Cellular Automaton on organic molecular assembly: 

Solving problems that even fastest supercomputers can not solve in a finite time (2010)

 

 

Cellular automaton is an useful tool to represent logical events in terms of patterns. We have described association of our research with CA in details here. Untill now Bernstein group made significant contribution in this field by creating several logic gates using the principle of Cellular Automaton.

 

 

However, building a 2 D CA grid has always been a challenge unresolved for decades. Here are the challenges.

 

1. A single CA cell should communicate with several neighbors in a quantum mechanical way, i.e. not one-by-one, rather all at a time. The problem with this approach is that imposing the condition of "equal probability" in a nearest neighborhood circuit. Its technologically impossible to create two identical CA cells, then making identical wiring between so many neighbors is impossible without self-assembly.

 

2. CA computers will not use software, the circuit should be built in such a way that it will undergo pattern evolution by itself, this is not as simple as it seems. First, the structure remembers the CA rules, how? Second, a massive selection of rules are automatically applied, how? The circuit must structurally reconfigure itself to exhibit both the qualities mentioned here.

 

3. A CA grid is only useful if some particular conditions are satisfied. (a) the starting of pattern evolution must be triggered from outside, not spontaneous. (b) Information must be erased reversibly, grid would be ready by then for the next evolution. (c) Rules must not vary locally at different places depending on the grid location.

 

 

All these problems have been resolved in the DDQ molecular CA grid.

 

 

 

An analogue computer Performs operations in a truly parallel manner. Meaning it can perform many calculations all at the same time. and operates using continuous variables. Meaning it uses numbers that that change not in steps, but change in a smooth continuous manner. One example is shown below.

 

 

By constrast, a digital computer can only perform sequential (one at a time) operations, and operates on discrete (noncontinuous) numbers. In the above we have simply replicated a kind of pattern. Such kinds of pattern evolutions are frequently observed in the field of unconventional computing, theoretically. However, when we realize it on a molecular grid, all cells update independently.

 

Is this something like 800 computers are working parallely? No not at all there is a significant difference between the parallel computers and parallely updating CA cells, simultaneity, spontaneous interactions.

 

 

Below is the image of encoding cancer cell evolution problem on the organic monolayer.

 

 

 

In the present case we have fusion of the two kind of computing. First, it does not use continuous variables rather uses discrete numbers to represent parameters, however, operations are almost like an analogue system. So we assign physical parameter existing in nature, and this parameter evolves with time to provide solution of the problem.

 

Below is the encoding of diffusion problem.

 

 

 

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