You could try Bump Mapping
Duplicate the pattern to a new layer Layer -> New Layer
Apply Colors -> Threshold to get black dividing lines on white.
Apply Filters -> Blur -> Gaussian blur with a small value
Hide this layer
Onto the original layer and apply Filters -> Map -> Bump Map using the top layer as the Aux Input.
Adjust sliders to suit.
This a 50 second animation of that https://i.imgur.com/zHrK9xr.mp4 Probably too much blur on the bump map, it is just a demo. Just experiment.
Duplicate the pattern to a new layer Layer -> New Layer
Apply Colors -> Threshold to get black dividing lines on white.
Apply Filters -> Blur -> Gaussian blur with a small value
Hide this layer
Onto the original layer and apply Filters -> Map -> Bump Map using the top layer as the Aux Input.
Adjust sliders to suit.
This a 50 second animation of that https://i.imgur.com/zHrK9xr.mp4 Probably too much blur on the bump map, it is just a demo. Just experiment.