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As you can see, they're not too flashy, just some ribbon (usually black) tacked on under the button loop for a bit of decoration.
Pretty soon, however, people were doing more complicated designs with the ribbon, and using color/s to symbolize military rank or political party affiliation, like wearing a mini-flag. The style of hat worn as part of military uniform was very important for identifying rank at the time.
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Edward Francis Cunningham: Portrait Prinz Friedrich Ludwig Karl von Preußen, c. 1786:
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Military-style cocked hats were also just plain fashionable in France during the reign of Louis XV & Marie Antoinette, and cockades became more decorative and complex.
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A young Marie Antoinette, 1771 (without the actual ribbon part of the cockade, but you can see clearly the way the loop & button work to cock the hat):
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The following two pictures are especially interesting because in addition to the cockades on their hats, the people each appear to be wearing a cockade on their jacket- the man's is actually an embroidered 'order' insignia (military or chivalric). The woman's is probably an order as well. I have a theory that military medals and insignia like these evolved from cockades, I'm still researching this. They did migrate from hats to clothing, in any case.
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The display of politics through wearing cockades took on major importance during and after the French Revolution- More about that in a future post.
References:
Classic Encyclopedia (the 1911 Encyclopedia Britannica rocks!)
Wikipedia article on cockades
Orders:
http://en.wikipedia.org/wiki/Order_of_chivalry
http://en.wikipedia.org/wiki/Military_orders
Fashion in the French Revolution by Aileen Ribiero
Queen of Fashion, What Marie Antoinette Wore to the Revolution by Caroline Weber