Diagonal and Non-Diagonal Glue Functions

The glue function of a tile system is said to either be diagonal or non-diagonal. Diagonal glue functions only allow for interactions in which the glues participating in the reaction must be similarly labeled. Non-diagonal glue functions, on the other hand, allow for interactions between glues with different labels. The reason for the names diagonal and non-diagonal comes from what happens if one lays the glues out on a grid. The numbers on the grids below represent the strength of attraction between the top and left glues representing any given cell. Looking at the two grids below, it can be seen that one grid, the one representing the diagonal glue function, has every number placed only in the center diagonal of that grid. While the other grid, representing the non-diagonal glue function has numbers spread throughout the whole of the grid. When designing tile assembly systems it is generally more favored, although not necessarily as easy or even possible, to design one that uses a strictly diagonal glue functions. The reasoning for this is that the diagonal class of glue functions allow for a clear seperation of the attraction between any one glue type and another leading towards something more physically viable and practical.