I devised a grammar for arithmetic expressions which is less readable than either standard or RPN notation.
Basically, an arithmetic expression is a tree. Standard notation indicates the shape of the tree with brackets, RPN by listing the nodes in the order of a particular tree walk. My notation visually indicates whether each node is connected on the right or left. Examples:
Standard: 1+2
RPN: 1 2 +
Tree: 1'+`2
Standard: 1*(2+3)
RPN: 1 2 3 + *
Tree: 1'*2'`+`3
It looks a bit nicer if ' and ` are mirror images in the font you are using, but it's still not very readable. I did hope that you could leave the tags off leaves and only put them on operators, but this isn't sufficient to make each tree shape unique.
The idea was just to find something visually interesting*