This is the idea behind Kolmogorov complexity[0], that the complexity of a string (finite or infinite) can be measured, relative to a programming language, as the the length of shortest program which produces it.
Precisely computing the Kolmogorov complexity of a given string could be very difficult, though. In general, it is uncomputable because we cannot decide if a given program will output a given string.
[0]: https://en.wikipedia.org/wiki/Kolmogorov_complexity
