# gem-graph is for: GE-ometric directed M-ulti-GRAPH >#### (1) A ***geometric*** graph is a graph whose nodes have coordinates in a space >#### (2) It is ***directed*** if its bonds are arrows >#### (3) It is a ***multi***graph if multiple arrows can be stacked from the same node to another >##### Note that 'directed' does not means 'oriented': a graph is oriented if one of its nodes is its root --- #### ***Geometric directed multigraphs*** have properties that make them suitable for the representation of complex phenomena. #### ***gem-graph*** is a software that enables modelling by rewriting a geometric directed multigraph. ## ______________________________________________________________________________________________________________ ### Faced with the difficulty of calculating the evolution of complex systems defined by - a great diversity of objects and - a great diversity of interactions, ### **The gem-graph rationale is:** #### 1. represent space #### 2. a discreet (non-continuous) space #### 3. a space whose all units are similar #### 4. links can be established between some of these units - they allow drawing **objects** (isolated connex parts of the graph) and **situations** (relative positions of objects) - for practical purposes, it is convenient to use **arrows** and to allow stacking many of them from the same node to another #### 5. an automaton, i.e. a set of states and transitions can rewrite this space #### 6. ***states*** can represent ***space*** - here, **space** can be understand as **a representation or approximation of a real space** - but a **state** can be a **space** as well as a text or any other set of symbols or writings (ex: tags) that can be drawn in the graph using the same encoding and a **state** can be an association of both. #### 7. transitions are all combinations of ***a single type of elementary transition*** #### 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. ยง7) which is the condition of their automatic management and edition. #### 9. no constraint on granularity: the scope of the arrows between space units is not limited #### 10. the computation is local, random, asynchronous #### 11. interfaces are possible with statistical and / or continuous fermion models: - spaces are then superimposed and conditions on intensive local variables (concentrations, temperatures, flows, etc...) can be added to the specific conditions of the gem-graph. #### 12. interfaces are possible with representations of bosons: - spaces are then superimposed and conditions on intensive local variables (flux, cross section, etc.) can be added to the specific conditions of the gem-graph. #### 13. the topology, the dimension and the magnitude of the space are not constrained --- > Locos, formas modumque coherentiae omium rerum status depingit. Nihil aliud comprehendet. > Eas res praecepta movet aut transformat. Nihil aliud facit. Quaedam tranformationes in sua potestate sunt. > Aliae transformationes 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. --- #### Design: two converging, complementary and interdependent approaches: - one goes **from** the available data structures and algorithms **to** the graph structure and the automaton it supports (synthetic or bottom-up approach) - the other goes **from** the gem-graph automaton constraints **to** the available software tools (analytical or top-down approach) #### today (28-03-2011) two texts are under development: * questions about the [architecture](architecture.md): identification and naming of the main parts of this program and data structures * [theoretical issues](theory.md) : Rewritten Geometric Directed Multigraphs Properties. (JS. dec 2017) This text could be a starting point for a publication ---