### Introducing the magic cycle button

The "cycle" button is an attempt to show the effect of the z->z^{2}+c transformation.
### Even newer, even more improved applet

### Technicalities

There's nothing hugely exciting going on here. One notable detail is that it isn't enough to apply the transformation to the pixels in th bitmap; that would result in terrible accuracy and hideous scaling effects. I modified the code to remember the exact value of each number plotted and use those bvalues in the transformation.
I considered a few ways to interpolate but eventually settled for a very simple solution: linear interpolation. Each point just moves in a straight line from its starting position to its image under the transformation. This has the advantage of keeping the two fixed points stationary. (It also is angle-preserving, but I probably wouldn't consider anything that wasn't).
### Source code

Julia4.java
Complex.java

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