The Interaction Combinators are possibly the simplest multidimensional system of interaction nets that is Turing-complete. What about interaction nets with only 2 ports - 1 principal, 1 auxiliary? What is the simplest of those systems which is Turing-complete?
Turing machines and unidimensional cellural automata may both be regarded as "unidimensional" interaction net systems (see Lafont's Interaction Combinators paper). So any simple UTM or Turing-complete cellula automaton induces a "simple" Turing-complete system. I'm afraid no better answer is known.
Anyway, "simple" is relative: the interaction net system corresponding to even a very small UTM is big compared to the interaction combinators. Cellular automata probably give smaller systems (although still bigger than the interaction combinators) but the interest of these is nevertheless unclear as no special feature of interaction nets is used about them, they are just paraphrases of the original model.