ThinkBlog

[What follows is something I just typed up to send to the Philosophy Club at GTC, since I’m the secretary and I’m into that sort of stuff, especially late in the morning. Enjoy.]

Hello, all!

What follows are some explanations of fractals &c.

1. Chaos Theory
2. Fractals
2a. Recursion
3. Quaternionic Fractals

1. Chaos Theory. Here’s a small introduction, very readable:
   http://www.webslave.dircon.co.uk/alife/chaos.html
From the introductory paragraph, “Chaos theory is about explaining apparent disorder in a very ordered way. Chaos theory states that things are not really random, just complex. Many apparently random events can be represented by a simple computation which, when iterated, produce complex results.” (To “iterate” is to perform some act again–in this case, to re-run the computation.)

2. Fractals. Here is a gloriously excellent FAQ (”Frequently Asked Questions” list) explaining everything you ever wanted to know and more.
   http://fractals.iut.u-bordeaux1.fr/f-art-faq/faq03.html
From the first question, “What is a fractal?”, we have the following: “A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole.”

2a. Recursion. In computer science, this kind of thing is heavily tied to recursion, which was also addressed cursorily in our discussion on randomness. Recursion is a means of fully describing a function/process by means of itself–that is, if a function calls itself and goes deeper and deeper into itself, it is said to be “recursive.” I said all that to say this, a very geeky comp.sci/chaos joke: “In order to fully understand recursion one must first understand recursion.” Chris E. may be the only one even chuckling at this point, but hey, it’s 3AM, I’m on a roll!

There are MANY megabytes’ worth of beautiful fractals, human-viewable, in the following online gallery, which if nothing else makes for a collection of trippy wallpapers for your Windows desktop:
   http://home.wtal.de/spiriteye/fractal/

3. Quaternionic Fractals. These are fractals which, when iterated, morph through time. That is to say, if we take a three-dimensional slice (think about that one) of a four-dimensional fractal, we can see it as it is in a particular point in time. An introductory page is here:
   http://info.lboro.ac.uk/departments/ma/gallery/quat/
However, that page is dry and not exactly the most concretely informative for the uninitiate. Here’s another page, that mentions quat.fractals and art (God’s and ours):
   http://www-uk.hpl.hp.com/brims/art/gallery/quat/

The cool stuff I saved for last. The following link is a site where there are 3D stereographic fractals! Okay, for those of you who don’t know what stereographic art is all about, you basically have to step back from your screen, cross your eyes until the one on the left and the one on the right combine in the middle, then focus on that middle picture. (This is NOT Magic Eye stuff, this is easier than that jazz–if you can cross your eyes, you can [probably] see this!)
   http://www.physcip.uni-stuttgart.de/phy11733/stereo_e.html

And the link that I first found this stuff on was a Java-based viewer of a few different fractals from the Julia set. Great fun if you have a Java-capable browser (IM or email me if it doesn’t show up/load and I’ll tell you how to install Java on your machine). See there at the bottom where it says “Fractal set” and has a series of arrows pointing left and right? Try clicking the single right arrow once and letting it re-draw. See the change in the fractal image? That’s what it means to take a 3D-slice of a 4D fractal!
   http://equinox.planet-d.net/java/fractals/

::deep breath:: Ahhh, the best part of waking up is metaphysics in your web browser!

[What follows is something I just typed up to send to the Philosophy Club at GTC, since I’m the secretary and I’m into that sort of stuff, especially late in the morning. Enjoy.]

Hello, all!

What follows are some explanations of fractals &c.

1. Chaos Theory
2. Fractals
2a. Recursion
3. Quaternionic Fractals

1. Chaos Theory. Here’s a small introduction, very readable:
   http://www.webslave.dircon.co.uk/alife/chaos.html
From the introductory paragraph, “Chaos theory is about explaining apparent disorder in a very ordered way. Chaos theory states that things are not really random, just complex. Many apparently random events can be represented by a simple computation which, when iterated, produce complex results.” (To “iterate” is to perform some act again–in this case, to re-run the computation.)

2. Fractals. Here is a gloriously excellent FAQ (”Frequently Asked Questions” list) explaining everything you ever wanted to know and more.
   http://fractals.iut.u-bordeaux1.fr/f-art-faq/faq03.html
From the first question, “What is a fractal?”, we have the following: “A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole.”

2a. Recursion. In computer science, this kind of thing is heavily tied to recursion, which was also addressed cursorily in our discussion on randomness. Recursion is a means of fully describing a function/process by means of itself–that is, if a function calls itself and goes deeper and deeper into itself, it is said to be “recursive.” I said all that to say this, a very geeky comp.sci/chaos joke: “In order to fully understand recursion one must first understand recursion.” Chris E. may be the only one even chuckling at this point, but hey, it’s 3AM, I’m on a roll!

There are MANY megabytes’ worth of beautiful fractals, human-viewable, in the following online gallery, which if nothing else makes for a collection of trippy wallpapers for your Windows desktop:
   http://home.wtal.de/spiriteye/fractal/

3. Quaternionic Fractals. These are fractals which, when iterated, morph through time. That is to say, if we take a three-dimensional slice (think about that one) of a four-dimensional fractal, we can see it as it is in a particular point in time. An introductory page is here:
   http://info.lboro.ac.uk/departments/ma/gallery/quat/
However, that page is dry and not exactly the most concretely informative for the uninitiate. Here’s another page, that mentions quat.fractals and art (God’s and ours):
   http://www-uk.hpl.hp.com/brims/art/gallery/quat/

The cool stuff I saved for last. The following link is a site where there are 3D stereographic fractals! Okay, for those of you who don’t know what stereographic art is all about, you basically have to step back from your screen, cross your eyes until the one on the left and the one on the right combine in the middle, then focus on that middle picture. (This is NOT Magic Eye stuff, this is easier than that jazz–if you can cross your eyes, you can [probably] see this!)
   http://www.physcip.uni-stuttgart.de/phy11733/stereo_e.html

And the link that I first found this stuff on was a Java-based viewer of a few different fractals from the Julia set. Great fun if you have a Java-capable browser (IM or email me if it doesn’t show up/load and I’ll tell you how to install Java on your machine). See there at the bottom where it says “Fractal set” and has a series of arrows pointing left and right? Try clicking the single right arrow once and letting it re-draw. See the change in the fractal image? That’s what it means to take a 3D-slice of a 4D fractal!
   http://equinox.planet-d.net/java/fractals/

::deep breath:: Ahhh, the best part of waking up is metaphysics in your web browser!