Visualizing Numbers with WebGl
July 11, 2013 4:17 AM Subscribe
How To Fold a Julia Fractal. A beautiful interactive introduction to complex numbers, fractals and waves. (Requires WebGL). To Infinity And Beyond is a similar introduction to calculus.
Try reloading it if you get a webgl error. I got one the first time I went to the page -- also, wait for the whole page to load before clicking anything.
posted by empath at 4:29 AM on July 11, 2013
posted by empath at 4:29 AM on July 11, 2013
Seems like a nice idea, but not working with Firefox 21.0 on Linux. The graphics appear briefly, then are replaced by a blank space. WebGL works here, the water demo linked from this page looks fine (although not as smooth as native non-browser GL).
posted by crazy_yeti at 4:33 AM on July 11, 2013
posted by crazy_yeti at 4:33 AM on July 11, 2013
Try with Chrome? That's what I viewed it on. It's actually really worthwhile for the math content, if not for the technology demo.
posted by empath at 4:37 AM on July 11, 2013
posted by empath at 4:37 AM on July 11, 2013
I really like Mandelbrot's ideas. I like his last TED Talk.
There's no practical depth to those ideas right now. NO ONE HAS EVER MADE A TECHNOLOGY, OR A REASONABLE PREDICTION, OR A REASONABLE SCIENTIFIC EXPLANATION using fractals.
It's an intellectual toy.
But many good theories began as toys. So I don't judge.
posted by twoleftfeet at 4:40 AM on July 11, 2013
There's no practical depth to those ideas right now. NO ONE HAS EVER MADE A TECHNOLOGY, OR A REASONABLE PREDICTION, OR A REASONABLE SCIENTIFIC EXPLANATION using fractals.
It's an intellectual toy.
But many good theories began as toys. So I don't judge.
posted by twoleftfeet at 4:40 AM on July 11, 2013
NO ONE HAS EVER MADE A TECHNOLOGY, OR A REASONABLE PREDICTION, OR A REASONABLE SCIENTIFIC EXPLANATION using fractals.
This is flat wrong. Get up on the wrong side of the bed this morning?
posted by empath at 4:44 AM on July 11, 2013 [3 favorites]
This is flat wrong. Get up on the wrong side of the bed this morning?
posted by empath at 4:44 AM on July 11, 2013 [3 favorites]
I had to reload this (Chrome OS X) the first time I saw it
It really is worth going to some trouble to find a browser that it works in. It made the elements of this part of math clear to me in a way that nothing else has.
posted by thelonius at 4:52 AM on July 11, 2013 [1 favorite]
It really is worth going to some trouble to find a browser that it works in. It made the elements of this part of math clear to me in a way that nothing else has.
posted by thelonius at 4:52 AM on July 11, 2013 [1 favorite]
Get up on the wrong side of the bed this morning?
No. Those aren't real "applications". There aren't useful consequences of "fractal theory". There really isn't a "fractal theory". You can formulate fractal dimension using Hausdorff-Besicovich dimension, and it's fine as a descriptive value (which is where those so-called "applications" arise) but it has no depth, mathematically, and has very little intellectual value on that level. Yet.
Many mathematical points of view seemed equally useless in their early days, and it's possible that fractals could become just as un-useless.
Right now though, it's shallow thought.
posted by twoleftfeet at 4:53 AM on July 11, 2013 [1 favorite]
No. Those aren't real "applications". There aren't useful consequences of "fractal theory". There really isn't a "fractal theory". You can formulate fractal dimension using Hausdorff-Besicovich dimension, and it's fine as a descriptive value (which is where those so-called "applications" arise) but it has no depth, mathematically, and has very little intellectual value on that level. Yet.
Many mathematical points of view seemed equally useless in their early days, and it's possible that fractals could become just as un-useless.
Right now though, it's shallow thought.
posted by twoleftfeet at 4:53 AM on July 11, 2013 [1 favorite]
You seem to be confused about what mathematics is, twoleftfeet.
posted by thelonius at 4:55 AM on July 11, 2013 [1 favorite]
posted by thelonius at 4:55 AM on July 11, 2013 [1 favorite]
There's no practical depth to those ideas right now. NO ONE HAS EVER MADE A TECHNOLOGY, OR A REASONABLE PREDICTION, OR A REASONABLE SCIENTIFIC EXPLANATION using fractals.
Mitchell Feigenbaum used fractals back in the 90s to make better maps:
The Atlas of the World was the result of an ambitious five-year effort that brought together designers, mathematicians, cartographers, editors, and digital technology. The maps were created using a new projection based on fractal geometry called Optimal Conformal Projection, developed for Hammond by Mitchell Feigenbaum, a noted physicist known for his work in chaos theory. The collaboration led to the creation of the most accurate maps yet published.
posted by Blazecock Pileon at 5:05 AM on July 11, 2013 [1 favorite]
Mitchell Feigenbaum used fractals back in the 90s to make better maps:
The Atlas of the World was the result of an ambitious five-year effort that brought together designers, mathematicians, cartographers, editors, and digital technology. The maps were created using a new projection based on fractal geometry called Optimal Conformal Projection, developed for Hammond by Mitchell Feigenbaum, a noted physicist known for his work in chaos theory. The collaboration led to the creation of the most accurate maps yet published.
posted by Blazecock Pileon at 5:05 AM on July 11, 2013 [1 favorite]
I shouldn't have blurted out what I blurted out.
But tell me two or three good theorems in "fractal theory" and I will concede the point. (I know of just one.)
posted by twoleftfeet at 5:09 AM on July 11, 2013
But tell me two or three good theorems in "fractal theory" and I will concede the point. (I know of just one.)
posted by twoleftfeet at 5:09 AM on July 11, 2013
Or hey, we could not have an argument that has nothing to do with the post.
posted by empath at 5:15 AM on July 11, 2013
posted by empath at 5:15 AM on July 11, 2013
Mod note: Comment deleted. Twoleftfeet, if you can't view the site, maybe just check out a different post instead of manufacturing an argument here.
posted by taz (staff) at 5:30 AM on July 11, 2013 [1 favorite]
posted by taz (staff) at 5:30 AM on July 11, 2013 [1 favorite]
Having watched the first animation (about spirals and angles and 360 not dividing by 1/sqrt(2), I have just two thoughts...
1) What the holy crap did I watch?
2) Ow, my head hurts.
On a tangential subject ( from empath's "flat wrong" link) - how did I not know about Digital Sundials?
Cue obligatory "Here, take my money" type comment...
posted by sodium lights the horizon at 5:45 AM on July 11, 2013 [1 favorite]
1) What the holy crap did I watch?
2) Ow, my head hurts.
On a tangential subject ( from empath's "flat wrong" link) - how did I not know about Digital Sundials?
Cue obligatory "Here, take my money" type comment...
posted by sodium lights the horizon at 5:45 AM on July 11, 2013 [1 favorite]
None of this was ever mentioned! There are so many beautiful crossovers that just never get talked about, and it's really quite terrible.
Yeah, doing 2D geometry in the complex plane is so much easier than doing it in R2 that I don't understand why you would do it any other way.
posted by Elementary Penguin at 5:51 AM on July 11, 2013
Yeah, doing 2D geometry in the complex plane is so much easier than doing it in R2 that I don't understand why you would do it any other way.
posted by Elementary Penguin at 5:51 AM on July 11, 2013
Yeah, doing 2D geometry in the complex plane is so much easier than doing it in R2 that I don't understand why you would do it any other way.
Because you are an elementary or middle school student?
posted by DU at 5:53 AM on July 11, 2013 [1 favorite]
Because you are an elementary or middle school student?
posted by DU at 5:53 AM on July 11, 2013 [1 favorite]
They actually teach middle school students about complex numbers nowadays. Just not well.
posted by Elementary Penguin at 5:55 AM on July 11, 2013
posted by Elementary Penguin at 5:55 AM on July 11, 2013
What a lovely math explanation. And a hell of a lot of work. I wonder if the Javascript was hand written or exported from Mathematica or something? The author Steven Wittens has many other lovely things on his site.
If you want to skip the math and just play with pretty fractals, here's a Mandlebrot/Julia explorer that runs in a browser (using canvas).
posted by Nelson at 8:43 AM on July 11, 2013
If you want to skip the math and just play with pretty fractals, here's a Mandlebrot/Julia explorer that runs in a browser (using canvas).
posted by Nelson at 8:43 AM on July 11, 2013
I wonder if the Javascript was hand written or exported from Mathematica or something? The author Steven Wittens has many other lovely things on his site.
See the author's post Making MathBox.
posted by Blazecock Pileon at 9:22 AM on July 11, 2013
See the author's post Making MathBox.
posted by Blazecock Pileon at 9:22 AM on July 11, 2013
"Because our brains don't do more than 3D natively, we can glimpse only slices of the hyperspaces necessary to put them on full display.
The closest I ever got to really understanding hyperdimensionality was on a very powerful trip having consumed a good 1/4 oz of psilocybin mushrooms back in 1998.
The ability to walk up stairs and intuit space folding around itself so I could literally "FEEL" wrapping around in a sort of mobius/escher staircase where I ended up where I began if I continued walking, and I understood it as a warping of the space via a higher dimension.
Of course I didn't visualize it, or perceive it in a literal sense, but it was a very strong feeling. Intuition doesn't even describe it. It was a physiological sense in the body. It was stronger than a mental picture. Perhaps even stronger than an abstract conception of a number. Because it was so outside of ordinary experience, of course, it was strange and unreal. Yet, I could see how this is almost the way we perceive in 3D. It's just that since we are accustomed to it, it's not "strange", but we are oriented and sense in a very physical way beyond mere vision to be attuned to this dimensionality.
There are ways to intuit beyond. I admit, that I only was capable of feeling this in 4 dimensions.
I do wonder of John Lilly's experiences, he claims to have gone into many many dimensions via the ketamine/iso-tank route.
Regardless, I think there is something with psychedelics that open the doors to higher dimensions (not some "god/spirit/alien plane", but a mathematical conception beyond our ordinary ken, and I think Mathematicians would do themselves a great benefit by working with them to contemplate higher dimensional orders, and other mathematical oddities outside the normal realm of thought).
My friend thought hippies/"drugees" (as he so politely calls them) like fractals because of the coloring of most fractals, and I informed him that it was much more than the colors...
posted by symbioid at 9:23 AM on July 11, 2013 [2 favorites]
The closest I ever got to really understanding hyperdimensionality was on a very powerful trip having consumed a good 1/4 oz of psilocybin mushrooms back in 1998.
The ability to walk up stairs and intuit space folding around itself so I could literally "FEEL" wrapping around in a sort of mobius/escher staircase where I ended up where I began if I continued walking, and I understood it as a warping of the space via a higher dimension.
Of course I didn't visualize it, or perceive it in a literal sense, but it was a very strong feeling. Intuition doesn't even describe it. It was a physiological sense in the body. It was stronger than a mental picture. Perhaps even stronger than an abstract conception of a number. Because it was so outside of ordinary experience, of course, it was strange and unreal. Yet, I could see how this is almost the way we perceive in 3D. It's just that since we are accustomed to it, it's not "strange", but we are oriented and sense in a very physical way beyond mere vision to be attuned to this dimensionality.
There are ways to intuit beyond. I admit, that I only was capable of feeling this in 4 dimensions.
I do wonder of John Lilly's experiences, he claims to have gone into many many dimensions via the ketamine/iso-tank route.
Regardless, I think there is something with psychedelics that open the doors to higher dimensions (not some "god/spirit/alien plane", but a mathematical conception beyond our ordinary ken, and I think Mathematicians would do themselves a great benefit by working with them to contemplate higher dimensional orders, and other mathematical oddities outside the normal realm of thought).
My friend thought hippies/"drugees" (as he so politely calls them) like fractals because of the coloring of most fractals, and I informed him that it was much more than the colors...
posted by symbioid at 9:23 AM on July 11, 2013 [2 favorites]
My friend thought hippies/"drugees" (as he so politely calls them) like fractals because of the coloring of most fractals, and I informed him that it was much more than the colors...
I don't know. The appeal of fractals among that set may be broader than just the colors, but I'm not convinced that it's deeper.
For what it's worth, though, one of my favorite things when I'm working through a math text is to revisit the double-starred problems that initially stumped me in a given chapter after a toke or two and watch them reliably fall before me. I don't really think that happens because the space of thoughts I can think expands or anything, but just that alternative formulations and spatial metaphors seem to come more easily, and at least one of them ends up being more useful than how I had originally framed the problem in my head.
But as far as intuiting four dimensions goes, I have to admit that this app has done more for me than any psychoactive substance I'm aware of.
posted by invitapriore at 10:28 AM on July 11, 2013 [1 favorite]
I don't know. The appeal of fractals among that set may be broader than just the colors, but I'm not convinced that it's deeper.
For what it's worth, though, one of my favorite things when I'm working through a math text is to revisit the double-starred problems that initially stumped me in a given chapter after a toke or two and watch them reliably fall before me. I don't really think that happens because the space of thoughts I can think expands or anything, but just that alternative formulations and spatial metaphors seem to come more easily, and at least one of them ends up being more useful than how I had originally framed the problem in my head.
But as far as intuiting four dimensions goes, I have to admit that this app has done more for me than any psychoactive substance I'm aware of.
posted by invitapriore at 10:28 AM on July 11, 2013 [1 favorite]
Oh, and I've been looking for a reason to bring this up for a while, because it needs to be said: I fucking. hate. the word "fractal." Everytime I say it or hear it said I feel like I'm choking on a Ninja Turtles lunchbox.
posted by invitapriore at 10:30 AM on July 11, 2013 [2 favorites]
posted by invitapriore at 10:30 AM on July 11, 2013 [2 favorites]
I really liked the linked post on fractals and found the graphical illustrations to be great, so I wandered around a few other posts on Wittens' site and also found them worth looking at.
Until I found one called "Storms and Teacups" which is his pontification on STEM gender/feminism issues.
And I read it, and I got very angry and disappointed.
So, you know, go ahead and appreciate the lovely tech and mathematical explanations, but do realize that, like Orson Scott Card's books, they're created by someone who is disgustingly high on privilege and entitlement and is smashingly proud to proclaim that he's totally lacking in empathy.
posted by seanmpuckett at 10:51 AM on July 11, 2013 [2 favorites]
Until I found one called "Storms and Teacups" which is his pontification on STEM gender/feminism issues.
And I read it, and I got very angry and disappointed.
So, you know, go ahead and appreciate the lovely tech and mathematical explanations, but do realize that, like Orson Scott Card's books, they're created by someone who is disgustingly high on privilege and entitlement and is smashingly proud to proclaim that he's totally lacking in empathy.
posted by seanmpuckett at 10:51 AM on July 11, 2013 [2 favorites]
Myself, I thought the article was chock full of smarm. But I think I'm just in a snarky mood, never mind me.
posted by JHarris at 12:59 PM on July 11, 2013
posted by JHarris at 12:59 PM on July 11, 2013
seanmpuckett:
"So, you know, go ahead and appreciate the lovely tech and mathematical explanations, but do realize that, like Orson Scott Card's books, they're created by someone who is disgustingly high on privilege and entitlement and is smashingly proud to proclaim that he's totally lacking in empathy."
Hahah wow. "Disgustingly high on privilege and entitlement"
Here's what really happened. I wrote one post. That post got lauded by men and women across the open source community, including people who organize conferences and run open source projects:
https://twitter.com/unconed/status/315875994110152705
It got spread far and wide, and received the majority of its traffic from private shares (50K+ hits, last time I checked). I also received tons of stories thanking me for writing that post, from people who constantly feel marginalized.
Only a few places universally hated it. Metafilter was one of them, and programmersbeingdicks still sends me daily traffic. (http://www.metafilter.com/126376) Of course, I was unable to defend myself here, because the thread got closed.
Other criticism involved calling it "laced with casual misogyny", "white male privilege", "the most sophisticated form of the virus yet" and other handy tropes that shut down discussion, that is, exactly what the post predicted would happen. The irony was apparently lost on the social justice crowd.
Remarkably however, despite the fact that people such as yourself universally called it garbage, not a single person has bothered to refute its points. They just threw feminist straw men at me.
And remarkably, a post that contains 70+ links to people who disagree is apparently biased, but an entire network of armchair feminists who all repeat each other, link to each other's blogs, and declare themselves the sole authority on gender issues, is not.
Oh and by the way, I'm gay, so I find your comparison to Orson Scott Card pretty offensive on a personal level. I wrote a single well-researched post with full citations, and apparently that makes me a persona non-grata of Card's level. The things I talked about are things that directly affect me, my work and my industry. I'm not sponsoring legislation that oppresses people, I'm just pointing out facts, calling for people to make up their own minds.
How's the weather up there on your high horse?
posted by unconed0 at 3:59 PM on July 12, 2013
"So, you know, go ahead and appreciate the lovely tech and mathematical explanations, but do realize that, like Orson Scott Card's books, they're created by someone who is disgustingly high on privilege and entitlement and is smashingly proud to proclaim that he's totally lacking in empathy."
Hahah wow. "Disgustingly high on privilege and entitlement"
Here's what really happened. I wrote one post. That post got lauded by men and women across the open source community, including people who organize conferences and run open source projects:
https://twitter.com/unconed/status/315875994110152705
It got spread far and wide, and received the majority of its traffic from private shares (50K+ hits, last time I checked). I also received tons of stories thanking me for writing that post, from people who constantly feel marginalized.
Only a few places universally hated it. Metafilter was one of them, and programmersbeingdicks still sends me daily traffic. (http://www.metafilter.com/126376) Of course, I was unable to defend myself here, because the thread got closed.
Other criticism involved calling it "laced with casual misogyny", "white male privilege", "the most sophisticated form of the virus yet" and other handy tropes that shut down discussion, that is, exactly what the post predicted would happen. The irony was apparently lost on the social justice crowd.
Remarkably however, despite the fact that people such as yourself universally called it garbage, not a single person has bothered to refute its points. They just threw feminist straw men at me.
And remarkably, a post that contains 70+ links to people who disagree is apparently biased, but an entire network of armchair feminists who all repeat each other, link to each other's blogs, and declare themselves the sole authority on gender issues, is not.
Oh and by the way, I'm gay, so I find your comparison to Orson Scott Card pretty offensive on a personal level. I wrote a single well-researched post with full citations, and apparently that makes me a persona non-grata of Card's level. The things I talked about are things that directly affect me, my work and my industry. I'm not sponsoring legislation that oppresses people, I'm just pointing out facts, calling for people to make up their own minds.
How's the weather up there on your high horse?
posted by unconed0 at 3:59 PM on July 12, 2013
unconed0, you wrote one long series of superficial statements, backed with anecdotes and opinion overwhelmingly more than evidence, from your own point of view. They're your opinions, and I largely disagree with them.
I don't hate you. I don't care to take the time to pick each of your ideas apart to show you where your assumptions weaken your case, cause you to contradict yourself, or make you sound like a self-aggrandizing asshole. I do suggest you consider social and cultural issues, when you choose to write about them, with the same open mindedness and willingness to consider all available evidence that scientists pride themselves on applying to their professional work. The casual heterocentrism you've experienced as a gay man may help you achieve this critical attitude more readily than a straight man might.
As one small example, you conveniently overlook Jezebel calling out racism and cultural appropriation in a fashion shoot in favour of calling women on policing each other's appearance. Jezebel's writing and editorial staff include several women of colour, and intersectionality of racism with sexism is one area that particular site tends to get right more often than not.
As the old fish said to the young fish, how's the water?
posted by thatdawnperson at 8:58 AM on July 13, 2013
I don't hate you. I don't care to take the time to pick each of your ideas apart to show you where your assumptions weaken your case, cause you to contradict yourself, or make you sound like a self-aggrandizing asshole. I do suggest you consider social and cultural issues, when you choose to write about them, with the same open mindedness and willingness to consider all available evidence that scientists pride themselves on applying to their professional work. The casual heterocentrism you've experienced as a gay man may help you achieve this critical attitude more readily than a straight man might.
As one small example, you conveniently overlook Jezebel calling out racism and cultural appropriation in a fashion shoot in favour of calling women on policing each other's appearance. Jezebel's writing and editorial staff include several women of colour, and intersectionality of racism with sexism is one area that particular site tends to get right more often than not.
As the old fish said to the young fish, how's the water?
posted by thatdawnperson at 8:58 AM on July 13, 2013
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I don't know why. I've been supporting WebGL for years.
posted by twoleftfeet at 4:23 AM on July 11, 2013