There's nothing as iconic as E=mc^2, but what a fun question! Here are some ideas.
- How about the minimal ANSI C program "int main(int argc, char argv) {return 0;}"?
- You could look up the code designed by Ada Augusta, Countless Lovelace. It's much like a spreadsheet.
- A few code snippets are of historical interest in that they have unfortunately caused satellites to fall out of orbit.
- Some code snippets have been used as email signatures for political reasons, such as short implementations of RSA or DeCSS.
- David A. Wheeler's website has a nice rundown of modern history's important software innovations, but only a couple of those, like RSA, can be implemented in a few (appropriately) cryptic lines.
- There are a number of mathematical algorithms of interest, such as the Euclidean algorithm for greatest common divisor (GCD) and the Newton or Newton-Raphson method.
- Some modern fundamental algorithms such as binary search and quicksort are compact.
- You might like some variant of "the computus", the formula for calculating the date of Easter. It bores me, but I enjoy the similar Zeller's congruence.
- The movie "The Social Network" features something like the tf-idf formula and the movie "A Beautiful Mind" features Nash equilibrium.
- The Ackermann function is fun, being a brief and notably slow formula for practically all arithmetic. Going the other way around you get Peano axioms and perhaps computations with Church numerals.
- A grammar for the lambda calculus can be three simple lines.
- Our gracious host in "The Roots of Lisp" states Lisp "eval" somewhat briefly, based on McCarthy's original, which Alan Kay called "Maxwell's equations of software".
- The truth table for NAND is a nice little graphic and the NAND function happens to be sufficient to implement all Boolean functions.
Now we could start to get into other diagrams from computer science and software engineering, but that's a vast area and you didn't actually ask for it.
