Even if you don't care about math, check out this pretty graph I made. I made the surface plot with Matlab, saved as an eps (encapsulated Postscript) file, then converted to a pdf with Preview.app on Mac OS X. In Matlab the figures never look this good, but when viewing it in Preview there's nice anti-aliasing and some awesome alpha transparency! Well, maybe it's only cool if you're a total nerd.
For those curious about what this is: I just did this homework assignment where I'm solving a simple parabolic partial differential equation in one spatial dimension, uτ = uξξ. We used the Method of Lines to discretize the spatial dimension, turning the problem into a system of ordinary differential equations. We tried solving that system using some different ODE solvers, and this plot was made using the simple, inaccurate, and non-stiff Explicit Euler method. It turns out that if you don't make your time time steps smaller than about ½ (Δ ξ)-2, where Δ ξ is the spatial step size, the solution is numerically unstable. This is why the u values are oscillating and blowing up to huge values near τ = 1 in this plot, making the actual solution impossible to see. If you're really curious, here is the assignment this is from.
Wow I'm amazed I could actually write that math just using HTML. Too bad everyone's browsers don't support some easy way of embedding LaTeX directly in HTML. Well, aside from jsMath, anyway, which I don't think I can use on LiveJournal since I'd have to embed JavaScript in my post.
