I had a small but talented group of students in my Fractals & Chaos mini-course this year. They used Fractal Explorer, Apophysis, Winfeed, and Chaoscope to create their final projects, which are displayed below. Enjoy!

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I had a small but talented group of students in my Fractals & Chaos mini-course this year. They used Fractal Explorer, Apophysis, Winfeed, and Chaoscope to create their final projects, which are displayed below. Enjoy!

These are Julia sets that were created by students in my Fantastic Fractals course. We used Winfeed to plot them (free download here).

Julia sets were first calculated by the French mathematician Gaston Julia. They are the result of iterating the the function f(z) = z^2 + c, where c is a complex number. Depending on the value of c, the iterations lead to “prisoner points” that stay close to the origin, “escaping points” that increase to infinity, or points that lie on a boundary between the prisoners and the escapees. The points on the boundary are the Julia Set. Until the advent of modern computers, we were unable to calculate Julia Sets with much accuracy. Now, however, we are able to see them in a matter of seconds.