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 Toroidia And Other Toroidal Graphics
Oolong
Posted: Jun 3 2005, 12:12 PM


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Any thoughts on my interactive applet Toroidia, the 3D equivalent, or indeed the related stills (the top two) on my Mathematical Still Images page - or on toroidal geometry in general...?

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DRobinson
Posted: Jun 17 2005, 04:38 PM


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Hi Fergus - I'd emailed you some months back about a processing port I'd made of the Toroidia applet (apologies for never replying to your reply, but here we are, no time like the present) - recently I added a frame blending capability, which radically alters the quality of the images, makes them a lot more psychedelic-looking and not so far from some of the trippy animations generated by Scott Draves' Electric Sheep project ... but with the big difference that Toroidia's graphics are being generated in realtime while the fractal flame code used in Electric Sheep takes 10 min. or more to complete a single frame and has to save them to the hard-drive before you get to see the results. Granted, they're larger/higher rez images, and of course the flame algorithm is quite different from drawing a 4-D torus (it uses Michael Barnsley's 'iterated function systems' / affine transformations) ... but the results are qualitatively similar, at least in some respects, and equally delicious, eye-candy-wise. Toroidia bites off a much smaller subspace of the impossible universe of all possible images than the subspace that Electric Sheep dips into (oo, funny: 'sheep dip'!) and after several days' immersion I'm noticing a certain redundancy & predictability in Toroidia's output ... the flip side of the same coin is I'm developing a better sense of where to go (slider settings) to find the prettiest specimens.

BTW, I'd be very interested in hearing your thoughts about why Toroidia's graphics should be so extraordinarily entrancing to the human eye-and-brain. To me it's a fascinating question but it's difficult for me to even begin to articulate anything like a satisfactory answer. (Mumbles something barely audible about resonances, beat frequencies, Pythagorean number theory ...)

Anyway, my suggestion for the next iteration of Toroidia: add frame blending! You'll be glad you did! I can send you the processing /Java code with the frame-blending bits if you like ...

&c/ D.
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Oolong
Posted: Jun 17 2005, 08:13 PM


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Hi D,

Thanks for that! Do please send me the source. Is the applet online anywhere? I've been looking at Processing a bit, and thinking that maybe I should port all my applets to it - it seems like there are quite a lot of fun things it should be easier to do that way, and it might also help me to reach a wider audience. Worth doing? What do you think? How easy did you find it to port Toroidia?

Incidentally, one very simple change I've been meaning to make to Toroidia, which I know will make a pretty big difference to the output (it's incorporated into the 3D version) is to include the option of drawing ellipses rather than spirals. If you're playing around with it anyway, fancy building that in?

I came across the recursive flame fractals used in the Electric Sheep project just a few weeks ago, and I was astonished that I hadn't seen them before. Great stuff! Haven't installed the screensaver itself on my home computer yet though.

I am also very interested in the question of why Toroidia is so entrancing. The same question, I think, applies to all my other applets, and the answer is surely much the same. I reckon you're on the more-or-less the right lines. Our brains are very very big on pattern recognition, symmetry-spotting. I'm inclined to think that this is <em>the</em> fundamental fact of our aesthetic sense, tempered by aversions and sentimental attachments, and complicated by emotional resonances (which are themselves almost certainly tied up with pattern recognition... I've seen it argued that our emotional responses to music are related to some isomorphism between the music itself and the functioning of our brains, an idea I'm sure is worth pursuing).

How we achieve pattern recognition is in turn most likely tied up with Fourier transforms, or something similar, these being a very natural way of achieving what our brains do.

Any thoughts?

- f.

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harry
Posted: Jun 18 2005, 12:56 PM


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Oolomg,
I hope that you do pursue working with the eliptical pattern. I find that my eye is always attracted to things which have a portion of the eliptical cone end incorporated into the shape. Recently I noticed that I was intrigued with the marvelous profile that a certain man had. One day while seated behind him I discovered that view from the side, from his forehead to the back of his neck was a slice of the eliptical cone end. The Volkswagon (the old ones) were shaped exactly like the narrow end of an elipse stood on end. My eye responds to anything which captures those curves. The 1953 Lincoln Continental was most pleasing to the eye for it was a small rectangle on top of a longer larger one.
Philosophically, the Urantia Book describes Paradise as an enormous island that is eliptically shaped. In that book much is said about being "encircuited" with God's pattern. In my mind I picture a moving dot repeating a circle and then departing from that path and launching out somewhat but only so far, soon returning to its circular path. In life I notice that I have values which constitute the core of my life. Nevertheless, from time I venture forth away from those values, but eventually return to my core values. Am I babbling? Yes, but my mind does consider such things. I was always intrigued with Classical Music, much because it was art imitating life. The better symphonies start with the suggestion of discord, and express the magnitude of the discord to the point of expressing grief at its own disharmony. However, eventually a faint feeble melody crops up briefly, only to be drowned out again by the clamour of discord. Eventually the larger body of instruments catches on and builds upon the glimmer of harmony and having discovered it, embraces it in harmonous recital. This is perfectly illlustrated in Violin Concerto in D, Op.35 by Tchaikovsky. Oolong, in that your interactive visuals illustate such principles, they are marvelous techno-art in my appraisal because they represent the cycles that we all go through only to return to our core values. My, my, I really am verbose this morning. Cheers. tongue.gif
harry


--------------------
Harry Hebert
Bible Cocoons
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DRobinson
Posted: Jun 18 2005, 07:50 PM


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Okay, I've zipped up the processing files and sent them winging their way to toroids@fergusmurray.co.uk & for good measure to fcm@oolong.co.uk as well, I hope one or the other makes it. They'll unzip to their own folder. Note that I'm assuming a Windows PC; included is a launch.bat file to open the applet in full-screen mode, otherwise it's index.html in the browser.

About processing, by all means try porting your applets over! Processing has recently-ish (as of April) gone beta, which means that alpha processing code doesn't run in the authoring environment but will of course continue to work as Java applets, since that's what they are ("processing extends BApplet" is how they put it, I believe). The good news is that the beta release includes support for openGL/jogl, albeit still a bit spottily ... implying that fast fullscreen graphics is distinctly more tangibly closer to actuality. Myself, I've not yet made the transition to the processing beta; too many irons, too many fires ...

For hints on converting older alpha code to processing beta (e.g. loop() is replaced by draw(), etc.) see http://processing.org/faq/changes.html

I think you'll find porting your applets is no problem, only took me an hour or so and I'm nothing near to a confident/competent programmer. Because it's just an extension of the BApplet class, processing (they say) allows reusing any Java bits, importing whatever Java libraries/classes, basically anything you've done can be embedded/wrapped in the processing frame. (Or so I gather from hanging around the processing discussion forums; btw the forums' search interface is very helpful.) But note that the default is 'float' for decimal numbers; to use doubles (which, processing's authors opine, aren't worth the extra CPU cycles for all the difference it makes on the screen) you'll have to explicitly declare them as such. Also you'll want to excise any GUI bits that make use of AWT; if I recall processing uses just a little bit of AWT, mostly it's up to you to roll your own GUI-ness. (For an amazing example of bells & whistles, cf. http://processing.andre-michelle.com/cytris/ .)

Re: frame blending -- I swiped the code from somebody else's processing demo (View Source Rules!) and I've zipped up a slightly modded version of this as well, it's a flock of 'boids' (well dart shapes actually -- and you *really* don't want to know how long it took me to work out the 3-D maths to get them drawing themselves properly!) that follow spiral paths around a (what else?) torus, heh, leaving pretty fading rainbow trails. Hit any key to toggle B/W backgrounds, spacebar to turn blending on/off. (Please excuse the sloppiness of the code -- it's not like I'm any kind of real programmer, the lad's just scratchin' his own itch.)

I'm very interested in getting Toroidia running full screen at decent frame rates; there's this little .exe file I found that can turn any applet into a Windows screensaver. (Once I get tired of counting Electric Sheep ... but I suppose getting tired is what counting sheep is *for*, mm?) -- Anyway here's hoping you can make some progress on this! I'm supremely looking forward to being able to fully exploit the graphics capabilities of these tremendously powerful, amazingly cheap machines we've got these days. (Though I have the impression that the closer it gets to realizing this, the harder it becomes to distinguish processing code from straight openGL ...)

As for the aesthetical, metaphysical, neuro- and psychological resonances of higher dimensional tori: yes I fully agree that pattern recognition is key. One perhaps doesn't hear so much about it these days, but there was a lot of talk in the cybernetics period (c. 1945-65) about self-exciting oscillatory nerve cell assemblies in the brain as a possible mechanism for most of what brains seem to do. And I was reading Diderot's dialogue "D'Alembert's Dream" (c. 1769) just the other day, there's this character named Diderot who expounds upon 'sensitive vibrating strings' ...

Quote: "A sensitive vibrating string oscillates and resonates a long time after one has plucked it. It's this oscillation, this sort of inevitable resonance, which holds the present object, while our understanding is busy with the quality which is appropriate to it. But vibrating strings have yet another property it's one that makes other strings quiver. And thus the first idea recalls a second, and these two a third, then all three a fourth, and so it goes, without our being able to set a limit to the ideas which are aroused and linked in a philosopher who meditates or who listens to himself in silence and darkness."

(Online text: http://www.mala.bc.ca/~johnstoi/diderot/conversation.htm .)

Surprisingly few contemporary neural researchers have been paying attention to the frequency domain, but Walter J. Freeman's work on chaos and entrainment in the rabbit olfactory bulb is definitely worth a look-see. (For a good overview of this work see: http://sulcus.berkeley.edu/FLM/MS/Physio.Percept.html .)

Hmmmm, starting to look like a lot of words. How about I give it a rest and get back to you anon?

-- Anon.
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DRobinson
Posted: Jun 18 2005, 08:04 PM


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Foo! Both emails bounced -- Fergus, what's a valid email address for you? (send it to nnvsnu_at_yahoo_dot_com if you like) -- D.
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harry
Posted: Jun 19 2005, 12:39 AM


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Oolong,
I've been studying the Toroidia , 3D equivalent, with the opening "dots" format. It seems that in the center is the mother of it all and that after a while something resembling a verticle pipe of dots takes shape and slowly expands without losing its shape until it gets lost into the child dots. Sort of like a creator getting out and hanging with the creation. Just another thought. The Dr. can help while I'm just a geek wannabe looking in and feeling that I should say something intelligent. biggrin.gif

Harry


--------------------
Harry Hebert
Bible Cocoons
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DRobinson
Posted: Jun 20 2005, 05:04 AM


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Oolong will this take? Fergus, I tried sending the zipped files to the gmail address you sent but it was bounced back to me undelivered ... maybe gmail doesn't want to play nice with yahoo mail. Anyway it's weird. Is it possible to upload files to this forum?

D.
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Oolong
Posted: Jun 20 2005, 10:41 AM


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Yup, you can upload files here - you'll need to make an account first I guess. I wonder why Gmail's not taking them - perhaps because they include potentially dangerous file types? Gmail is a bit arsey about this sort of thing...

Cheers!

- f.
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DRobinson
Posted: Jun 20 2005, 05:21 PM


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Okay I'm a member, but I don't see that there's any provision to upload files. Maybe I'm missing something ...
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Oolong
Posted: Jun 20 2005, 05:57 PM


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Do you not have a 'File Attachments' box when you reply to a message?
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DRobinson
Posted: Jun 21 2005, 03:42 AM


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Not that I can see ...
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Oolong
Posted: Jun 21 2005, 01:50 PM


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Oh, bugger... quite right, I hadn't tested to see what things look like for ordinary members - looks like you need to be an admin to upload anything, regardless of the settings for allowing uploads from members. I'm hoping there's a way around this, but I'll have to get back to it later...
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DRobinson
Posted: Jun 21 2005, 10:07 PM


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Glad it wasn't just me ... meanwhile here are a couple of links to things of potential interest / relevance. The first is to Joost Rekveld, a Dutch experimental film-maker, who's written a nice non-technical essay on symmetry & harmonics -- http://www.lumen.nu/rekveld/texts.html .

The other's just some more eye-candy -- http://imagesavant.com/ ... pretty pretty though.

Oh and here's a third, Rudy Rucker's reaction-diffusion (real number domain) cellular automata program, CAPOW -- http://www.cs.sjsu.edu/faculty/rucker/capow/intro.html (well nothing very toroidal about it, though one could splice the top and bottom together, and the left and right sides, making a donut ...)

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DRobinson
Posted: Jun 25 2005, 03:11 AM


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Found this processing demo (and sourcecode) that features frameblending, as you can see it's pretty straightforward to implement and the results are lovely ...

LemurP5

Ta.
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