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# Self-assemblying Classes of Shapes with a Minimum Number of Tiles, and in Optimal Time

@inproceedings{Becker2006SelfassemblyingCO, title={Self-assemblying Classes of Shapes with a Minimum Number of Tiles, and in Optimal Time}, author={Florent Becker and Ivan Rapaport and Eric R{\'e}mila}, booktitle={FSTTCS}, year={2006} }

- Published 2006 in FSTTCS
DOI:10.1007/11944836_7

In this paper we construct fixed finite tile systems that assemble into particular classes of shapes. Moreover, given an arbitrary n, we show how to calculate the tile concentrations in order to ensure that the expected size of the produced shape is n. For rectangles and squares our constructions are optimal (with respect to the size of the systems). We also introduce the notion of parallel time, which is a good approximation of the classical asynchronous time. We prove that our tile systems… CONTINUE READING

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