1.Create a new function three_d_walk(num_steps) that performs a 3-dimensional random walk of length num_steps, by starting at the origin (x, y, z) = (0, 0, 0) and rolling a fair 6- sided die to determine the direction of each step (up, down, left, right, front, back). The function should return the column vectors [x, y, z] which record the coordinates of each step of the walk.
Hint: use the two_d_walk_UDLR(num_steps) function as a template.
2. Create a new script visualize_3_d_walk that calls your function in 1. and uses the plot3() and scatter3() functions to visualize the results of a 3-dimensional walk of 10, 000 steps.
Hint: use the visualize_walks script as a template.
3. Write a script average_distance_plot that uses the distance_of_walkers() function to perform 10, 000 UDLR and angle walks of length num_steps for each value of num_steps in the list 10:10:1000, and returns the average distance from the origin in column vectors averages_UDLR and averages_angle.
Your script should also plot the resulting averages against the vector 10:10:1000 on the same axis. Use a red solid line with square markers for the UDLR averages, and a blue solid line with circle markers for the angle average. Include a legend, label your axes appropriately, and include a descriptive title.
4. Using the graph in 3., hypothesize about the functional relationship between the number of steps in a walk and the average distance of the walker from the starting point. Does the relationship seem to depend on which type of walk (UDLR or angle) is performed?
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