Assignments for CS 111

Create a new app called ChaosGameApp that has the procedures described below.

This app consists of two parts:

a drawing portion
a non-graphical portion that has a collection of various mathematical procedures

The overall theme is while loops and creating and updating variables by observing patterns in the computational process.

Canvas Functionality

Touch Interaction

Here is how to wait until the player touches the screen and how to extract the touch coordinates:

Touch touch = canvas.waitForTouch();
double touchX = touch.getX();  
double touchY = touch.getY();

Note that **touch, touchX, touchY** could be any names of your choice.

Random Integers

Here is how to get a random integer in a given range [a , b]:

int number = canvas.getRandomInt( 10, 20 );  // picks random integer in [10..20] inclusive

Note that **number** could be any name of your choice.

ChaosGameApp: Drawing Portion

drawPattern(x1, y1, x2, y2, x3, y3, n)

This procedure takes as parameters:

three (x, y) pairs which represent the coordinates of the vertices of a triangle
number n which represents a number of trials/repetitions; for testing use a big number for n, 10000 or more

The procedure works as follows:

Wait for player to touch the screen anywhere inside the triangle, draw the point of touch (in black) and remember its coordinates
Repeat the following steps as many times as specified by n:
Pick a random number in [1..3] (inclusive; use canvas.getRandomInt):
- for 1, move the point of touch halfway towards vertex (x1, y1) and draw the point at its new position in red
- for 2, move the point of touch halfway towards vertex (x2, y2) and draw the point at its new position in green
- for 3, move the point of touch halfway towards vertex (x3, y3) and draw the point at its new position in blue

Essentially, the original touch point gets updated by moving around the triangle towards the vertex chosen by the random number and gets drawn in the corresponding color.

Halfway towards means that the (x, y) coordinates of the point get updated to be the average of its current coordinates and the coordinates of the chosen vertex.

Here is an example of a possible execution when the game is run for only 2 moves in the triangle (50, 100), (300, 100), (200, 380) and the player touched point (260,200):

(click image to enlarge)

drawPattern(50, 100, 300, 100, 200, 380, 2)

player touched point (260,200)
the die first rolled 3, so the point moved halfway to vertex 3 (200,380) and the point coordinates became (230,290) where 230=(260+200)/2 and 290=(200+380)/2) with color BLUE
the die next rolled 1, so the point moved halfway to vertex 1 (50,100) and the point coordinates became (140,195) where 140=(230+50)/2 and 195=(290+100)/2) with color RED (the point used its new coordinates)

Play the game a few times with different triangles and different starting touch points. Use big numbers for n, 10000 or more.

What types of patterns could you create?

ChaosGameApp: Math Portion

mystery(n)

This procedure computes the sum of the first n >= 0 terms in the following summation:

-4.0 + 4.0/3 - 4.0/5 + 4.0/7 - 4.0/9 + 4.0/11 - ... and so on

(Note: mystery(0) returns 0, since we asked for 0 terms.)

What mystery number is computed by this procedure? Try large values of n and then change the name mystery to a more appropriate name.

double cfrac(int n)

This procedure computes a continued fraction up to depth n >= 0. A continued fraction is an expression of the form given below. (Note: cfrac(0) returns 0.)

Hint: It is easier to work backwards (bottom to top) one fraction per loop cycle.

n = 0
returns: 0

n = 1

  1
-----
1 + 0

returns: 1

n = 2

   1     
-------
      1
1 + -----
    2 + 0

returns: 0.6666667

n = 3

    1
--------
       1
1 + -------
          1
    2 + -----
        3 + 0

return: 0.7

n = 4

    1
--------
       1
1 + --------
           1
    2 + -------
              1
        3 + -----
            4 + 0

returns: 0.6976744186046512

n = 5

   1
-------
      1
1 + -------
          1
    2 + -------
              1
        3 + -------
                  1
            4 + -----
                5 + 0

returns: 0.6977777777777778

n = 100

   1
-------
      1
1 + -------
          1
    2 + -------

           .. .. .. ..

                     1
            99 + -------
                 100 + 0

returns: 0.697774657964008

double carfc(int n)

This procedure computes a different continued fraction up to depth n >= 0. (Note: carfc(0) returns 0.)

Hint: It is easier to work backwards (bottom to top) one fraction per loop cycle.

n = 0
returns: 0

n = 1

  1
-----
2 + 0

returns: .5

n = 2

   1
-------
      3
2 + -----
    4 + 0

returns: 0.36363636363636365

n = 3

   1
-------
      3
2 + -------
          5
    4 + -----
        6 + 0

returns: 0.3815789473684211

n = 4

   1
-------
      3
2 + -------
          5
    4 + -------
              7
        6 + -----
            8 + 0

returns: 0.3795620437956204

n = 5

   1
-------
      3
2 + -------
          5
    4 + -------
              7
        6 + -------
                  9
            8 + ------
                10 + 0

returns: 0.37974515529599157

n = 100

   1
-------
      3
2 + -------
          5
    4 + ---------

      .. .. .. ..

                    199
            198 + -------
                  200 + 0

returns: 0.37973195474099564

In public void run(), for each procedure give at least three test cases of your own that demonstrate that your code is correct. These could be commented out as we do in class.

CS 111
Computer Science I

ChaosApp

Canvas Functionality

ChaosGameApp: Drawing Portion

ChaosGameApp: Math Portion

CS 111 Computer Science I

ChaosApp

Canvas Functionality

ChaosGameApp: Drawing Portion

ChaosGameApp: Math Portion

CS 111
Computer Science I