We introduce Parametrized Recurrent Systems (PRS) as a tool for image
generation. They are an extension of Mutually Recursive Function Syste
ms allowing variable transformations (depending on parameters). A spec
ial case of PRS are MRFS with pasting, a very natural and convenient p
ractical tool for image design. PRS cannot be step by step simulated b
y MRFS, however, we show that every PRS can be converted into an MRFS
with the same number of transformations that generates the same image
(attractor).