DNA and fractals

DNA is a very interesting molecule, not only for its peculiar role in life. It has a solid structure and the Watson-Crick complementarity allows the construction of complex structures, by exploiting the so called sticky ends, that is, non-paired single strands that urges to be coupled with their complementary ones. 

So, if we manipulate some DNA and give it a regular shape, we can "connect" multiple pieces like a nano-puzzle. Actually, we don't do anything as the DNA makes a self-annealing and spontaneously builds nano-structures, according to the shapes we defined and a starting seed, that is, an initial DNA sequence. More precisely, the process is driven by the encoding of the sticky ends, that decides which shapes can link to each other and how. 

It is very easy to develop a simulator, so tonight I did my own. As a test, I used the "pieces" and the seed that make the DNA construct a Sierpinsky fractal.  

My simulation of DNA self-assembly, using Sierpinsky tile set

I implemented it in a couple of hours, so my simulation algorithm is largely inefficient. For instance, it makes a "scanline" testing of all cells at each iteration, instead of keeping track of the free sticky ends in the assembly.   This means that the complexity grows with lattice's size and with the number of different pieces, too much for testing serious scenarios. Furthermore, it's a strategy that makes the whole process strictly deterministic, introducing a "bias" in the annealing process which proceeds in a very regular way (from bottom to top, from left to right). In order to reproduce all the various mistakes that can happen in the annealing process, a stochastic algorithm should be employed.

By the way, the result is interesting and fascinating. The overall technique resembles the cellular automata, in particular the fact that local rules lead to emergent phenomena, complex and unpredictable.