Retina can operate in multiple modes, but the most relevant one for computations (and the Turing-complete one) is Replace mode. In Replace modmode you give Retina an even number of source files. These are then paired, the first of each pair being a regex, and the second a replacement. These are then executed in order, manipulating the input step by step. The regex can also be preceded by a configuration (delimited with `). The most important option (which makes Retina Turing-complete) is +, which makes Retina apply the replacement in a loop until the result stops changing. In the following examples, I'm also using ;, which suppresses output on intermediate stages.