  We give a new algorithm for generating Greechie diagrams with arbitrary
chosen number of atoms or blocks (with 2,3,4,... atoms) and provide a computer
program for generating the diagrams. The results show that the previous
algorithm does not produce every diagram and that it is at least 100,000 times
slower. We also provide an algorithm and programs for checking of Greechie
diagram passage by equations defining varieties of orthomodular lattices and
give examples from Hilbert lattices. At the end we discuss some additional
characteristics of Greechie diagrams.
