Notation for iterative process on set

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How can I define a software program's iterative function with the below defined constraints using mathematical notation?

  • $T$ is the set of individual glyphs that are stringed together in a container (png file), called $I$.
  • One iteration results in $t_i$ being identified (boxed) in $I$, the result being $I_i$; $I_i$ is the input to the next iteration.
    • That is, $t_i+1$ is now identified in $I_i$, the result of which is $I_i+1$
  • The final result is $I_n$ where all $t$ have been identified.

This is what I currently have, but it doesn't fill me with great confidence.

$\sum\limits_{t = 0}^n f(t, I_{t-1}) = I_t $