On deterministic, constant memory triangular searches on the integer lattice

Recently it has been shown that four constant memory, deterministic agents are able to discover the integer lattice if only local, constant-size communication is allowed. Moreover, if the agents' choices are determined with the help of a fair coin, it has been shown that three are necessary and sufficient to discover the integer lattice. In this paper, we show that three deterministic agents cannot find the integer lattice and sketch a possible characterization for one explorer, three beacons type of exploration algorithm.