Tile deflation, also simply called deflation, is the replacement of a tiling by a finer pattern of smaller similar tiles according to a fixed geometric rule (Gardner 1989). Repeated application produces successive levels of a substitution tiling while retaining the original overall scale.
For a rule with uniform scale factor 
, tile inflation
enlarges the pattern by 
and replaces it with tiles of the original sizes. Omitting this enlargement gives
tile deflation, with child tiles scaled by 
relative to the corresponding parent tile types
(Frank 2008). For example, dividing a square into four
equal squares gives a tile deflation rule with child side
lengths half the original. For Penrose tiles, the
corresponding length ratio is 
, where 
is the golden ratio (Treibergs).
Terminology varies. Tile inflation also denotes regrouping tiles into larger tiles, in which convention tile deflation reverses the regrouping (Gardner 1989). Rules for Penrose tiles can cross whole-tile boundaries while respecting triangular half-tiles (Frank 2008).
