I've tried to generate the WOW ftod image and don't seem to get the same image as shown on the ftod page. What is even weirder is that at SF5 it generates one image and at SF6 it generates another. I'm using use Fractint 20.04 under XP. I placed the images on the web for comparison. At SF5: http://rogerkaufman.mystarband.net/WOW.SF5.gif At SF6: http://rogerkaufman.mystarband.net/WOW.SF6.gif -- No virus found in this outgoing message. Checked by AVG Anti-Virus. Version: 7.0.289 / Virus Database: 265.4.2 - Release Date: 11/24/2004
On Thursday 25 November 2004 7:02 am, Vortex Swirling wrote:
I've tried to generate the WOW ftod image and don't seem to get the same image as shown on the ftod page. What is even weirder is that at SF5 it generates one image and at SF6 it generates another. I'm using use Fractint 20.04 under XP.
I placed the images on the web for comparison.
Hmm. Although I can't reproduce the images you have, I do see a difference between the image generated with Fractint and Xfractint. Jonathan
I downloaded VS' images and opened them in Fractint. Opening VS' SF5 image in SF5 and changing from SF5 to SF6 does change the image to his SF6 image, as does opening the SF5 image in SF5 and then zooming in a bit (to get the same 'resolution' as the SF6 image). On looking at the pars taken from VS' images, they appear to differ from the FOTD image only in having 'params=16/0' instead of params=100/0. When both images are opened and the first parameter is set to 100, you get the FOTD image. Don't know why two images that look different produce the same image when the same single change is made, which is a more interesting question. Mike Just in case we've got different fractint.cfg, here are mine: SF5 ,SuperVGA/VESA Autodetect , 0, 0, 0, 0, 27, 640, 480,256,Works with most SuperVGA SF6 ,SuperVGA/VESA Autodetect , 0, 0, 0, 0, 27, 800, 600,256,Works with most SuperVGA Jonathan Osuch wrote:
On Thursday 25 November 2004 7:02 am, Vortex Swirling wrote:
I've tried to generate the WOW ftod image and don't seem to get the same image as shown on the ftod page. What is even weirder is that at SF5 it generates one image and at SF6 it generates another. I'm using use Fractint 20.04 under XP.
I placed the images on the web for comparison.
Hmm. Although I can't reproduce the images you have, I do see a difference between the image generated with Fractint and Xfractint.
Jonathan
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On Thu, 25 Nov 2004, Vortex Swirling wrote:
I've tried to generate the WOW ftod image and don't seem to get the same image as shown on the ftod page. What is even weirder is that at SF5 it generates one image and at SF6 it generates another. I'm using use Fractint 20.04 under XP. (...) According to 20.03, you are chanjing the polynomial degree from 100 to 16, but I can't explain the difference between SF6 and SF8. I get the one with SF8 when I use your parameters.
All the recent developments with orbital rendering in Fractint - for which I say well done, beautiful, some pars from me to follow soon - also makes me think of another fractal type composed of curved lines, namely Klienian Groups, e.g. as at http://klein.math.okstate.edu/IndrasPearls/ It would be great to have these incorporated into Fractint. One suggestion - another dream of mine - would be to enlarge the L-systems possibilities to enable L-systems lines themselves to be curved, e.g. according to various user-input equations for curved lines such as the circle and parts of it, spirals, parabolae, hyperbolae, etc. THIS would in tself be a huge increase in the capabilities of Fractint's L-systems programming, whether or not it led to Kleinian groups being added to Fractint. Tony Hanmer
Tony Hanmer <a.hanmer@gmail.com> wrote:
All the recent developments with orbital rendering in Fractint - for which I say well done, beautiful, some pars from me to follow soon - also makes me think of another fractal type composed of curved lines, namely Klienian Groups, e.g. as at http://klein.math.okstate.edu/IndrasPearls/
Great link! Thankyou, Tony.
It would be great to have these incorporated into Fractint. One suggestion - another dream of mine - would be to enlarge the L-systems possibilities to enable L-systems lines themselves to be curved, e.g. according to various user-input equations for curved lines such as the circle and parts of it, spirals, parabolae, hyperbolae, etc.
Yes! That would be nice. You seem to be the local expert on L-systems: might you answer a question about them? Are they, in general, the iteration of geometrical shapes, thus not necessarily made up only of line segments, nor necessarily only at integer divisions of 360 degrees orientation? I think you were implying in some of your previous posts that maybe the Mandelbrot set could be theoretically rendered as an L-system. I suspect that it can, but obviously being able to plot curved shapes would help achieve that. Also, being able to use more complicated formulas to specify the base shape's size and direction would help. Perhaps a parser to user-specify these attributes? ---Hiram
Well, I'd not go so far as to call myself an L-systems expert, though I've played with the type a lot over the last 4 years. As I understand them, L-systems can be made of geometrical shapes which are themselves made of straight line segments; and by using the second method of programming them in Fractint - d instead of f, Angles explicitly specified, etc. - any angle, including non-integer ones, is possible. (Please someone correct me if I'm wrong.) But regarding the M-set, I checked out its shape a while ago as merely a set of 1 cardioid and infinite circles. Turns out that they aren't quite circles after all, and they aren't even off circularity by the same amount in each case. So that complicates things. Also, the M-set and current L-systems programming seem to be SO different from each other that I despair of the latter ever rendering the former - at least, as L-systems are used in Fractint at the moment. I think that adding curves to L-systems would not help this, though it would still obviously hugely extend the possibilities in other ways. Tony Hanmer
At 04:48 PM 12/1/2004, you wrote:
Tony Hanmer <a.hanmer@gmail.com> wrote:
All the recent developments with orbital rendering in Fractint - for which I say well done, beautiful, some pars from me to follow soon - also makes me think of another fractal type composed of curved lines, namely Klienian Groups, e.g. as at http://klein.math.okstate.edu/IndrasPearls/
Great link! Thankyou, Tony.
Jos Leys has programmed Klienian Groups into some private UF formulas of his, both 2D and 3D versions. They are quite impressive. http://users.pandora.be/jos.leys/ Ken...
Wow, such a quick response to my request for Kleinian groups in Fractint! Something up your sleeve, hmmm, Gerald? Much appreciated, and fascinating to play with. I see what you mean about its limitations, but the variety of images it makes available (again, due to passes=o) is astounding. (Are they all K-groups?) Feels like an early Christmas present, especially with the fascinating Buddahbrot thrown in! That =o option is really getting a lot of attention. Thank you very much one and all. Tony Hanmer
Tony Hanmer wrote:
Wow, such a quick response to my request for Kleinian groups in Fractint!
The quick response came from the fact the formula was already there in slightly different form to use Fractint's orbit window (accessed by <ctrl>+<o>). I only had to rip out some (now unnecessary) loop logic - and voila!
Something up your sleeve, hmmm, Gerald? Much appreciated, and fascinating to play with. I see what you mean about its limitations, but the variety of images it makes available (again, due to passes=o) is astounding. (Are they all K-groups?) [...]
I just implemented what's described here (PDF file!)... http://klein.math.okstate.edu/IndrasPearls/tools/twogen.pdf ...simplyfying it to the parabolic case (that's what the "Parab" means in the formula name). As I understand it, these could be described as (generalized) circle inversions, basically taking (four) circles touching one another and looking for the set of points remaining invariant under all possible inversions. In the "KleinGroupTest" par changing p2 from (1.95, 0.04) to (2.0, 0.0) produces such an Apollonian Gasket. But since circles (and lines) can be represented by operations with Hermitean matrices - and circle inversions by Moebius transformations... http://klein.math.okstate.edu/~wrightd/INDRA/Hcircles/ http://klein.math.okstate.edu/~wrightd/INDRA/MobiusonCircles/ ...one can abandon the notion of tangential circles and start to tweak the Moebius transformations to deform the resulting invariant point set. I have other formulas for this (PDF file!): http://klein.math.okstate.edu/IndrasPearls/tools/jorgensen.pdf and some of those: http://klein.math.okstate.edu/IndrasPearls/limitsets/puncture.html but the more complicated the process, the more defective the pictures produced by the naive random method I am using. About two years ago Morgan L. Owens came up with an idea to implement Kleinian Groups as escape time fractals, but this applies to circle inversions, not the more general transformations. ...and as Ken Childress has pointed out, Jos Leys gallery of Kleinian Group images is a "must-see". Regards, Gerald
Tony Hanmer wrote:
All the recent developments with orbital rendering in Fractint - for which I say well done, beautiful, some pars from me to follow soon - also makes me think of another fractal type composed of curved lines, namely Klienian Groups, e.g. as at http://klein.math.okstate.edu/IndrasPearls/ It would be great to have these incorporated into Fractint.
Such as the example below? Sadly it suffers from the same shortcomings as inverse iteration of Julias - the orbit points don't cover the whole fractal evenly, which calls for a way to check if a pixel is visited too often and switch to one of the other transformations accordingly (as can be done for the Julia_inverse type). Ah, yes - don't wait for the picture to finish, it takes a long time... Regards, Gerald ----------------- Begin .par (and frm:) -------------------- KleinGroupTest {;Kleinian Group for passes=o ; reset=2004 type=formula formulafile=fractint.frm formulaname=KleinianParab passes=o center-mag=0/0/0.9/1/-90/3.88578058618804789e-016 params=2/0/1.95/0.04/1/1234 float=y maxiter=600 inside=255 periodicity=0 orbitdelay=100 colors=@gamma1.map } frm:KleinianParab {;after "Indra's Pearls" ;by Mumford, Series und Wright ;Two-generator-group, commutator trace fixed to -2 ;------------------------------------- ;p1 : Trace a ;p2 : Trace b ;p3r: Trace ab choice (0|1) ;p3i: Seed for random number generator ;------------------------------------- ; srand(imag(p3)) ; rt = sqrt(sqr(p1*p2)-(sqr(p1)+sqr(p2))*4) IF (p3) tab = (p1*p2-rt)/2 ELSE tab = (p1*p2+rt)/2 ENDIF rt = (tab-2)*p2/((p2+(0,2))*tab-2*p1) ; a14 = p1/2 a2 = (p1*tab-2*p2+(0,4))/((2*tab+4)*rt) a3 = (p1*tab-2*p2-(0,4))*rt/(2*tab-4) ; b23 = p2/2 b1 = b23-(0,1) b4 = b23+(0,1) ; last = floor(imag(rand)*4) z = pixel: IF (last == 0) IF (rand > 0.67) z = (a14*z+a2)/(a3*z+a14) ELSEIF (rand > 0.33) z = (b1*z+b23)/(b23*z+b4) last = 1 ELSE z = (b4*z-b23)/(b1-b23*z) last = 3 ENDIF ELSEIF (last == 1) IF (rand > 0.67) z = (a14*z+a2)/(a3*z+a14) last = 0 ELSEIF (rand > 0.33) z = (b1*z+b23)/(b23*z+b4) ELSE z = (a14*z-a2)/(a14-a3*z) last = 2 ENDIF ELSEIF (last == 2) IF (rand > 0.67) z = (b1*z+b23)/(b23*z+b4) last = 1 ELSEIF (rand > 0.33) z = (a14*z-a2)/(a14-a3*z) ELSE z = (b4*z-b23)/(b1-b23*z) last = 3 ENDIF ELSE IF (rand > 0.67) z = (a14*z+a2)/(a3*z+a14) last = 0 ELSEIF (rand > 0.33) z = (a14*z-a2)/(a14-a3*z) last = 2 ELSE z = (b4*z-b23)/(b1-b23*z) ENDIF ENDIF last == last } ----------------- End .par (and frm:) --------------------
participants (8)
-
brewhaha＠freenet.edmonton.ab.ca -
Gerald K. Dobiasovsky -
Hiram Berry -
Jonathan Osuch -
Ken Childress -
Mike Traynor -
Tony Hanmer -
Vortex Swirling