DNA NANOTECHNOLOGY AND ITS BIOLOGICAL APPLICATIONS - Bio-Inspired and Nanoscale Integrated Computing - page 366

Figure 13.11. A modulo-2 version of Pascal's Triangle, known as the Sierpinski
Triangle [11]. (Figure adapted with permission from [11].)

Figure 13.12 gives Winfree's design for a self-assembled binary counter [12],
starting with 0 at the first row, and on each further row being the increment by 1 of
the row below. The pads of the tiles of each row of this computational lattice were
designed in a similar way to that of the linear XOR lattice assemblies described in
the prior section. The resulting 2D counting lattice is found in MUX designs for
address memory, and so this patterning may have major applications for
patterning molecular electronic circuits.

0 1 0 1

0 0

0

0 1

1

0 0 0 1 1 a

0 0

0 1 0 1

0 0 1 1 0 1 0 1

0 a

0

0 0

0 0 1 1

1

0 1 1 0

1

0 0 1 1

0 0

1

0 0 0 0 1 0 1 1

0 a

0 0 1

0 0

S

0 1 a 0 0 0 1 1 0 1 a

0 0

0 0 0 1

0 00 0 0 0 1 1

0 a

0 0 0

0

0 0 0

0

S

Figure 13.12. A modulo-2 version of Pascal's Triangle (known as the Sierpinski
Triangle) [11].