Universität Hamburg - Fachbereiche - Fachbereich Mathematik

Explanation of the Applet Quasiperiodic

We deal with a parametrization of a plane curve (x(t), y(t)) with both components x(t) and y(t)



being quasiperiodic with frequencies 1 and w. The parameter t runs from 0 to tE with stepsize dt. If dt is small, you see the "real" curve (you can try it, but you should reduce tE also). The most impressing pictures you get for those dt which are close to a rational number with small denominator. dt may be varied by using the scrollbar.

You could start with a circle which you get by setting a2=0=b2, dt=0.01, tE=10. Then you may increase a2 and b2 with w=5. You will see symmetric closed curves. Now study a2=b2=0.5 and a2=-b2=0.5. Watch and explain the difference!

In general you will get nice pictures if you choose w close to a natural number and dt close to a rational number wirh small denominator.

Enjoy it!