Platform Color Designs for Interactive Molecular Arrangements

It has been shown that alternating attachments of two types (species) of floating molecular (DNA based) tiles on a predesigned array that consists of communicating neighboring DNA tiles complementary to the floating tiles can dynamically simulate some types of cellular automata (CA). We show that the model can simulate any elementary one dimensional CA confirming the universal computational power of the model. We address the question of which design of the platform array provides communication across the whole plane. We show that for square tiles only the checkerboard arrangement of the two species can provide communication between any two tiles of the plane. On the other hand, there are an uncountable number of arrangements of two colors of hexagonal tiles on the plane which provide communication between any two tiles.

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