From Tetris to polyominoes generation

The behaviour of a bad Tetris player suggests a class of polyominoes that we call prefix-closed. Such a class contains all polyominoes P such that for any integer i>0 the first i columns of P form a polyomino. We provide a simple discrete dynamical system that allows us to define an algorithm for generating all prefix-closed polyominoes of size n in constant amortized time using O(n) space.