Drag the [color=#ff00ff]magenta/pink[/color] point around on the complex plane. The [color=#38761d]green[/color][color=#333333] points rep[/color]resent successive iterations of the [math]z_{n+1}=z_n^2+c[/math], [math]z_o=0[/math] rule, where c is determined by the magenta/pink point.[br][br]I used this construction in a quick "Complex numbers are not as lame as you think" lesson for my PreCalculus class. In order not to hint at how the lesson would unfold, I avoided providing vocabulary such as "cardioid" and "Mandelbrot Set" within the construction.[br][br]Addition of the "trace orbit point" and "clear trace" options were inspired by [url=https://www.youtube.com/watch?v=FFftmWSzgmk]this Numberphile video[/url], and the featured [url=https://www.geogebra.org/m/BUVhcRSv]Geogebra construction by Ben Sparks[/url]. With this option checked, points that cause the orbit to diverge (i.e. they spiral outward) leave a [color=#ff0000]red[/color] trace, and points that do not cause the orbit to diverge (i.e. they spiral inward) leave a [color=#00ff00]light green[/color] trace.