Gem-graph/README.md

# 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

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#### ***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.

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### 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 or it can be any 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. §7) 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:
- times and 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:
- times and 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

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> 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.

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#### 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 

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