Here's my effort - blatant rip-off, just playing with GIMP. I didn't bother with most of the detail stuff, though I added a stroke around the continents.
tiletest.png
Also attached is the brush I created to facilitate this.
tiles.zip

I was able to follow the tutorial quite closely, with a few exceptions....

1) Gimp does not stroke along a selection well with an angular animated brush like this one. It is better to keep converting the selections into a path, then stroking the path (don't know why....)

2) No colour jitter. I got around that by creating a fairly busy gradient of the colours I wanted (or pick a pre-set) and check the "use colour from gradient" box in the pen tool.

3) I was WAY too lazy to do the expanding circle thing, so I just created a spiral in inkscape (one drawing object), converted it to a path and imported it into GIMP.

4) As always, the layer effects don't translate, as GIMP doesn't have them. I create a 50% greyscale layer, bumpmap it with the source image, and adjust the curves with necessary, applying it in overlay mode to accomplish a similar effect.

-Rob A>