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carving in the ground
(credit /u/Aisamai). This is one carving of many found in the Ancient Wyvern arena. There are also various larger carvings of the same design in this area. Due to Filianores symbolism with the floral crest found both on the Cloranthy ring and in the center of this carving, I believe that the Nameless King, despite abandoning his kind, carved this pattern as tribute and in affection for his youngest sister.
Another detail to note about these carvings is that they are surrounded by a ring, perhaps representing Filianore's residence and affiliation with the ringed city, furthering the strong link between these floral crest carvings and Filianore.
This sentimental side of the Nameless King has been seen before as early as dark souls 1 where the sunlight blade states that;
When the eldest son was stripped of his deific status, he left this on his father's coffin, perhaps as a final farewell.
This isn't exactly a groundbreaking discovery but I found that it adds a nice dimension to the character of the nameless king and his betrayal as being a hard choice for him, wrought by emotion, as he clearly still held great respect for his father and affection for his sister. This discovery also sheds some light on questions raised in an old post and is one of numerous examples of FromSoftware's incredible attention to detail.
tldr; The Nameless King carved a tribute to his youngest sister, in the form of a floral crest.