Monday, July 04, 2005

apparently math and art do mix

Researchers have created a program that uses the Boltzmann equation to model the interaction of ink and paper, enabling more realistic software painting techniques. The Boltzmann equation describes the dynamics of an ideal gas and is often not used for denser gases and liquids (like ink), but curiously it is used for modeling galactic dynamics... being mostly empty space, galaxies (at some very large scale and under certain assumptions about viscosity and collisions) resemble a gas. Hrmmm, that reminds me of a Steven Wright joke:

"I was walking through the park last night when a spaceship landed in front of me and a one inch tall alien got out. I said to him, 'are you really one inch tall'? 'No', he replied, 'I'm just really far away'."

The Boltzmann equation is known to have no closed-form solution for higher densities (i.e. it is a Serious Pain In The Ass to integrate, like most thermodynamics problems), so those researchers must have found a way to optimize the equations to get real-time results. Whatever they did, the end result is some pretty pictures.