Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Working in Winfree's abstract tile assembly model,  show that a constant-sized tile assembly system can be programmed through relative tile concentrations to build an $n\times n$ square with high probability for any sufficiently large $n$. This ansrs an open question of Kao and Schller [Automata, Languages and Programming, Lecture Notes in Comput. Sci. 5125, Springer, Berlin, 2008, pp. 370-384], who shod how to build an approximately $n\times n$ square using tile concentration programming and asked whether the approximation could be made exact with high probability.  show how this technique can be modified to ansr another question of Kao and Schller by showing that a constant-sized tile assembly system can be programmed through tile concentrations to assemble arbitrary finite scaled shapes, which are shapes modified by replacing each point with a $c\times c$ block of points for some integer $c$. Furthermore,  exhibit a smooth trade-off beten specifying bits of $n$ via tile concentrations versus specifying them via hard-coded tile types, which allows tile concentration programming to be employed for specifying a fraction of the bits of “input” to a tile assembly system, under the constraint that concentrations can be specified to only a limited precision. Finally, to account for some unrealistic aspects of the tile concentration programming model,  show how to modify the construction to use only concentrations that are arbitrarily close to uniform.
['David Doty']
I am writing a research paper on a idea Randomized Self-Assembly for Exact Shapes
[{"from": "human", "value": "I am writing a research paper on a idea Randomized Self-Assembly for Exact Shapes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Working in Winfree's abstract tile assembly model,  show that a constant-sized tile assembly system can be programmed through relative tile concentrations to build an $n\\times n$ square with high probability for any sufficiently large $n$. This ansrs an open question of Kao and Schller [Automata, Languages and Programming, Lecture Notes in Comput. Sci. 5125, Springer, Berlin, 2008, pp. 370-384], who shod how to build an approximately $n\\times n$ square using tile concentration programming and asked whether the approximation could be made exact with high probability.  show how this technique can be modified to ansr another question of Kao and Schller by showing that a constant-sized tile assembly system can be programmed through tile concentrations to assemble arbitrary finite scaled shapes, which are shapes modified by replacing each point with a $c\\times c$ block of points for some integer $c$. Furthermore,  exhibit a smooth trade-off beten specifying bits of $n$ via tile concentrations versus specifying them via hard-coded tile types, which allows tile concentration programming to be employed for specifying a fraction of the bits of \u201cinput\u201d to a tile assembly system, under the constraint that concentrations can be specified to only a limited precision. Finally, to account for some unrealistic aspects of the tile concentration programming model,  show how to modify the construction to use only concentrations that are arbitrarily close to uniform."}]