E1:Choose the power k = 2 and store the contour of the "apple man" in your memory.

E2: Choose a slightly different value of k and reflect how the change originates.

E3:  Type integers 1 to 10 into the text field. Watch for symmetries, study how they relate to k, and how the structure originates.

E4: Type a very high integer for k, e.g. 1000. The fractal looks close to a circle. Why? Take a look at the boundary several times magnified.

E5: Choose integer or rational k. Use the selection rectangle of the mouse to deeply intrude into the fractal, and look for especially attractive structures. Where are they? Why? (not an easy question).