(Simulation: self-avoiding random walk) A self-avoiding walk in a lattice is a path from o...

(Simulation: self-avoiding random walk) A self-avoiding walk in a lattice is a path from one point to another that does not visit the same point twice. Self avoiding walks have applications in physics, chemistry, and mathematics. They can be used to model chain-like entities such as solvents and polymers. Write a program that displays a random path that starts from the center and ends at a point on the boundary, as shown in Figure 1a or ends at a dead-end point (i.e., surrounded by four points that have already been visited), as shown in Figure 1b. Assume the size of the lattice is 16 by 16.

FIGURE 1 (a) A path ends at a boundary point. (b) A path ends at dead-end point. (c and d) Animation shows the progress of a path step by step.