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.
% java Ordered 10 17 49 true % java Ordered 49 17 10 true % java Ordered 10 49 17 false
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 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 formulate 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 Ordered.java, RGBtoCMYK.java,
Checkerboard.java,
RandomWalker.java and RandomWalkers.java.
Finally, submit a readme.txt
file and answer the questions.