The Top Knot Hair pin has long been suspected of being an indicator of fire nation royalty.?? However with the latest episode I think I have puzzled out what they all mean.
The Patterns are
Five Pronged Gold:???? Seen on Firelord Azulon, Firelord Ozai:
-It is obvious that this Pin represents the Firelord
Three Pronged Red:?? Seen on Lu Ten, Seen on Azula after Azulons death
-Given the appearance of the pin on Lu ten and Azula the pin most likely represents the heir apparent to the throne.?? Or at least the one in direct line of succession.???? Prior to Lu Ten's death Azula wore a different pin.??
Two Pronged Red:???? Seen on Azula Prior to Azulons Death
-This pin most likely represents the heir presumptive (2nd in line of succession), Zuko does not have the pin as he is an exile and thus doesn't wear such a thing, though even before his exile he was never the firelords favored child and thus might not have been Heir Presumptive even then.
Two Pronged Gold:???? Seen on Lady Ursa
-Most likely denotes first lady of fire nation, as Iroh's wife is passed, though does not denote firelady.
Gold Band:?? Seen on Ozai Prior to Firelord ascension, seen on Iroh after his brothers acension.
-Most likely denotes Heir Presumptive?? might be a stand in for the two pronged red symbol.?? May have no significance.
Red Band:?? Seen on Iroh prior to Firelord Ozai's Ascension.
-Most likely denotes heir apparent might be stand in for 3 pronged red.?? May have no significance.
It is unknown what if any color and pattern corresponds to the firelady but given the patterning and coloration 3 pronged gold would be appropriate.????
There are several other possibilties, including generalized royalty, as well as coming of age issues.???? but given the Imperialistic nature of the nation, the identification of Heirs is the most likely point.