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I've created 20X20 tiled clones with the randomize factor set to 2% (X) and 2% (Y). The end result looks like this:

enter image description here

Is there a way to remove or minify the overlap of the squares such that their distribution is more uniform?

I think I ended up getting approximately the effect I wanted by just creating a tile grid of 20X20 squares and using the tweak tool move objects in random directions and tweak tool rotate options. Curious still if Inkscape has an extension that could achieve this also using the pictured squares as input.

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Use the 'Remove Overlaps' functionality of the Align and Distribute dialog (Ctrl+Shift+A).

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I would rescale the clone source. That should help space everything out a bit better. After all, that's the whole point of clones - you can edit the source, and all the clones will update.

An example

enter image description here

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