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>"First, we will define the space as a grid of cells. We want to smoothly move paints, or different colors, around in this space. To do this, we will use two maps, specifically two 2D arrays, to capture the information for each cell. The color map stores the color values of each cell, while the velocity map stores a vector that represents the velocity, i.e. the information about the speed and direction of the water flow in each cell." First of all, great article! Second, there's something weird-but-interesting going on in the quote I've highlighted, above... First, we have Conway's Game Of Life: https://en.wikipedia.org/wiki/Conway's_Game_of_Life To recap, Conway's Game Of Life is sort of like a one array (representing the screen), 2D simulation. Whereas the above fluid simulation uses two arrays, two maps, in 2D... My question, my curiosity, is simply this: What would happen if we used three or more arrays, three or more maps, in 2D? Like, n-maps, n-arrays (the "higher dimensional generalization" if you will...) to represent things other than velocity... What would our simulation look like, then? For example, some interesting things to play with, in this space, might include (but not be limited to, as Lawyers would say!): Acceleration, Jerk, Snap, Crackle and/or Pop: https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv... Basically, if velocity is the first derivative of position (and thus should go in the second (n+1) array or map), then maybe other derivatives can go in the higher dimensional map appropriate to them. Oh sure, they could be computed on-the-fly too... but that's no fun! In fact, what might be interesting might be to see side-by-side graphics of higher-dimensional maps along with the base-level map, as the simulation (be it Life or Fluid Dynamics or ?) evolves! What could be discovered? Well, I as-of-yet don't know obviously... but it seems like these concepts should mesh together somehow... Anyway, great article! |