This is a toy model of the sandpile toy model, (or Bak–Tang–Wiesenfeld model for the mathematically inclined). It demonstrates self-organizing criticality in nonequilibrium systems.

Each cell represents a pile of blocks. A pile can only grow as high as 4 blocks. As soon as it reaches that state, it collapses and its blocks are distributed around. Since cells around it also have a height of their own, they might collapse in turn if they reach 4 blocks.

This means an avalanche happens, a chain reaction of collapses. In the graph upright, in green is the oscilloscope for avalanche sizes. In blue blue is a log-log graph of avalanche sizes vs frequency. With time, the distribution of avalanche sizes converges towards 1/f noise. This means there is less and less entropy (another way of saying more information) in the system as time passes.

This provides an insight into emergent behavior, and among other things the emergence of life (defined as entropy reduction, which is the only thing everybody seems to be able to agree on anyway when talking about life).

"The computer models of "sandpiles" developed by Bak and his colleagues specified things like the roundness of the grains being added to the pile, their stickiness, and so on. They looked at what happens if grains are added at random over the surface of the pile, and at what happens if they are always dropped from the same place. But you don't need a computer (or a sandpile to play the sandpile game and get insight into one of the most fundamental laws affecting nonequilibrium systems, including living systems. In his book How Nature Works, Bak describes how anybody can get an insight into the sandpile model by using ordinary children's building blocks." Using a grid of squares a chessboard would be ideal), you can place blocks on the squares to a maximum height of, say, three blocks, at random, so that on some squares there are no blocks, on some one, on others two, and on some three (checker pieces work just as well, if you can get hold of enough of them, or coins). We choose an arbitrary rule that says that once a stack reaches four blocks high it goes critical, and all four blocks corresponding to grains of sand) in that stack are taken off, with one of them added to each of the four squares at the sides of the critical square, or allowed to "fall off" the side of the board as appropriate. If this makes one of those squares go critical, repeat the process. Now, add blocks one at a time, at random, to the grid (you can choose the square to add a block to by rolling dice, or using a random number generator on a computer). At each step, move the blocks in accordance with the rules. Watch how the system moves toward the critical state, with "avalanches" on all scales and "sand" being pushed off the edge of the grid as new material is added from above. In the self-organized critical state, both in the computer models and in this "model of a model," the avalanches obey a power law."
— John Gribbin, Deep Simplicity