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Jonoska, N. ) UCNC 2012. LNCS, vol. 7445, pp. 34–62. Springer, Heidelberg (2012) 9. : Algorithmic Self-Assembly of DNA. PhD thesis, California Institute of Technology (June 1998) 10. : Intrinsic universality and the computational power of self-assembly. In: MCU: Proceedings of Machines, Computations and Universality, September 9-12. Electronic Proceedings in Theoretical Computer Science, vol. 128, pp. 16–22 (2013) 11. : Active self-assembly of algorithmic shapes and patterns in polylogarithmic time.

First, in the → → case of no movement we have − u =− u . Thus we have a rule of the form r = → − → − (s1, s2, b, u ) → (s1 , s2 , b , u ), where the monomer pair may change state (s1 = s1 and/or s2 = s2 ) and/or change bond (b = b ), examples are shown in Figure 1(b). If si ∈ {s1, s2} is empty and si is not, then the rule is said to induce the appearance of a new monomer at the empty location. If one or both monomer states go from non-empty to empty, the rule induces the disappearance of one or → → both monomers.

Figure 3 shows a simple example construction using only local rules, while Figure 2 gives two examples of agitation. The model uses a two-dimensional triangular grid with a coordinate system using axes x and y as shown in Figure 1(a). A third axis, w, is defined as running → → → through the origin and − w = −− x +− y = (−1, 1), but we use only the x and y → → → coordinates to define position. The axial directions D = {±− x , ±− y , ±− w } are → − 2 the unit vectors along axes x, y, w. A pair p ∈ Z is called a grid point and has → → → the set of six neighbors {− p +− u |− u ∈ D}.