Press [MODE] and select Graph....... FUNCTION. Also, split the screen by selecting the following in Page 2:

In the Data/Matrix Editor screen, highlight the c1 column header and define
c1 = seq(rand(100),n,1,50)
Give an identical definition to column c2.
This is such that the two columns together give the (x,y) coordinates of 50 points chosen at random in a 100 by 100 square.

Press [F2] Plot Setup then press [F1] Define. Complete the dialog box as shown to set up the scatter plot:

Press [¨][WINDOW] and enter the following values:

Pressing [¨][GRAPH] will produce the following scatter plot, with the left screen showing 0 < x,y < 100.

Superimposing the quarter-circle is done by pressing [¨][Y=] and defining
y1 = sqrt(10000 - x²)

Moving across to the Text Editor screen allows the explanatory text to be entered. We counted the number of points inside the quadrant manually, and at each run through of the simulation only the numbers highlighted in red in the screenshot below were altered.

A new set of random numbers is generated every time the Data/Matrix Editor is called up. From the GRAPH screen, press [APPS] 6:Data/Matrix Editor 1:Current. When the table has been generated anew, press [¨][GRAPH] for a new scatter plot. Updating the Text Editor as described above provides a new frame for the animation.

Use the TI-GRAPHLINK to capture each screenshot, copy each image into a graphics software package to save as a .gif file, and use these individual images with your chosen GIF Animation programme.