It'd be fun to look through all the different ways it appears. If I had to summarize why, I'd note that the golden ratio is well known to appear in pentagrams and that much of the structure of the above image reflects that:
Show[Show[
Flatten[Table[
CompleteGraph[i, VertexSize -> 0,
EdgeStyle -> Thickness[0.00003]], {i, 1, 60}]]],
CompleteGraph[5, VertexSize -> 0, EdgeStyle -> Red],
CompleteGraph[3, VertexSize -> 0, EdgeStyle -> Red]]
