Click the green flag and each ball will move up until it is the same distance from the apple as from the nearest bow tie. This makes a parabola. Each ball keeps track (using lists) of whether or not any bow tie is closer than the apple. If you move the apple up, it will change the shape of the parabola. Hit spacebar to restore default position of apple and bow ties.
A parabola is the set of balls (points) that are equally distant from a bow tie and an apple. The apple is the focus, the focal point. The bow ties are lined up on a baseline called the directrix. So a parabola is the set of all points whose distance from the focus is the same as the distance from the directrix. When the directrix is at y = - 0.25, and the focus is at y = + 0.25, then y = x^2 (x-squared). So the balls should move until their y coordinates is the square of the x coordinate. But all the balls in this program do is follow their very simple rule: move until they are just as far from the focus as from the directrix. You will see a ball end up at x = 1, y = 1, another ball at x = 2, y = 4, and so on. (We use this same grid in a paper folding project, where you fold the points on the directrix to the focus). I have the ball clone itself. Then each cloned keeps and updated list of whether or not any bow tie is closer than the apple.
