During the Dreamtime, the Wondjina (or Wandjina) are said to have come to Earth and created the landscape.
How did they travel? Were they able to move independently or did they ride on some other creature?
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They seem to be able to move independently. According to a wondjina artist, they walk, and travel, as the rain does.
Long Watty says Wandjina came from ground, live in clouds, rain comes after he lift cloud, rain go down. Rain travels as the Wandjina walks - Wandjina travels. Then Wandjina goes down with rain (or as rain?) and into ground again.
Wanjina: Notes on Some Iconic Ancestral Beings of the Northern Kimberly by Kim Ackerman
In the same paper, Ackerman presents a number of tellings of a flood caused by the Wanjina, in which references can be seen to the Wanjina walking, or at least using their feet for travel.
Then this man comes down - this Wanjina - then he walks, he walks.
That Wanjina means that he is glad that he sunk the people down ... and he walks proudly into the hills.
Wodjin slipped and hurt his foot, and decided to stay, and transformed himself into the painting.
I have not found any references to indicate any conveyance or animal they might ride on (no idea where the silver boomerang thing came from).