Used both in my most recent wood block renders. The more variety of reversible distortions wht more cooler results. Just wondering. 
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From the little I know, some filters and operations are inherently reversible. Most are not strictly reversible. You could probably do a web search to find out. I also came across a paper recently showing progress in reversing non-reversible filters.
In terms of the examples in your title, I may be wrong but I think they are transformations into another space with a way to return to the original space. We do that sort of thing more often than we think; e.g., gamma and color space / model transformations.
Yeah; with a little coaxing, I got a few more to work. Also, I forgot about GIMP’s own whirl and pinch which actually gives a bit better result for this. I posted a result at GIMPChat.
Hi Lyle, The swirl and pinch version is great, you should add it to your swami thread.
