I recently saw something that set me wondering how to create a realistic-looking (2D) lava lamp-like animation, for a screen-saver or game.
It would of course be possible to model the lava lamp’s physics using partial differential equations, and to translate that into code. However, this is likely to be both quite difficult (because of several factors, not least of which is the inherent irregularity of the geometry of the “blobs” of wax and the high number of variables) and probably computationally far too expensive to calculate in real time.
Analytical solutions, if any could be found, would be similarly useless because you would want to have some degree of randomness (or stochasticity) in the animation.
So, the question is, can anyone think of an approach that would allow you to animate a realistic looking lava lamp, in real time (at say 10-30 FPS), on a typical desktop/laptop computer, without modelling the physics in any great detail? In other words, is there a way to “cheat”?
One way to cheat might be to use a probabilistic cellular automaton with a well-chosen transition table to simulate the motion of the blobs. Some popular screensavers (in particular ParticleFire) use this approach to elegantly simulate complex motions in 2D space by breaking the objects down to individual pixels and then defining the ways in which individual pixels transition by looking at the states of their neighbors. You can get some pretty emergent behavior with simple cellular automata – look at Conway’s game of life, for example, or this simulation of a forest fire.