How many potential ingress glyphs are there?

[Simon Bridge]

Ingress is a virtual relaity video game which includes a "glyph hacking" minigame which is basically a shrt-term memory test. It involves drawing figures on a template of dots or nodes (in a hexagonal arrangement) according to rules involving drawing lines between dots.

My mind being what it is, I keep getting distracted by wondering how to go about figuring the total number of possible glyphs.

I figure the number should be finite since you can, in principle, connect all the dots following the rules.
There are many ways to draw each glyph but it is not just a matter of traversing the dots - you have to traverse the path (though you can start from anywhere on the path). But I keep getting bogged down with trying to get a systematic way of counting the possible paths.

For details:
https://support.google.com/ingress/answer/4574603?hl=en
http://glyphtionary.com/

 

[mfb]

What are the rules? If you have n possible, independent connections that can be either used or unused, you just have to find that number n. If it has to be traversable, you get an additional condition that is messy to evaluate.

 

[Simon Bridge]

They are in the links - there are 11 nodes, 6 in a hexagon, 4 in a box inside the hexagon, and one in the middle.
The glyphs are lines drawn linking the nodes.

Lessee:
Stand the hexagon on one corner, and number those nodes clockwise 1-6 starting at the top one, put another in the center and call it 11.
The box is positioned so that node 7 is between 6 and 11, node 8 is between 2 and 11, node 9 is between 3 and 11, and node 10 is between 5 and 11.

One may draw a glyph, i.e the "create" glyph, by traversing the nodes: 5-10-11-8-2
Going the other way is fine - anything that ends up drawing that shape is the same glyph.
But the connections have to be straight - going from 5-2 would involve a curved line so does not count, a straight line path from 5-2 would have to intercept 10,11,8 as well so it's the same glyph.
You are allowed to reuse nodes though, and lines are allowed to cross, as in the "resistance" glyph: 8-7-1-11-4-10

There's pictures in the links, descriptions, and examples.

Yes, it has to be traversable ... the glyphs have to be drawn without lifting the finger (object used to draw) from the screen/page.

That's the messy bit having trouble with... especially since some nodes block some possible connections so, for eg, there are not 10 possible 1-step links from node 1 but 7. In the game, 2 of these possibilities are, as yet, unused.

It may not be possible to figure it out except maybe brute force on a computer.

 

[mfb]

Even brute force could be tricky. I count 38 possible connections. Something like ~.1 to 1% of them could be traversable, that leaves of the order of 100 million to 1 billion glyphs.