"Reverse engineering" of a geometric illustration The following enigmatic illustration can be found here, unfortunately without any accompanied comment or short description:

Can you deduce its meaning? What was the way it was constructed?
 A: Seems to be an embedding of the Fano plane (7 points) into a larger projective plane (with 13 points).
A projective plane consists of a set of lines, a set of points, and a relation between points and lines called incidence, having the following properties:
Given any two distinct points, there is exactly one line incident with both of them.
Given any two distinct lines, there is exactly one point incident with both of them.
There are four points such that no line is incident with more than two of them.
The second condition means that there are no parallel lines. The last condition excludes the so-called degenerate cases (see below). The term "incidence" is used to emphasize the symmetric nature of the relationship between points and lines. Thus the expression "point P is incident with line l " is used instead of either "P is on l " or "l passes through P ".
There are many of these objects, some derived from real/complex geometry, some from finite fields.
For the Fano plane, have a look at 1 and proceed from the links there.
