14. The method of claim 13, wherein:
in step (ii), the multimer of seed tiles is formed in a plane with a top and bottom face from the monomers of seed tiles through the annealing of a plurality of sticky ends with nucleic acid sequence complementarity at the adjacent edges of monomeric seed tiles; and the plurality of single stranded nucleic acid ends that protrude perpendicularly from the top or bottom face of each monomeric seed tile are on the same face of the multimer of seed tiles;
in step (iii), the formed multimer of seed tiles is mixed with monomers of 1G tiles and the monomers of 1G tiles are allowed to anneal to each other and to the multimer of seed tiles to form a stacked multimer of seed and 1G tiles that serves as a first recognition complex for self-replication, wherein:
the annealing of monomers of 1G tiles to each other through sequence complementarity between the plurality of protruding single stranded ends at the edges of adjacent monomeric 1G tiles forms a multimer of 1G tiles in a plane with a top and bottom face;
the plurality of single stranded nucleic acid ends protruding perpendicularly from the plane of the substantially two dimensional monomeric 1G tiles are on the same face of the multimer of 1G tiles; and
the annealing of monomers of 1G tiles to the monomeric seed tiles in the multimer of seed tiles is through sequence complementarity between the plurality of single stranded nucleic acid ends that protrude perpendicularly from the planes of the monomeric daughter tiles and the monomeric seed tiles so as to form the stacked multimer in which the plane of the multimer of seed tiles is parallel to the plane of the multimer of 1G tiles and joined thereto by sticky end cohesion;
in step (iv), at least two of the plurality of annealed sticky ends between adjacent monomers in the multimer of daughter tiles forming the first recognition complex are allowed to react to covalently link with complementary strands in the at least two annealed sticky ends so as to be resistant to heat denaturation at a melting temperature (Tm) which denatures the sticky end cohesion between the monomers of seed tiles and monomers of 1G tiles;
in step (v), the sticky end cohesion between monomers of seed tiles and monomers of 1G tiles is denatured by heating at the Tm so as to separate the multimer of 1G tiles, which is resistant to heat denaturation, from the multimer of seed tiles to release the multimers of the first recognition complex;
in step (vi), the heat resistant multimer of 1G tiles are allowed to anneal with monomers of 2G tiles and the monomers of 2G tiles are allowed to anneal to each other to form a second stacked multimer of 1G and 2G tiles that serves as a second recognition complex for self-replication, wherein:
monomers of 2G tiles are annealed to each other through sequence complementarity between the plurality of protruding single stranded ends at the edges of adjacent monomeric 2G tiles to form a multimer of 2G tiles in a plane with a top and bottom face;
the plurality of single stranded nucleic acid ends protruding perpendicularly from the plane of the substantially two dimensional monomeric 2G tiles are on the same face of the multimer of 2G tiles; and
the monomers of 2G tiles are annealed to the monomeric 1G tiles in the heat resistant multimer of 1G tiles through sequence complementarity between the plurality of single stranded nucleic acid ends that protrude perpendicularly from the planes of the monomeric 2G tiles and the monomeric 1G tiles so as to form the second stacked multimer in which the plane of the heat resistant multimer of 1G tiles is parallel to the plane of the multimer of 2G tiles and joined thereto by sticky end cohesion;
in step (vii), at least two of the plurality of annealed sticky ends between adjacent monomers in the multimer of 2G tiles forming the second recognition complex are allowed to react to covalently link the complementary strands in the at least two annealed sticky ends together so as to be resistant to heat denaturation at the Tm which denatures the sticky end cohesion between the monomers of the 1G tiles and monomers of 2G tiles;
in step (viii), the sticky end cohesion between the heat resistant multimer of 1G tiles in one plane and the heat resistant multimer of 2G tiles in a second parallel plane is denatured by heating at the Tm to separate the heat resistant multimer of 2G tiles from the heat resistant multimer of 1G tiles to release the heat resistant multimers of 1G and 2G tiles from the second recognition complex;
in step (ix), the heat resistant multimer of 1G tiles and the heat resistant multimer of 2G tiles obtained from step (viii) are mixed with monomers of 1G tiles and 2G tiles with monomers of 1G tiles being allowed to anneal to each other and to the heat resistant multimer of 2G tiles and monomers of 2G tiles being allowed to anneal to each other and to heat resistant multimers of 1G tiles, both forming the second stacked multimer that serves as the second recognition complex, wherein
the monomers of 1G and 2G tiles are annealed to corresponding monomers of 1G and 2G tiles through sequence complementarity between the plurality of protruding single stranded ends at the edges of adjacent monomeric 1G or 2G tiles to form a multimer of 1G tiles and a multimer of 2G tiles, both of which have a plane with a top and bottom face;
the plurality of single stranded nucleic acid ends protruding perpendicularly from the plane of the substantially two dimensional monomeric 1G tiles and the plane of the substantially two dimensional monomeric 2G tiles are on the same face of the multimer of 1G tiles and the multimer of 2G tiles, respectively; and
the monomers of 1G or 2G tiles are annealed respectively to the monomeric 2G or 1G tiles in the multimer of 2G or 1G tiles through sequence complementarity between the plurality of single stranded nucleic acid ends that protrude perpendicularly from the planes of the monomeric 1G tiles and the monomeric 2G tiles so as to form the second stacked multimer in which the plane of the multimer of 2G tiles is parallel to the plane of the multimer of 1G tiles and joined thereto by sticky end cohesion;
(x) at least two of the plurality of annealed sticky ends between adjacent monomers in the multimer of 1G tiles and in the multimer of 2G tiles in the second recognition complex are allowed to react to covalently link the complementary strands in the at least two annealed sticky ends together so as to be resistant to heat denaturation at the Tm which denatures the vertical sticky end cohesion between monomers of 1G tiles and monomers of 2G tiles;
(xi) the sticky end cohesion between the heat resistant multimer of 1G tiles in one plane and the heat resistant multimer of 2G tiles in a second parallel plane is denatured by heating at the Tm to separate the heat resistant multimers and release them from the second recognition complex;
(xii) repeating steps (ix)-(xi) one or more times to self-replicate and exponentially amplify multimers of 1G and 2G tiles.