Tile inflation, also simply called inflation, is a replacement operation that enlarges a tiling and replaces the enlarged pattern with copies
of the original tile types at their original sizes according to a fixed rule (Ogievetsky
and Papadopolos 2001, Frank 2008). For a uniform enlargement, the dilation
has a scale factor 
, called the inflation factor. Repeated application
of the rule produces successively larger patches used to construct a substitution
tiling. Omitting the enlargement and applying the subdivision at the original
overall scale instead gives tile deflation, whose
tiles are smaller than the original tile types.
When each enlarged tile is exactly a union of whole original tiles with disjoint interiors, the operation is called stone inflation (Ogievetsky and Papadopolos 2001). More general rules allow replacement tiles to cross the boundaries of individual enlarged tiles, as occurs in rules for Penrose tiles (Frank 2008).
For example, a square enlarged by a factor of 2 can be dissected into four squares of the original size. The Mosseri-Sadoc tiles admit stone inflation with inflation factor equal to the golden ratio. In contrast, the six traditional golden tetrahedra do not admit stone inflation by any positive integer power of the golden ratio (Ogievetsky and Papadopolos 2001).
