In quantum field theory class, we are doing spinors. The representations of the Lorentz algebra $\mathfrak{so}(3,1) = \mathfrak{su}(2) + i \mathfrak{su}(2)$ are indexed by two integers. Then (1,2) and (2,1) are the left and right spinor representations, $\phi_a, \phi_{\dot{a}}$.
In the homework, we're asked to prove identities using spinor notation like $\psi\chi = \chi\psi$ and $(\psi\sigma^\mu\chi^\dagger)^\dagger = \chi\sigma^\mu\psi^\dagger$ by unsuppressing the indices (so $\psi \chi = \psi_a \chi^a$ and $\psi^\dagger \chi^\dagger = \psi^{\dagger\dot{a}} \chi_{\dagger\dot{a}}$.
I started developing "box" notation to keep track of which index is being matched/contracted with which other index in expressions like $ \epsilon^{ab}\epsilon^{\dot{a}\dot{b}}\sigma^\mu_{a \dot{a}}\sigma^{\nu}_{b\dot{b}} $. Since these are anticommuting variables, such notation would have to remember order of multiplication.
I started coming up with nice ways to handle upper and lower indices with upward and downwoard pointing boxes, tricks for handing Dirac and Majorana spinors and Hermitian conjugates. Has diagrammatic calculus for spinors already been built somewhere?? I think Penrose did such a thing for twistors.