  We review Kajiwara and Watatani's construction of a C*-algebra from an
iterated function system (IFS). If the IFS satisfies the finite branch
condition or the open set condition, we build an injective homomorphism from
Kajiwara-Watatani algebras to the Cuntz algebra, which can be thought as the
algebra of the lifted system, and we give the description of its image.
Finally, if the IFS admits a left inverse we show that the Kajiwara-Watatani
algebra is isomorphic to an Exel's crossed product.

Operator Algebras;Dynamical Systems