This applet plots (x/y,y) for each simplified fraction x/y. The Farey Fraction number line applet at http://www.geogebratube.org/student/m12717 shows the Farey sequences one at a time, and this pattern applet shows a pretty visual of how fractions with each denominator are added. Start by increasing the maximum denominator until the screen is filled.
There are many curves visible in the picture, and checking the "Show Curves" box will show some of the most prominent (more impressive when the denominator is maximized). Students can also enter their own curves -- it's a little tricky because the picture shows x as a function of y, and geogebra does not like y in the denominator. But if expressions are simplified a bit, you can test other curves, e.g instead of entering x = (y-1)/2y, enter 2 x y =y-1.
