Use the message passing technique to simulate a random walk of n objects on a "periodic" or "circular" integer lattice. The rules are described as the following: 1. The lattice can be discretized as N grid points with a location at 1, 2, ..., N.
2. Initially, the n objects can be placed anywhere randomly in the lattice. One or more objects can occupy the same grid point at any given time.
3. Each object must flip a coin before moving a step: Move 1 step to the right (Head) or Move 1 step to the left (Tail).
4. If an object located at grid point N moves 1 step to the right, it should land in grid point 1. If an object located at grid point 1 moves 1 step to the left, it should land in grid point N.
The lattice should be distributed into np partitions where np is the number of workers (cpus/cores). For example, for the case where N=10 and np=2, worker 1 is taking care of grid 1, ..., 5, and worker 2 is taking care of grid 6, ..., 10.
Utilize the commands labSend, labProbe, labReceive, and labBarrier to deal with objects crossing partitions. Stop the simulation when all objects achieve M steps. Plot the initial and final positions of all objects.