Some time ago I wrote article How to decode stereogram by Photoshop.
I made a small experiment and it’s possible to achieve similar results by GIMP.
Here is stereogram (Magic Eye Picture) created by Easy stereogram builder.
Open file in GIMP. Duplicate the layer.
Change layer mode to Difference.
Select Move tool from GIMP toolbox (M).
Start moving the layer to the right. You can use arrows to move the layer. If you prefer mouse then click, press and hold CTRL key to avoid shifting in both X and Y axes.
Here is the result:
