Here we see an example of the Fourier Series being applied in an unusual way. The basic idea is that using the Fourier Series, one can create a kind of morph between images. Along with the demonstration Applet, the complete animated sequence has been provided below.

Sorry gotta have Java if you want the full thing.

Click "more" to step forward in the transition between images. Click "less" to step backward in the transition. Here's the whole thing animated.

The basic idea behind this tranformation is that the harmonics making up the Fourier Series for each row of pixels (separated into red, green, and blue components) are sequentially replaced from lowest to highest. This results in a literally "vibrant" transformation where one can see the old image seemingly "shake out" into the new image. The transition could be made smoother, particularly near the begining. It would simply be required to break up the process of replacing one harmonic with another by allowing harmonics of greater amplitude difference to transition through intermediate values instead of using direct replacement.

Classes	Class File	Source File
FourierDemo2	FourierDemo2.class	FourierDemo2.java
shtick.math.FourierSeries	shtick/math/FourierSeries.class	shtick/math/FourierSeries.java
shtick.math.FourierBasis	shtick/math/FourierBasis.class	shtick/math/FourierBasis.java