Wednesday, November 21, 2007

1.506 591 77 ± 0.000 000 08. Duh!


I can't believe how often this stupid blog sends me scurrying off to Google so I can keep up.

Bad enough that I've never heard of this "Black Adder" show that Hugh Laurie used to be in and that everyone's suddenly talking about. But now Kaye, in one of the many comments on Michelle's excellent "House" post from last night, compares our blog to something called a Mandelbrot set. Huh? That sounds like actual smart shit and, like so many of brilliant Kaye's brilliant allusions, sailed way over my head.

So I looked it up. I'll save you the trouble. Part of the definition, from Wikipedia: "Mathematically, the Mandelbrot set can be defined as the set of complex c-values for which the orbit of 0 under iteration of the complex quadratic polynomial x2 + c remains bounded."

Of course. Man, I can't believe I spaced that stuff out.

That bit of mathematical expression in the headline of this post is an estimate of the area of a Mandelbrot set. And the photo above, lifted from Wikipedia, is described as an "initial image of a Mandelbrot set zoom sequence with continuously coloured environment."

Cool. What all this has to do with the price of rice or the allure of M&M I haven't quite figured out. Must do further calculations.

11 comments:

freda said...

Duh, I second that.

I'm glad I'm not the only one who never heard of black adder. This blog is truly enlightening.

kateco said...

Hey -- here's the deal -- the groovy goodness of the Mandlebrot Set is its fractal nature which means it is self-similar at all scales, so the tiniest little corner of its map contains "copies" of the map itself. You can "zoom into" the map infinitely and find swirly copies of the original funky shape as in the image with this post.

Now the reason I said that M&M had mandlebrotty goodness is that it is a little address that contains all the internet goodness -- "zoom into" M&M and there's SEO and super good UGC and Britney and Liveblogging and utter and slideshows and House all of the internet (perhaps less some porn and jihadi blogs). M&M is the interwebs man.

Okay, okay so Val got it ... then again, we're geeks in love.

kateco said...

and you *must* see Black Adder.

Mark said...

I'm about half-frightened that that starts to make sense to me, but also fully flattered on behalf of M&M. That was a really nice geeky compliment.

Thanks Kaye.

Val said...

Mark, you need to take a trip down the rabbit-hole. Here are some fractal-generating programs that implement the Mandelbrot set and many more, all with some kind of zoom capability. I was completely obsessed with this stuff in the late 80s thru mid-90s.

For Mac OS X:

GNU XaoS, with a Mac OS X version, is fast and easy -- hold down the mouse button to zoom in, right-mouse-button (Control-click on Mac?) and you fly in or out.

Fractal Domains, a full-featured viewer and editor that gives you all sorts of control over the rendering.

Fracture, a shareware screensaver. Look, Ma, no hands!

For Windows:

ChaosPro, a full-featured renderer ported from the Amiga. Also maintains a page listing a bunch of other fractal generators with comparisons to ChaosPro, as well as nice theory and tutorial pages.

Fractal Explorer looks to be from Russia, is free, has no Help file but should be fairtly simple to use. Implements lots of formulae including a 3D landscape generator.

Visions of Chaos generates creates a ton of images -- fractals like the Mandelbrot and Julia sets, as well as lots of cellular automata, L-systems and more. Trialware.

More info:

Here's a page listing a wide variety of different sorts of fractals. I'm rather partial to the L-systems....

Enjoy!

kateco said...

oh yeah -- i forgot to say mandlebrot zoom ins are also psychedelic. just like M&M.

Mark said...

Who bogarted my downlow.txt file?

Thanks guys, this is cool.

freda said...

Who bogarted my downlow.txt file?

OK, back to google

kateco said...

hahaha

Michelle said...

I love your fractalness of M&M comment Kaye. I think it's so cool that the blog makes you feel that way. but then, it does me too --- even more so thanks to the comments from you and val. Thanks for the great link cloud val. Very cool.

Who needs a compound? We have the interwebs.

Ethan said...

The best things about fractals is they are very useful to describe graph structures (such as social networks). N-dimensional data-sets become much more interesting when you can calculate dimensionality as a means of ascribing cuts and weights to the graph and its edges. Its quite arbitrary somewhat (how do you represent n-dimensions in 2d space), but fun. Oh how I miss grad-scool.