Clark Kimberling, Second-degree involutory symbolic substitutions,
Forum Geometricorum, 8 (2008) 175--182.
Abstract: Suppose a,b,c are algebraic indeterminates. The mapping (a,b,c)
-> (bc,ca,ab) is an example of a second-degree involutory symbolic
substitution (SISS) which maps the transfigured plane of a triangle to itself.
The main result is a classification of SISSs as four individual mappings
and two families of mappings. The SISS (a,b,c)->(bc,ca,ab) maps the circumcircle
onto the Steiner ellipse. This and other examples are considered.