Short bio: Computer Scientist, FOSS supporter (read more)
Tux Machines (TM)-specific
I can hear everybody now: "Petey!" you all say, slapping your foreheads Howie-Mandel-style, "Can't be!!!" Everybody knows that Mirrored Ball on Checkered Plane is the exclusive domain of 3D ray-tracers, in programs like Yafray and Blender and POVray, and in fact is such a cliche that it's the canonical first image you post in a POVray group as a rite-of-passage.
You're right; I'm pulling your leg. Gimp isn't a ray-tracer, no way, no how. To quote the Cheese Shop sketch, I was deliberately wasting your time. However, you can fake it. So this will be a faux Mirrored Ball on Checkered Plane. Not for art's sake, nor skill's, but for the sake of being a smart-ass.
How to do Mirrored Ball on Checkered Plane in Gimp
1. Start your new file and make a checkerboard with Filters-> Render-> Pattern-> Checkerboard. Do a little math to be sure the checkerboard maps evenly to the plane.