63 lines
4.0 KiB
Markdown
63 lines
4.0 KiB
Markdown
# gem-graph is for: GE-ometric directed M-ulti-GRAPH
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>#### (1) A ***geometric*** graph is a graph whose nodes have coordinates in a space
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>#### (2) It is ***directed*** if its bonds are arrows
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>#### (3) It is a ***multi***graph if multiple arrows can be stacked from the same node to another
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>##### Note that 'directed' does not means 'oriented': a graph is oriented if one of its nodes is its root
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---
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#### ***Geometric directed multigraphs*** have properties that make them suitable for the representation of complex phenomena.
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#### ***gem-graph*** is a software that enables modelling with a geometric directed multigraph.
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## ______________________________________________________________________________________________________________
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### Faced with the difficulty of calculating the evolution of complex systems defined by
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- a great diversity of objects and
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- a great diversity of interactions,
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### **The gem-graph rationale is:**
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#### 1. represent space
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#### 2. a discreet (non-continuous) space
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#### 3. a space whose all units are similar
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#### 4. links can be established between some of these units
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- they allow drawing **objects** (isolated connex parts of the graph) and **situations** (relative positions of objects)
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- for practical purposes, it is convenient to use **arrows** and to allow stacking many of them from the same node to another
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#### 5. an automaton, i.e. a set of states and transitions can rewrite this space
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#### 6. ***states*** can represent ***space***
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- here, **space** can be understand as **a representation or approximation of a real space**
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- 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.
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#### 7. transitions are all combinations of ***a single type of elementary transition***
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#### 8. the coding of static information (states) and dynamic information (transitions) is distinct
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- 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.
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#### 9. no constraint on granularity: the scope of the arrows between space units is not limited
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#### 10. the computation is local, random, asynchronous
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#### 11. interfaces are possible with statistical and / or continuous fermion models:
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- 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.
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#### 12. interfaces are possible with representations of bosons:
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- 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.
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#### 13. the topology, the dimension and the magnitude of the space are not constrained
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---
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> Locos, formas modumque coherentiae omium rerum status depingit. Nihil aliud comprehendet.
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> Eas res praecepta movet aut transformat. Nihil aliud facit. Quaedam tranformationes in sua potestate sunt.
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> Aliae transformationes alii succedere debent.
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> Interpositus status inter illas et istas jacet.
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> Ab antecedente statu primarum ad sequentem statum secundarum iter nullius est nisi per suorum interpositum statum.
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---
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#### Design: two converging, complementary and interdependent approaches:
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- one goes **from** the available data structures and algorithms **to** the graph structure and the automaton it supports (synthetic or bottom-up approach)
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- the other goes **from** the gem-graph automaton constraints **to** the available software tools (analytical or top-down approach)
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#### today (28-03-2011) two texts are under development:
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* questions about the [architecture](architecture.md): identification and naming of the main parts of this program and data structures
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* [theoretical issues](theory.md) : Rewritten Geometric Directed Multigraphs Properties. (JS. dec 2017)
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This text could be a starting point for a publication
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---
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