Editing Self-replication (section)

===Self-replicating tiling===
{{See also|Self-similarity}}

In [[geometry]] a self-replicating tiling is a tiling pattern in which several [[congruence (geometry)|congruent]] tiles may be joined together to form a larger tile that is similar to the original.  This is an aspect of the field of study known as [[tessellation]].  The "[[sphinx tiling|sphinx]]" [[hexiamond]] is the only known self-replicating [[pentagon]].<ref>For an image that does not show how this replicates, see: Eric W. Weisstein. "Sphinx." From MathWorld--A Wolfram Web Resource. [https://mathworld.wolfram.com/Sphinx.html https://mathworld.wolfram.com/Sphinx.html]</ref>  For example, four such [[concave polygon|concave]] pentagons can be joined together to make one with twice the dimensions.<ref>For further illustrations, see [http://www.geoaustralia.com/italian/Sphinx/Guide.html Teaching TILINGS / TESSELLATIONS with Geo Sphinx] {{Webarchive|url=https://web.archive.org/web/20160308171305/http://www.geoaustralia.com/italian/Sphinx/Guide.html |date=2016-03-08  }}</ref> [[Solomon W. Golomb]] coined the term [[rep-tiles]] for self-replicating tilings.

In 2012, [[Lee Sallows]] identified rep-tiles as a special instance of a [[self-tiling tile set]] or setiset. A setiset of order ''n'' is a set of ''n'' shapes that can be assembled in ''n'' different ways so as to form larger replicas of themselves. Setisets in which every shape is distinct are called 'perfect'.  A rep-''n'' rep-tile is just a setiset composed of ''n'' identical pieces.
{|
|- style="vertical-align:bottom;"
|[[File:Self-replication of sphynx hexidiamonds.svg|thumb|left|text-bottom|260px|Four '[[Sphinx tiling|sphinx]]' hexiamonds can be put together to form another sphinx.]]
[[File:A rep-tile-based setiset of order 4.png|thumb|right|text-bottom|290px|A perfect [[Self-tiling tile set|setiset]] of order 4]]
|}
{{clear}}