Doom's travels ranged far and wide. These doodles appear to date from a time that Doom was particularly interested in chinese culture and history. Dragons and the color red figure strongly in Doom's art from this era.
In ancient China, there were many legends depicting dragons and phoenixes together, some of which label the dragon as the high emperor, and the phoenix as the empress.
Whichever the case, it is certain that these two drawing were done in correlation, and are some clue to the origins of the old legends.
Beginning with the largest symbol at the head of the circle, and continuing clockwise:
Flora and Fauna