Abstract: A resilient mat system where a mat has overall mat thickness T, and the mat has an upper layer with an upper layer thickness t, and a plurality of supporting resilient substructure columns, each column having a relatively uniform height h, such that T=t+h, wherein the ratio of h:t>3.5 for values of T>about 0.9 inch. Each column has a column wall that surrounds a central void in the column with the void opening at a bottom of the column. The column has lower zone that is a more compressible, relatively collapsible zone, and an upper zone that is a less compressible, relatively uncollapsible zone. There is a fenestrated mat connector with connector fenestrations sized and numbered to receive the bases of a plurality of columns from two mats therein.