Each four-celled animal tiles the plane

Abstract

An animal A is a set of unit squares in the plane, parallel to the axes, and with corners at integer lattice points. We show that any animal A with four cells tiles the plane, in the sense that infinitely many copies of A, translated by integer vectors and possibly rotated through 90°, 180°, or 270°, can be placed so as to fill plane exactly without overlap. © 1985.