The Fractal Graph data structure is a
DataStructure (invented by Mark Janssen) which extends the historical evolution of data types to its ultimate end-point. Just as a simple Graph extended Trees which extended
LinkedLists, et cetera, the
FractalGraph can incorporate all the former and represent any known relationship of the real world. As such it is a data structure to end all data structures. It is the data structure to use once one has understood that
AllDataRelatesToOtherData and wants to make the
PerfectSystem.
In a fractal graph, any vertex in the graph can consist of a further graph (hence its fractal property). Ultimately a fractal graph creates an n-dimensional space in which there is no
a priori ordering. Any ordering is accomplished by implementing a "grouping methodology".
(...Accomplished with the VotingModel. --MarkJanssen)
A graph in which "any vertex in the graph can consist of a further graph" is already known has a nested graph, and I don't recall any mention in the literature of a Mark Janssen inventing it. Unless, of course, a fractal graph differs in some identifiable way from a nested graph. Does it?
"...already known has a nested graph", Ummkay.... Where do you think this is so? Also, apparently you don't know that the Internet does act as a publishing medium. It must be referenced with date and time data, otherwise it is like any printed work.
There are references in ACM and IEEE publications at least as old as 1994; I didn't bother searching elsewhere or further back. Of particular relevance to your interests might be http://dl.acm.org/citation.cfm?id=174608.174610 Try Google Scholar (http://scholar.google.co.uk/scholar?hl=en&q=%22nested+graph%22) for more.
A graph encompasses all other linked data structures, by definition. A Tree,
LinkedList, etc. is a specific kind of graph.
"Fractal" implies self-similarity at macro and micro levels, which doesn't seem to be the case here. I think you mean "nested". Of course, a nested graph is a well-known structure. If your Fractal Graph has vertices that contain graphs, it's a nested graph. In programming, nested graphs are quite common. Indeed, the data in RAM of a typical running program can be modelled as a nested graph.
It is not "quite common". The idea of RAM in a running program is besides the point. In any case, it is "the case here", but one should note that in order to have a fractal geometry that is "stable", you still need to anchor things somewhere.
Actually, it is "quite common". Social networks form nested graphs, and are frequently simulated as nested graphs. Typical variable declarations and references in function/procedure definitions in imperative programming languages form a nested graph and may be explicitly regarded as such by compilers for memory allocation and optimisation purposes. Similarly, class instance references in a typical OO language form a nested graph.
- How are social networks "nested graphs"? All the "1 billion" connections in facebook can be modeled by a simple graph. You are wrong.
- Social network software may be implemented as a simple graph based on a "friendship" relation, but organisation of a social graph into (say) communities based on a "community interaction" relation, with "friendship" relations within each community, can be effectively represented by a nested graph.
I don't disagree that you need an "anchor" -- though what that has to do with the present discussion, I know not -- but how is what you describe "fractal"? Can you show how your
FractalGraph is distinct from a nested graph?
{I agree that nesting is not necessary, it just makes too many ways to represent the same kind of info being that the same thing could be represented via graph pointers to be begin with.}
You mean a nested graph is a graph? I agree. Would the original author of this page be so kind as to illustrate a
FractalGraph, so that we can see how it differs from a graph?
- Unfortunately, the limitations of ASCII make it a bit difficult.
- I'm sure there are notations you could use, or provide a description of its distinguishing characteristics.
{I wonder if it allows overlaps. One of the flexibility features of graphs is that you can link any node to any other node with relative easy. Strict nesting prevents such, and fuzzy nesting makes nesting non-helpful.}
Not sure what you mean by "overlaps".
I'm not sure either.
See also
UnifiedDataModel,
GraphTheory,
PangaiaProject