How can I implement an applet using BBcode?

[pjkcards]

Hello,
I run a puzzle solving forum, and I would like to add a feature, but I am having a problem finding out how I can do it.

This is the feature. When someone types something such as:
[alg puzzle=4x4]r u r' u'[/alg]

Then it would output an image with the result. r u r' u' is an algorithm that would be performed on the puzzle.

Similar to this. But I'd like the applet only to appear when the user clicks an image preview, similar to this.

I know this will be difficult, but hopefully both links I provided will give you an idea of how they did it. Thanks in advance.