  Graph-Rewriting Automata (GRA) are an extension of Cellular Automata to a
dynamic structure using local graph-rewriting rules. This work introduces
linear algebra based tools that allow for a practical investigation of their
behavior in deeply extended time scales. A natural subset of GRA is explored in
different ways thereby demonstrating the benefits of this method. Some elements
of the subset were discovered to create chaotic patterns of growth and others
to generate organic-looking graph structures. These phenomena suggest a strong
relevance of GRA in the modeling natural complex systems. The approach
presented here can be easily adapted to a wide range of GRA beyond the chosen
subset.
