Aztec Diamond

Author

Eric W. Weisstein
February 10, 2011

This notebook downloaded from http://mathworld.wolfram.com/notebooks/RecreationalMath/AztecDiamond.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/AztecDiamond.html.

©2011 Wolfram Research, Inc. except for portions noted otherwise

Counts

ad={x,y}/.Table[{ToRules@Reduce[Abs[x-1/2]+Abs[y-1/2]<=n,{x,y},Integers]},{n,10}];

Length/@ad

Table[2n(n+1),{n,10}]

Figure

square[{x_,y_}]:=Line[({x,y}-1/2+#)&/@{{0,0},{1,0},{1,1},{0,1},{0,0}}]

V5

Show[GraphicsArray[Table[Graphics[square/@ad[[n]],AspectRatio->Automatic],{n,5}]],ImageSize->500]

V6

GraphicsRow[Table[Graphics[square/@ad[[n]],AspectRatio->Automatic],{n,5}]]