How to implement a gravity system like Puzzle Uo Poko?

[IrSoil]

Are you set on solving in via physics\gravity? Since the system in the video has nothing to do with one:

• You just have a grid (stored as 2d array) - the State, and have a function like Evolve(State);
• Evolve(State) analyse the state and if any moves are possible - performs it.
  • Probably it have a feature like “process only top element of each column per Evolve(State) call”, but it’s something you may experiment with later;
• The move is a something like:
  • Check Grid[i][j] element:
    • If it’s a stone and it have a place to go left - go left
      • In code it’s something along the lines “check i’m the stone, check left, check left and down, perform”: if(Grid[i][j].NotEmpty() && Grid[i+0][j+1].Empty() && Grid[i+1][j+1].Empty()) {PerformMove(i,j,i+1,j+1);};
    • if it have a place to go right - go right
    • if it have no places to go - do nothing
  • repeat for every Grid[i][j] (optimizations are possible, but it’s the simplest solution)
• perform is a two steps:
  • make actual move of element Grid[i][j] to Grid[i+1][j+1]
  • animate the move
    • once animation is over - go for next iteration of Evolve(State)
• Once Evolve(State) not changing the State anymore - you may let user perform input and add a new element into the Grid

Note that the Grid in the video have an offset of 0.5 element for odd rows - your manipulations with indexes of the Grid have to properly handle this feature.
Well, overall it’s something like this.