Iterative Self-assembly with Dynamic Strength Transformation and Temperature Control

We propose an iterative approach to constructing regular shapes by self-assembly. Unlike previous approaches, which construct a shape in one go, our approach constructs a final shape by alternating the steps of assembling and disassembling, increasing the size of the shape iteratively. This approach is embedded into an extended hexagonal tile assembly system, with dynamic strength transformation and temperature control. We present the construction of equilateral triangles as an example and prove the uniqueness of the final shape. The tile complexity of this approach is O(1).