Each four-celled animal tiles the plane (Q1078572)

Assume that an animal A is a set of (not necessarily connected) unit squares in the plane, with corners at integer lattice points. D. A. Klarner had asked whether copies of A, suitably translated by integer vectors and rotated through suitable multiples of a right angle, can tile the plane, filling it completely and without any but measure zero overlap. The author shows that copies of any animal consisting of four unit squares tile the plane. He gives an example of a connected six-unit- square animal copies of which will not tile the plane and also formulates several open questions.