Shake Packing

Pack n unit squares (rotation allowed) into the smallest square by shaking the box.

current side—

best (session)—

best known—

n shake intensity shrink rate tries (K)

Best-known values: Erich Friedman, Squares in Squares. n>16 is not listed (—). proven optimal vs best known (not proven). Best-known values are packings found by people, not an upper bound on what a heuristic can reach — a gap of 0% is the target.

Context: the 3D n=12 unit-cube record 2.931514578 (tweets by @yoheinakajima / @kamadox) used the same shake-the-box idea; this demo is a 2D re-implementation.