COS 126 Conditionals and Loops |
Programming Assignment |
The goal of this assignment is to write five short Java programs to gain practice with expressions, loops and conditionals.
Hint. Math.max(x, y) returns the maximum of x and y.
If all three red, green, and blue values are 0, the resulting color is black (0 0 0 1).% java RGBtoCMYK 75 0 130 // indigo cyan = 0.423076923076923 magenta = 1.0 yellow = 0.0 black = 0.4901960784313726
% java Distinct 876 5309 5309 There are 2 distinct values. % java Distinct 17 17 17 There is 1 distinct value.
% java Checkerboard 4 % java Checkerboard 5 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
% java RandomWalker 10 % java RandomWalker 20 (0, -1) (0, 1) (0, 0) (-1, 1) (0, 1) (-1, 2) (0, 2) (0, 2) (-1, 2) (1, 2) (-2, 2) (1, 3) (-2, 1) (0, 3) (-1, 1) (-1, 3) (-2, 1) (-2, 3) (-3, 1) (-3, 3) squared distance = 10 (-3, 2) (-4, 2) (-4, 1) (-3, 1) (-3, 0) (-4, 0) (-4, -1) (-3, -1) (-3, -2) (-3, -3) squared distance = 18
% java RandomWalkers 100 100000 % java RandomWalkers 400 100000 mean squared distance = 100.15086 mean squared distance = 401.22024 % java RandomWalkers 100 100000 % java RandomWalkers 800 100000 mean squared distance = 99.95274 mean squared distance = 797.5106 % java RandomWalkers 200 100000 % java RandomWalkers 1600 100000 mean squared distance = 199.57664 mean squared distance = 1600.13064
As N increases, we expect the random walker to end up further and further away from the origin. But how much further? Use RandomWalkers to formualte a hypothesis as to how the mean squared distance grows as a function of N. Use T = 100,000 trials to get a sufficiently accurate estimate.
Remark: this process is a discrete version of a natural phenomenon known as Brownian motion. It serves as a scientific model for an astonishing range of physical processes from the dispersion of ink flowing in water, to the formation of polymer chains in chemistry, to cascades of neurons firing in the brain.
Submission.
Submit the files RGBtoCMYK.java, Distinct.java,
Checkerboard.java,
RandomWalker.java and RandomWalkers.java.
Finally, submit a readme.txt
file and answer the questions.