Cool Math Pictures

If you search arnold tongues in google images, you might be surprised to discover that the lovely photo at left is not the first, or even the most eye-popping image that is retrieved.

Instead (and no offense to Mr. Schwartzenegger's unique performance), I hope you would be as mesmerized as I am by a boldly-colored panel that looks like it could have been taken from off the cover of some fantastic retro-science-fiction magazine...


...You stare in awed horror at an apocalyptic sky dotted with swooping UFOs, while an army of alien invaders advances over the barren desert landscape...

Last night, Rob came into the kitchen as I was cleaning up after a chocolate-chip-cookie fest and said...with typical nonchalance..."Hey, ya wanna see somethin' cool?" He's actually been showing me quite a few interesting pictures these past few weeks. Mostly ideas for homework projects to use in the computational physics course he teaches at the college, the images have ranged from the somewhat more familiar Mandelbrot set...

...to last night's unveiling of the Arnold tongues (two above), a bifurcation diagram of the circle map (doesn't this look like it could be found at a modern art museum)...

...and a comparatively simple--but sublime and elegant--logistic map...

Maybe because it's a bunch of lines rendered in (my favorite) black-and-white, this last graphic immediately sent my mind spinning off into a creative frenzy. This looks like something I might draw...or rather...it looks like something I wish I'd drawn...or even better, I thought, "I could use these graphics as inspiration for my next Masterpiece!!!" 

Now, I've still got an inspiration or two bouncing around in my subconscious, and I did fool around with some sketches this afternoon (which I'm sorry to say I won't show unless I finish), but what's occurred to me since that initial spark is the truly incredible thing about these graphics is that they were generated through mathematical functions...just sets of parameters run through a computer code a b'jillion times until these surreal and beautiful patterns emerged from the chaos. A butterfly flaps its wings in Paris and...

Once we got past memorizing multiplication tables in elementary school, whatever aptitude I might have had for mathematics faded away into oblivion. There are all sorts of ideas about why people get scared away from math. In spite of the current trendiness of "nerd" culture, it unfortunately remains a popular subject to hate (on an episode of Star Trek Enterprise I watched last night, Hoshi even used the phrase "calculus equations" to represent her frustrated feelings toward the impossibly difficult language she was trying to decode), and I'm ashamed to say I was chief among the haters. The grades on my senior-year high school report card were admirable...well, except for that D in trig/pre-calc (I don't remember a single thing from that class except that logarithms were impossible and I had a crush on a boy that sat nearby...not that HE cared). I dropped out of the only college math class I ever tried to take at the U of U, and I can't tell you how overjoyed I was when I found out I wouldn't have to take ANY math to graduate from Juilliard.

In the intervening years, I've begun to appreciate all that I've missed by not giving math a chance. Now (even though I still squint and wrinkle my forehead whenever a page of numbers presents itself to me), I sometimes even fantasize about going back and refreshing my algebra well enough to approach calculus with an open mind. Just think of all the cool graphics I might eventually be able to create!

(an image of the Chirikov Standard Map taken from Wikipedia)