A unique species of cephalopod in the alternative Earth in which the story of Nation unfolds. In the book, this is an intelligent and amphibious species of octopus which is capable of living independently out of water, and which has learnt to climb trees to seek its prey, avoid its predators, and indulge its sense of curiosity about the world around it. They apparently make grand house-pets.
On Roundworld, there is genuinely a species of tree-climbing crab, but the tree-climbing octopus comes out of the same bestiary in which Drop bears are to be found and for much the same reason: to see how much bullsh*t the naive and unwary traveller will swallow when it comes from concerned and knowledgeable natives.
See HERE first:- 
See HERE after reading the first link:-