# LAB 12

## Objectives

- Simulate Motion
- Experience Random Walk

# TASK

In this lab you will develop a program to simulate the random movement of robots. You will also re-run the simulation after introducing a symmerty-breaking field.
Write a *main* program as follows:

program Lab12
implicit None
integer*4 duration /100/, maxExp /10000/
real*8 distance(10000), angle(10000)
call simulate(duration, maxExp, distance, angle)
call showDistribution(maxExp, distance, angle)
end

The robot starts at the origin and then moves one unit toward the right, left, up, or down, in one second. The choice of direction is uniformaly-distributed. We will allow the robot to move about for 100 seconds and record the polar coordinates of its final position in the two arrays distance (away from origin) and angle (of the final radial with the x-axis). We will take the angle in radians between -pi/2 and +pi/2. The above experiment will be repeated maxExp times (100,000 in the above main).
Main invokes *simulate* which populates the arrays. Note that it should work for any duration (not just 100) and any maxExp (not just 100,000). It does the simulation by invoking the sub

subroutine step(x,y)
implicit None
integer*4 x, y

which takes the starting point coordinates (x,y) and return the new ones, also in x,y.
The show sub simply tabulates the two arrays on a disk file so that each record would have three numbers: the experiment number, the distance, and the angle
Run the program and (using Excel) generate a chart with the experiment# on the x-axis and the distance as well as the angle as two series on the y-axis.

Modify the step subroutine so that the robot chooses to go EAST 40% of the times and chooses the other 3 directions with probability 20% each. Run the modified program and generate a chart using the new data. Prepare for checking:

- Original Program Listing
- Modified step subroutine
- The two charts (before and after the EAST bias)
- A brief explanation of the charts (just examine the charts and state any observation you see and its justification).

*Fall2002/HR*