60 lines
3.6 KiB
Markdown
60 lines
3.6 KiB
Markdown
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# GE-ometric D-irected M-ulti-GRAPH (gem-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 links are arrows
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### (3) It is a multigraph if several arrows can be superimposed from one node to another
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##### NB "directed" does not mean "oriented": a graph is oriented if one of its nodes is its root.
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#### 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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---
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### Project documentation:
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* questions about the [architecture](architecture.md): identification and naming of the main parts of this program and the data structures.
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* questions about the [theory](theory.md): properties of rewritten geometric directed multigraphs. (JS. Dec 2017)
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---
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Faced with the difficulty of computing the evolution of complex systems defined by
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a great diversity of objects and
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a large diversity of interactions,
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The rationale for the gem graph is:
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1. To represent the space
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2. A discrete space (not continuous)
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3. A uniform and Cartesian space
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4. Links can be established between some of these units
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They allow to draw objects (isolated related parts of the graph) and situations (relative positions of objects)
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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
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5. An automaton, i.e. a set of states and transitions can rewrite this space, with version management
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6. The states can represent the space
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Here, the space can be understood as a representation or an approximation of a real space.
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But a state can be a space as well as a set of symbols (e.g. tags)
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which can be drawn in the graph using the same encoding or it can be any combination of the two.
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7. Transitions are all combinations of a single elementary transition type consisting of:
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- a single condition (how many arrows at this point? - compare to a predefined number))
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- a single assignment (define n arrows at the same place)
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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)
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which is the condition for their automatic management and editing.
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9. Constraint on granularity: the range of arrows between spatial units is increased by the local space (discrete/continuous ?)
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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
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11. Interfaces are possible with statistical and/or continuous fermion models.
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Time and space are then superimposed and the conditions to intensive local variables
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(concentrations, temperatures, flows, etc ...) can be accessed by means of a specific gem-graph condition
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12. Interfaces are possible with boson representations.
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Time and space are then superimposed and conditions on local intensive variables (flux, cross section, etc.)
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13. The topology, dimension and magnitude of the space are not constrained
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14. Represent and optimize graphs
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---
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> Locos, formas modumque cohérentiae omium rerum status depingit. Nihil Aliud comprend.
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> Eas res praecepta movet aut transformat. Nihil aliud facit. Quaedam transforme en sua potestate sunt.
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> Aliae transforme 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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