Fibonacci pattern, red, connected dot array. When I wrote the script that connected all of the vertices, it was a challenge to figure out how they would connect properly to form this nice network you see here. Instead of finding some profound mathematical relationship to connect them, I simply had the program measure the distances of all vertices in relation to eachother. Then the program simply took the first few smallest distances and made them possible candidates for "connecting".
But just connecting those still produced a lot of necessary connections (triangles), so one more condition had to be made. Using the existing distance arrays, the program calculated the average distance of all neighbor's closest vertices. So finally when determining of two neighbor vertices would become connected, their distance was checked against the average mentioned above, and if they were close enough (within a very small tolerance) they were allowed to form an edge.
This was a fun project! I'm hoping to develop this further for more shapes and objects. And who knows what sort of discoveries can emerge from this masterpiece of nature...the golden ratio.