Abelian sandpile simulation dating
Complete descriptions of Sandpile methods. It means that sand is not magically appearing or disappearing the mass of the system is stable, like in reality. Note how the sand accumulates at the base, and the walls slowly become flat while growing and covering underlying elements. Each summary is followed by a list of complete descriptions of the methods.
In practice, self-organized criticality is often taken to mean like the sandpile model on a grid graph. That configuration is stable. What you're looking at is a flipbook generated in Houdini and the surface is a HeightField. Basically, this meant that the larger the avalanche or catastrophe, the less frequent this event would occur.
In the example below, the size of an avalanche is taken to be the sum of the number of times each vertex fires. It does this by seeking out a so-called critical threshold, around which complex behavior tends to be found. For example, for most graphs, once sand is dropped on the graph, no sequence of additions of sand and stabilizations will result in a graph empty of sand.
Wherever insights come from, the sandpile reminds us that the really interesting phenomena in math, like the really interesting phenomena in physics, often happen at the phase transitions. The frequency of avalanches is inversely proportional to their size. The sand starts from a veeery unstable configuration and slowly rearranges in a way that is stable.
They found that these avalanches created a phenomena, which Per Bak noted followed the theory of Self-Organized Criticality. See the section on Discrete Riemann Surfaces for the language of divisors and linear equivalence. In other words, a lot of resources. Thus, each configuration stabilizes to a unique stable configuration. Imagine a rectangular grid, where each cell can hold maximally three grains of sand.