I love the way candles flicker. It's a great effect and I almost want to see it replicated in an actual lightbulb. I was curious if there is any way to express that mathematically? I'm not that familiar with physics but I go in assuming that most things can be expressed in math, just very complex in some cases!
If you want to determine physical causes of flame shape evolution, you would have to consider all processes taking place (chemical, phase changes, fluid dynamics, heat, ...); they are described using known differential equations, i.e. in one point in space. The exact global solution then requires those equations to hold simultaneously (coupling between processes) in all points of your domain, but such (analytical) solution it is only obtainable in very special cases. Approximate global solution is found numerically, by discretizing your problem in space and time, and requiring those differential equations to hold only in finite number of points in some approximate (though mathematically precisely defined) manner.