60 lines
3.6 KiB
Markdown
60 lines
3.6 KiB
Markdown
# 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.
|
|
|
|
---
|
|
|
|
### Project documentation:
|
|
* questions about the [architecture](architecture.en.md): identification and naming of the main parts of this program and the data structures.
|
|
* questions about the [theory](theory.en.md): properties of rewritten geometric directed multigraphs. (JS. Dec 2017)
|
|
|
|
---
|
|
|
|
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
|
|
|
|
|
|
---
|
|
> 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.
|
|
---
|