This paper addresses one of the fundamental questions in the theory of hard
-disk packings-how order within a system relates to packing density. The al
gorithm presented is a seed-based, growth protocol in which new disks are a
dded sequentially to the surface of a growing cluster. The angular position
of the new disk is chosen based on the minimization of an objective functi
on designed to control order, as measured by the global bond-orientational
order parameter psi(6), which varies between 0 and 1 (with 1 indicating per
fect hexagonal close-packed order). Modifying the objective function allows
the final packing fraction to be biased while maintaining tight control ov
er psi(6). Inside of the range 0 less than or equal to psi(6)less than or e
qual to 0.70, the targeted order parameter psi(6) is achieved to within two
decimal places of accuracy. Furthermore, it is found that random structure
s (psi(6)similar to 0.01) can be generated with packing fractions in the ra
nge 0.40 less than or equal to eta less than or equal to 0.77. Interestingl
y, the algorithm can produce nonequilibrium hard-disk configurations that a
re considerably more disordered than those typical of the equilibrium fluid
. (C) 2000 American Institute of Physics. [S0021-9606(00)50436-X].