With this logo I then came up with more various different ideas, of how as a shortened version you can just use the A from the logo then using the logo you can create the button/tag/ leather patch design. 

 I thought this would look good as maybe a square button? Also this could then be used for the leather patch. The design came from the elements in the periodic table and I think this could be really effective. It could also be used for the tags and have the size in the top corner where the atomic number would go.