The octopus was chosen as the symbol for several reasons:
First, the octopus is extremely intelligent. It has both short and long term memory and high problem-solving skills. The second reason is that they are highly adaptable to their surroundings. The octopus is the only creature in nature that has the ability to change not only its color, but also it’s skin texture. It is able to completely meld with its environment. Some species are also able to mimic the shape and movement of other animals and appear to be the predator to the creature that was chasing them. The third is their movement within water. The octopus is able to glide easily, yet has the strength to attack and defeat aggressive creatures such as sharks. And, since they do not have skeletons, they are very elusive and natural escape artists.

Quotes from Bruce Lee

“Be like water making its way through cracks. Do not be assertive, but adjust to the object, and you shall find a way round or through it. If nothing within you stays rigid, outward things will disclose themselves.”

“Don't get set into one form, adapt it and build your own, and let it grow, be like water. Empty your mind, be formless, shapeless — like water. Now you put water in a cup, it becomes the cup; You put water into a bottle it becomes the bottle; You put it into a teapot it becomes the teapot. Now, water can flow or it can crash. Be water, my friend.”

Life at the Sanctum, training at the Sanctum

The octopus becomes a very useful totem. It is used in a way that reflects our way of thinking and fighting. One must be inquisitive, and always look for a way in and a way out. Always be thinking about the opponent’s limbs and using yours as if you had eight and not just four. Always be thinking about the counter to the counter to the counter. Keep your opponent tight, and relax in order to get a better position. Move like you are in water, be ready to be gentle, be ready to crash, be ice, be vapor. You must always adapt or you will stagnate and be useless. And always lend an arm to those who need learning, because you can always learn from any encounter.