CtXh bplex

xholonWorkbook.xml

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<Notes><![CDATA[
What is the Category?Xholon
------
Title: CtXh bplex
Description: 
Url: http://www.primordion.com/Xholon/gwt/
InternalName: 346f8fc1ab75a1a43450b4561967b171
Keywords: 

My Notes
--------
4 July 2023

### bplex
"bplex" is my name for a structure that can be used in Xholon apps.
A bplex is a chain or cycle of links between nodes, where each link has the same port name.
Nodes A B C partipate in bplex Platypus if
 - A has a port called Platypus that links to B, and
 - B has a port called Platypus that links to C, and
 - C optionally? has a port called Platypus that links to A.

I have used this in the Island Game app to connect a Stick, Vine, and Thorn into a Fishing Rod.
 - the three nodes become a Fishing Rod by virtue of sharing this bplex.
 - this is instead of enclosing the three nodes by a FishingRod node.
 - When a fish bytes on the Thorn, the Thorn sends a message along the frod bplex, and
   eventually some node intercepts the continuous message and performs a frod action.
   In the Island Game, this active object is the Castaway Avatar.

TODO
- how can I describe this structure mathematically?
- what existing math structure does it resemble?

###Math, Category Theory
- a bplex is a set of arrows
- can be expressed as a set of pairs
 - ex: ["A,B", "B,C", "C,A"]

###Graphviz

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Tue Jul 04 11:54:34 GMT-400 2023 1688486074752
model: CtXh bplex
www.primordion.com/Xholon

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See also: http://www.webgraphviz.com/
See also: http://rise4fun.com/agl/

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###Using bplex to represent a Hypergraph?
Let nodes be a set of Node objects {a,b,c,d,e,f,g,h,i,j}
Let containers be a set of Container objects {r,s,t}
Node objects are inside Containers as follows:
r: a,b,c
s: a,c,d,e,f
t: a,e,f,g,h,i,j
Instead of representing r,s,t as actual nodes, represent them as 3 bplexes

r = a->b->c
s = a->c->d->e->f
t = a->e->f->g->h->i->j

r,s,t arrows could be shown using three different colors

TODO:
- draw this example using Graphviz

###options
- array or linked list
- chain or cycle
- singly-linked or doubly-linked
- Set or Array
  unordered or ordered

###Category
What is the Category?

In Dev Tools, I can get the Stick node as temp0.
I can then do:

temp0.frod.frod.frod == temp0
RESULT: true

or:
temp0["frod"]["frod"]["frod"] == temp0

or I could compose these using JS compose:

((node) => {
  console.log(node.name())
  const compose = (...fns) => x => fns.reduceRight((y, f) => f(y), x)
  const funk = node => node.frod
  const one   = compose(funk)(node)
  console.log(one.name())
  const two   = compose(funk,funk)(node)
  console.log(two.name())
  const three = compose(funk,funk,funk)(node)
  console.log(three.name())
})(temp0)

###bplex is used in grid ?
- Xholon grids use a bplex to connect a sequence of rows,
  and bplexes to connect the cells in each row
  - both forward and backward
  - and these optionally wrap around
  - so maybe a "bplex" is a generalization of this idea?

###Generalized bplex
- any sequence of nodes connected in sequence by arrows with the same name
 - or by arrwos that are the same function or relation?
- typically, not following edges that already exist in the base tree
- as a minimum, there are at least two links in the sequence ?
 - BUT, for generality, there could be 1 or 0

###Convert Xholon Tree into a bplex
- visit each node, and/or work through a in|pre|post|etc-order traversal
- all nodes are now in an array
- go through all nodes in the array
 - convert each parent+next node into a link to next named after the parent
  - the link/port name shoud be the result of calling parent.name()
   - ex: if this node is a "Room" and parent is a "House", then the bplex port name might be "house_37" _
  - set the parent and next nodes to null
- nodes would retain their Xholon id
- this is not a particularly good representation
 - nodes and parents would now have a hard time locating each other
- my conclusion:
 - a bplex is a useful tool under certain circumstances, but not for capturing the entire system structure
 - it's useful as an adjunct/additional way of connecting things
 - a type of link graph, or a way of thinking about individual link graphs

###Is a bplex a port graph?
- maybe ?

###Recall the concept of Place Graph and Link Graph
- from Milner
- a bplex is probably only useful in the context of Link Graph

References
----------
(1) search: port graph

(2) https://math.stackexchange.com/questions/1118344/what-is-the-name-of-a-graph-structure-with-ports#2597225
    What is the name of a graph structure with 'ports'?
    - has some good examples and responses

(3) https://scholar.google.com/scholar?q=%22port+graph%22

(4) Labelled Port Graph – A Formal Structure for Models and Computations, Maribel Fernandez, Helene Kirchner, Bruno Pinaud
    - I downloaded this

(5) https://porgy.labri.fr/
    PORGY
    The visual graph rewriting platform

]]></Notes>  

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