"Grid models" in finite geometry include the 4-row 2-column
"brick space" arrays of the R. T. Curtis Miracle Octad Generator.
The remarks below on grid models suggested this post's title,
"Function Decomposition and the Klein Quadric." The result of
applying the Cullinane decomposition theorem to the final
remarks in Cameron's Parallelisms of Complete Designs —
http://m759.net/wordpress/?s=Brick+Color+Monolith .
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Connecting Diverse Mathematical Fields
The grid model acts as a unifying framework for several other abstract concepts:
Summary
The 4×4 grid model acts as a "kaleidoscope" of mathematical structure. Just as a kaleidoscope rearranges simple elements into symmetric patterns, this grid rearranges simple binary tiles to reveal the invariant structures of finite geometries, sporadic groups, and error-correcting codes. It transforms what appears to be a simple problem of tiling into a visualization of the affine 4-space over GF(2)
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