Iterations of [math]f(x) = x^2 - b[/math] - iterations go from [color=#ff0000]red[/color] to [color=#00ff00]green[/color]. You can drag the red point [color=#ff00ff]B1[/color], the y-intercept [color=#b20ea8]b[/color], or change the number of iterations [color=#1551b5]n[/color] up to n=100 - drag the start of the bottom window down.
Also see my next applet, [url=http://www.geogebratube.org/student/m133195]fixed points[/url].