GE-ometric D-irected M-ulti-GRAPH (gem-graph)

(1) A geometric graph is a graph whose nodes have coordinates in a space

(2) It is directed if its links are arrows

(3) It is a multigraph if several arrows can be superimposed from one node to another

NB "directed" does not mean "oriented": a graph is oriented if one of its nodes is its root.

Directed geometric multigraphs have properties that make them suitable for the representation of complex phenomena. gem-graph is a software that allows modeling by rewriting a directed geometric multigraph.

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Project documentation:

• questions about the architecture: identification and naming of the main parts of this program and the data structures.
• questions about the theory: properties of rewritten geometric directed multigraphs. (JS. Dec 2017)

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Faced with the difficulty of computing the evolution of complex systems defined by a great diversity of objects and a large diversity of interactions,

The rationale for the gem graph is:

1. To represent the space
2. A discrete space (not continuous)
3. A uniform and Cartesian space
4. Links can be established between some of these units They allow to draw objects (isolated related parts of the graph) and situations (relative positions of objects) for practical reasons, it is convenient to use arrows and to allow a large number of them to be stacked from one node to another
5. An automaton, i.e. a set of states and transitions can rewrite this space, with version management
6. The states can represent the space Here, the space can be understood as a representation or an approximation of a real space. But a state can be a space as well as a set of symbols (e.g. tags) which can be drawn in the graph using the same encoding or it can be any combination of the two.
7. Transitions are all combinations of a single elementary transition type consisting of:
   • a single condition (how many arrows at this point? - compare to a predefined number))
   • a single assignment (define n arrows at the same place)
8. The coding of static information (states) and dynamic information (transitions) is distinct. The purpose of this restriction is to maintain a strict homogeneity of the rules (cf. §7) which is the condition for their automatic management and editing.
9. Constraint on granularity: the range of arrows between spatial units is increased by the local space (discrete/continuous ?)
10. The calculation is local, random (choice of orientation of the local space, choice of the result of the actions of two rules whose set of conditions is superimposable), asynchronous
11. Interfaces are possible with statistical and/or continuous fermion models. Time and space are then superimposed and the conditions to intensive local variables (concentrations, temperatures, flows, etc ...) can be accessed by means of a specific gem-graph condition
12. Interfaces are possible with boson representations. Time and space are then superimposed and conditions on local intensive variables (flux, cross section, etc.)
13. The topology, dimension and magnitude of the space are not constrained
14. Represent and optimize graphs

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Locos, formas modumque cohérentiae omium rerum status depingit. Nihil Aliud comprend. Eas res praecepta movet aut transformat. Nihil aliud facit. Quaedam transforme en sua potestate sunt. Aliae transforme alii succedere debent. Interpositus status inter illas et istas jacet. Ab antecedente statu primarum ad sequentem statum secundarum iter nullius est nisi per suorum interpositum statum.

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