**MS&E 319, Spring 2004. Molecular Self-Assembly: Models and Algorithms**

**Instructor: Ashish Goel**

**HW 1. Due 4/29/4.**

- Install xgrow, and
explore running xgrow with some example tile sets. This simulator is available
from http://www.dna.caltech.edu/Xgrow/xgrow_www.html
- Consider the counter
that uses different primes to count based on Chinese remaindering. To
understand this counter, run the program xgrow on the tile set primes_2_3_5.tiles
using the command

xgrow primes_2_3_5.tiles block=12 size=32 T=3

Also use this as an example to
understand xgrow. Drop by my office (make an appointment) if none of this makes
sense. The tile set was automatically generated by the program primes.C, which is
well-commented. Use this program to generate some more simple prime counters.
Red tiles correspond to tiles labeled 0.

- Now read the paper “Optimal self-assembly of
counters at temperature two”. Observe that the prime counters
are not partial order systems (and hence their dependence graph may be
acyclic). Also, the prime counters do not have the deterministic RC
property.
- Prove that the prime
counter system assembles into a unique terminal assembly.
- Analyze the assembly
time of this system.