[math-fun] seven of three

yet another pretty matrix: k = 4; vec = IntegerDigits[Range[0, 3^k - 1], 3, k] - 1; or, all (-1,0,1) vectors of length k, sev = Outer[Plus, vec, vec, 1] /. (q : {__Integer}) /; (Min[q] < -1 || Max[q] > 1) :> 0 /. (q : {__Integer}) :> 1 + FromDigits[q + 1, 3]; .. added in all possible ways, and replacing (-1,0,1) vecs with 1, the others with 0 (those containing -2 or 2). ListDensityPlot[sev /. i_?Positive -> 1, Mesh -> False] .. results in a fractal plot of 7 hexagons, made of 7 hexagons, made of ... and its determinant is 1. The '1''s are of course counted as 7^k. Beauty is in the eye of the beholder. W.