feb 1998 00:07:56 -0500 (EST) From: ao950@freenet.carleton.ca (Paul Derbyshire) Subject: Re: (fractint) fractal hardware engine Won't the serial port I/O speed become a serious bottleneck? It must be orders of magnitude slower than a PC bus. I wouldn't think all the megahertz in the world would make much difference if your FPU communicated to the CPU/memory at only 57600 baud... - -- .*. Friendship, companionship, love, and having fun are the reasons for -() < life. All else; sex, money, fame, etc.; are just to get/express these. `*' Send any and all mail with attachments to the hotmail address please. Paul Derbyshire ao950@freenet.carleton.ca pgd73@hotmail.com - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 21 Feb 1998 07:26:03 -0600 From: Janet Preslar Subject: (fractint) Fractals needed -- Among the Stars Fellow Fractal Artists =97 I am looking for fractal images that (loosely or literally) depict stars,= moons, constellations, planets, etc. to be used in conjunction with a ballet performance the last weekend in March. In my real life I direct a company= of young ballet dancers which will present their annual spring show that wee= kend. This year's show, titled "Among the Stars" is comprised of seven abstract ballets which are inspired by the afore-mentioned heavenly bodies. I woul= d like to use fractal images, transferred to photographic slides, which will be projected onto the cyclorama (backdrop) during and between the ballets. I invite all of you wonderful fractal artists to submit images that fall = into this celestial category for consideration. There is no limit on the numbe= r of images you may submit -- nor do we have an exact number we are looking fo= r. The only suggestion I have is that, with rare exception, images with a black background will work the best for this project. The deadline for submissi= on is Friday, March 13, 1998. Due to hardware and software limitations I may not be able to recreate yo= ur fractal from parameter files, so please submit all images to be considere= d by sending me their URL's. Any size, from thumbnail to 1024 x 768 will be ok= for initial consideration. If you do not have access to a website, please ema= il me for further instructions at preslar@memphisonline.com Images best suited to the ballets will be chosen from those submitted. On= ce an image is chosen the fractal artist will then need to temporarily post on = their web site (or snail mail) a large (my test image was 3072 x 2304) resoluti= on file that I can then have transferred to slide film. While there is no money in the budget for compensation to the artists, I = will certainly credit your work in the program. I will also host, indefinitely= , a gallery of the images on my web site with links to your galleries or web = pages. If you have specific questions please contact me directly. I hope this project will both inspire you artistically and help introduce= more of the general public to our Wonderful World of Fractals. Have fun! Janet Preslar mailto:preslar@memphisonline.com http://www.ParkeNet.org/jp - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 21 Feb 1998 10:24:38 -0500 From: "Jason Hine" Subject: Re: (fractint) Aproximating the M-Set with geometrical shapes Mrvn Wrote: >What I now wonder is, if anyone knows how to construct a good >aproximation of the mset by gemoetrical shapes. Dr. Frank Jones, a lecturing professor at Colorado State University in Ft. Collins, claims that the entire M could (theoretically) be constructed with nothing more than a piece of string, a thumbtack or two, and a pencil. Your question has prompted me to add a page describing Dr. Jones' ideas to my home page - the method is best explained with pictures. I will try to get that done by this afternoon, but no promises! Jason Hine - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ Date: Sat, 21 Feb 1998 18:11:12 -0600 From: "Justin A. Kolodziej" <4wg7kolodzie@vms.csd.mu.edu> Subject: (fractint) Re: Mail delivery failed: returning message to sender Well, is it? :-) Justin K. - -- Justin A. Kolodziej I sense a great disturbance in the Source. Justin Kolodziej is 4wg7kolodzie@vms.csd.mu.edu Marquette University is www.mu.edu - - - ------------------------------------------------------------ Thanks for using Fractint, The Fractals and Fractint Discussion List Post Message: fractint@xmission.com Get Commands: majordomo@xmission.com "help" Administrator: twegner@phoenix.net Unsubscribe: majordomo@xmission.com "unsubscribe fractint" ------------------------------ End of fractint-digest V1 #114 ******************************