Paint By Constants: Julia Sets

This applet lets you "paint" different julia sets based upon the values you put into the complex constant input box. Move the black X, or the paintbrush around until you see the graph you selected. Some suggested complex constants are: -1 - 0.2i, .12 + .74i, -.5 + .55i, 0 + i. (Note: if you choose too large of numbers the graph will not appear since it will be off the grid.)

1. What are some differences and similarities you see when you look at different Julia sets?
2. What type of trend do you see within the Julia sets? Do they grow large or stay within a certain range?
3. What topic of mathematics might we put these Julia sets under and why?

This applet allows the user to draw their own julia sets. throughout the construction they should be able to see that these graphs that are created through complex constants are not like graphs we see in the "real world". These graphs instead create patterns within themselves and tend to stay within a restricted area, growing towards themselves more often than out. The user should also be able to identify that these sets are fractals.

Alycia Jacobson, 15 November 2013, Created with GeoGebra