Power law
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The zero of a sandpile
Pile grains of sand on a grid, and whenever a cell holds four, let it topple and pass one grain to each neighbour. The order in which cells topple turns out not to matter, and the piles that keep recurring when sand is dropped at random form a group — one whose size is the number of spanning trees of the grid. Its zero is not the empty grid but a fractal picture of nested squares, and sand dropped on a single cell spreads into a round pile with the same kind of pattern inside.
A cluster grown by random walkers
Release a particle far away, let it wander until it touches a growing cluster, and freeze it there. Twenty thousand particles later the cluster is a branching tree whose mass grows like the radius to the power 1.7. Every simulation agrees on the number; the only theorem says it is at least 1.5.
Named alongside it
The objects these essays reach for when they reach for this one.
Abelian groupBox countingCellular automatonDeterminantFractalFractal dimensionGrowth modelHarmonic measureRandom walkSelf-similaritySimulationSpanning tree