House Targaryen is famous for their dragons. Currently, Daenerys has three cool dragons. Concidentally, we too have three species of seadragon in the ocean! Seadragons are relatives to the more well-known seahorses. Like the seahorse, male seadragons carry and brood the babies until birth. The known species are the leafy seadragon, weedy seadragon, and ruby seadragon.
Leafy and weedy seadragons are endemic to the Australia's southern coastal waters. Endemic species are only found in one area, which may make them more vulnerable to extinction. This kind of sounds like the Targaryens, or what's left of them (ahem).
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Heck, even the three dragons have similar colors as the three seadragons. Drogon is red like the ruby seadragon, Rhaegal is green like the leafy seadragon, and Viserion is creamy white like ... part of the weedy seadragon.
Do seadragons breathe fire? No, but I'd like to imagine that they wish they could.
Are seadragons terrifying? No ... unless you are a tiny crustacean.
And if seadragons were the sigil of House Targaryen, they will certainly sound a lot less scary.