ATI. formation patches

I trsut that most guys here are aware of at least the basics of modern military heraldry since WWI with such renown military outfits as the BIG RED 1 (US Army's 1st Inf Div), DESERT RATS (British Army 7th Armd Div), SCREAMIN' EAGLES (101st Airborne Div), ALL AMERICANS (82nd Airborne), etc. This practice of establishing distinctive shoulder patches AFAIK goes back to WWI, at least for the US Army, when the 81st Inf Div from South Carolina designed the CAROLINA WILDCAT shoulder patch, and other formations followed suit, including thru design competitions, such as for the 2nd ID INDIANHEAD. Does anybody know of any other designs which were proposed for these and other outfits during the process of organising and mobilising for war ? How would these outfits have developed to today had other different formation signs been chosen ?