Random Walker Collisions In lecture, we saw how to model the behavior of a random walker on a 2D grid using a Monte Carlo simula
tion. In this problem, we will investigate collisions between two of these random walkers. Specifically, use your simulation to track the distances of the two walkers until they collide. 1. Start by writing a MATLAB script to simulate the path that the single random walker A takes on an 11 x 11 grid of tiles. Let this random walker use a random compass as shown in class. Thus, the probability p of moving in the North, East, South, and West directions is given by 0.2. The remaining probability is the one used to stay put. If the random walker tries to move "past" one of the boundaries on its turn, his position does not change (you can think of this as a particle bumping into a wall and staying still). Choose a random tile to let the random walker A start his walk. Lastly, write a function to update the position of the random walker A. The function must use exactly the function header shown below, i.e. the function name and number and ordering of inputs and outputs must be followed exactly. function (x,y) = Randwalk_2D (x0, y0, BC) Here, x0 and y0 are the initial positions of the random walker, BC is the array of boundary conditions, and x and y are the updated positions of the random walker. 2. Add the random walker B to your simulation who moves according to its own randomly generated values using the same compass as the random walker A in Part 1. Let the random walker B start his walk on the tile that is furthest away from the start tile of walker A. At each iteration, both walkers move simultaneously to an adjacent tile using the rules outlined in Part 1. Continue updating the position of both walkers until a collision occurs (or until the maximum number of iterations, which is set to 1000, is reached). More precisely, a collision occurs when both random walkers occupy the same tile after both have completed their move. Furthermore, a collision occurs when both random walkers are next to each other and move to the other one's tile. Note that in this instance, the collision appears on their way, but both random walkers will end up on tiles that are again next to each other. In other words, collision also appears when their paths cross. 3. Track the movement of each random walker by storing their positions in four 1D-arrays associated with their x- and y-positions in the grid. After the simulation, calculate for each iteration the distance between the random walkers A and B, and plot the results vs. the number of iterations to see when the two random walkers A and B came close to each other and when they were far away from each other.
