You need Saulgoodes overlay bg script to add reflection to the image.
I can not get GAP to work correctly in Gimp-2.8 so i just use Map Object.
One seamless 370x370 tile and map orientation 15 degree intervals up to 180 (12 layers).
You will keep having to duplicate your pattern before each map and place it on top.
Then duplicate layers from layer 1 to about layer 12 and place them on top.
Then i added a white glow with a blur for reflection.Then set it's opacity real low.Place it as the bottom layer (bg layer)
After that run Filters>Animation>Overlay Background.
And it's all done. This is an animated PNG so if you can not see it try the FireFox browser.

That's pretty cool Rod. I've had some problems with map object, but one frame at a time it should be easy enough to copy/paste as new layer if it insists on creating a new image.

I was thinking of grabbing Gimp-2.6.12 portable and just using it for GAP but nahh.
Map Object works pretty good on its own for rotation type animations.Probably not as smooth of an outcome but close enough for me.

neat !

That's pretty cool, but the texture seems to be flowing downward... I'm sure it's just something goofy with my browser.

Edit: no, it's definitely an optical illusion. I crossed my eyes and it started flowing correctly. If I cross them the other way, it becomes a hexagon waterfall.

My Wife looked at it and she said it looks like it's flowing to the left, even crosseyed. Which is what i see.
Merrak are you sure you're not seeing things?