What algorithm does Excel use to recalculate formulas?

Question

Are the formulas represented in a syntax tree then recalculated using a design pattern like the Visitor pattern? How would you go about reproducing the recalculation process

Answer 1

Are the formulas represented in an AST then recalculated using a design pattern like the Visitor pattern?

You're thinking interpreter, not visitor. While treewalking using a visitor can be employed in conjunction with interpretation, employing an interpreter makes more sense here (hence the name). What this does is basically what friol wrote, i.e. traverse the tree in post-order and execute the function associated with each node.