I must admit that I am no good at math. I look at mathematical equations and I might as well be looking at a blank piece of paper. Me + Math = No Good. I was, actually, no good in school in general. All the more reason to highly encourage my children to do a whole heck of a lot better than I did. On top of that, with having two daughters I want to make sure that if they have any interest in the math or sciences that I will bend over backwards to make sure that they have the encouragement they need to excel (here and here are articles about girls and science & math). Even if I’m no good at either of them.
Lately, we have been listening to a play list that I have named “Geek Rock?” on the mp3 player in the car. On that list I have some They Might Be Giants, Barenaked Ladies, Leonard Nimoy singing “The Ballad of Bilbo Baggins”, Paul & Storm and Jonathan Coulton. Some tunes may not be appropriate for the kids but I don’t focus too much on that and The Elder Extroverted One seems to be alright with it. We discuss words you shouldn’t say and move on. Well, one song in particular has caught the EEO’s attention and has gotten stuck in her head. Which has led to some mathematical explorations in which I am in no way equipped to guide her. So, we are just exploring it together and we’ll find out where it leads us. The particular song is Jonathan Coulton’s “Mandelbrot Set”.
The other night as I was hanging out with the Elder Extroverted One during the night-time routine (stories, backrubs etc.) and she blurts out a line from the song, “Mandelbrot’s in heaven, at least he will be when he’s dead” and says that the song is stuck in her head. So, that led us to Wikipedia for a search on what exactly, if anything, a Mandelbrot Set is and whether it exists. Turns out it is real and it is very mathematical like. From wikipedia:
In mathematics the Mandelbrot set, named after Benoît Mandelbrot, is a set of points in the complex plane, the boundary of which forms a fractal. Mathematically the Mandelbrot set can be defined as the set of complex values of c for which the orbit of 0 under iteration of the complex quadratic polynomial zn+1 = zn2 + c remains bounded. That is, a complex number, c, is in the Mandelbrot set if, when starting with z0 = 0 and applying the iteration repeatedly, the absolute value of zn never exceeds a certain number (that number depends on c) however large n gets.
Um…er…okay? Hey wait! I know fractals! Those are cool patterns and stuff! The Elder Extroverted One really enjoyed the examples of fractals. Which led us down another trail of different examples of fractals and we found a fractal based on the Julia Set! How awesome is that? Here’s an example:
The EEO’s favorite quote from the wikipedia entry is, “Thus the behavior of the function on the Fatou set is ‘regular’, while on the Julia set its behavior is ‘chaotic‘.” Oh yeah, she can be chaotic and in no way regular.
This exploration into fractals and mathematics will hopefully instill a joy and curiosity of math and sciences that will last a lifetime and it was all brought about by the wonderful geeky music of Sir Jonathan Coulton. Wait, what? He hasn’t been knighted? Well, he should be dagnabit!
My new mission is to learn as much as I can about this and try to find this fractal on a t-shirt for the Elder Extroverted One to proudly wear and proclaim her geekiness!