  The Dynamical Graph Grammar (DGG) formalism can describe complex system
dynamics with graphs that are mapped into a master equation. An exact
stochastic simulation algorithm may be used, but it is slow for large systems.
To overcome this problem, an approximate spatial stochastic/deterministic
simulation algorithm, which uses spatial decomposition of the system's
time-evolution operator through an expanded cell complex (ECC), was previously
developed and implemented for a cortical microtubule array (CMA) model. Here,
computational efficiency is improved at the cost of introducing errors confined
to interactions between adjacent subdomains of different dimensions, realized
as some events occurring out of order. A rule instances to domains mapping
function $\phi$, ensures the errors are local. This approach has been further
refined and generalized in this work. Additional efficiency is achieved by
maintaining an incrementally updated match data structure for all possible rule
matches. The API has been redesigned to support DGG rules in general, rather
than for one specific model. To demonstrate these improvements in the
algorithm, we have developed the Dynamical Graph Grammar Modeling Library
(DGGML) and a DGG model for the periclinal face of the plant cell CMA. This
model explores the effects of face shape and boundary conditions on local and
global alignment. For a rectangular face, different boundary conditions
reorient the array between the long and short axes. The periclinal CMA DGG
demonstrates the flexibility and utility of DGGML, and these new methods
highlight DGGs' potential for testing, screening, or generating hypotheses to
explain emergent phenomena.
