>"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 <i>two maps</i>, specifically <i>two 2D arrays</i>, to capture the information for each cell. The <i>color map</i> stores the color values of each cell, while the <i>velocity map</i> stores a vector that represents the velocity, i.e. the information about the speed and direction of the water flow in each cell."<p>First of all, great article!<p>Second, there's something <i>weird-but-interesting</i> going on in the quote I've highlighted, above...<p>First, we have Conway's Game Of Life:<p><a href="https://en.wikipedia.org/wiki/Conway's_Game_of_Life" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Conway's_Game_of_Life</a><p>To recap, Conway's Game Of Life is sort of like a <i>one array</i> (representing the screen), 2D simulation.<p>Whereas the above fluid simulation uses <i>two arrays</i>, two maps, in 2D...<p>My question, my curiosity, is simply this:<p>What would happen if we used <i>three or more arrays</i>, <i>three or more maps</i>, in 2D?<p>Like, n-maps, n-arrays (the "higher dimensional generalization" if you will...) to represent things other than velocity...<p>What would our simulation look like, then?<p>For example, some interesting things to play with, in this space, might include (but not be limited to, as Lawyers would say!): <i>Acceleration</i>, <i>Jerk</i>, <i>Snap</i>, <i>Crackle</i> and/or <i>Pop</i>:<p><a href="https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_derivatives_of_position" rel="nofollow noreferrer">https://en.wikipedia.org/wiki/Fourth,_fifth,_and_sixth_deriv...</a><p>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.<p>Oh sure, they could be computed on-the-fly too... but that's no fun!<p>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!<p>What could be discovered?<p>Well, I as-of-yet don't know obviously... but it seems like these concepts should mesh together somehow...<p>Anyway, great article!