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Sai Emrys wrote:
> On 1/29/06, Sai Emrys <[log in to unmask]> wrote:
> 
>>Arbitrary in my use: any node can be connected to any number of other
>>nodes. (assuming it's on the node-and-connection sort of style, which
>>it need not be if it has a fusional morphology)

What's fusional morpholgy?

>>I still don't see how you can say it's 6. Could you please show me the math?
>>
>>I'm not sure about cases where 'neighbors' are directly touching, but
>>it's obviously false if they can be simply connected by lines. E.g.:
>>
>>[paste this into a notepad w/ an equal-width font]
>>
>>1 2 3
>> \|/
>>4-O-5
>> /|\
>>6 7 8

This shows a system made up of paired (2) connections.  "\" 
(link) connects to "1" and "O."  "O" only has one connection, to 
link.  Also in this scheme "2" cannot immediately link to "5" 
since it becomes indeterminate whether that also links "2" to "3" 
or "O."

>>... and that's not even using multiple 'layers', or variable length
>>connecting lines, branching ones, or anything like that.
>
> Actually, no - simpler:
> 123
> 4O5
> 678
> 
> There, you have 8 connections, all directly touching the central
> character, all of the same size.

No you have 4 (primary) connections since there's no real-world 
way for items 1, 3, 6, and 8 to actually contact O, and there's 
no means for distinguishing O-3 connections from 2-4 connections. 
  To distinguish O-3 from 2-4 you'll need to add gaps in the pattern

12
4O5
67

which in turn brings the connections down to 6.

In the system:

1   3
  \2/
  4O5
  /7\
6   8

"O" has five connections: 2, 4, 5, 7, and link, at the expense of 
wasted space.  (Thus, this is a system of connectivity 5 that 
isn't space-filling.)

Connectivity is very important in circuit-board design and you 
might to look up the constraints involved in that area.

-- 
Jefferson
http://www.picotech.net/~jeff_wilson63/myths/