I like that tower. Very ethereal.
You should build a scale model to investigate they way the tower responds to loads. I'm wondering, upon reaching a critical side load, will itl buckle like a tube would or bend like a sapling?
For an actual structure consider true aircraft cable and spruce or steel spars. You might want to go to Aircraft Spruce and Speciality
for that stuff. The reason I suggest that is to ensure known material strength and consistent quality (since you may have someone up on top).
Tap some structural engineer to give you a hand with the strucural analysis and to recommend cable and spar sizes. If you don't get a response from an engineer here, then drop by your local university engineering department.
"Government is not reason; it is not eloquent; it is force. Like fire, it is a dangerous servant and a fearful master."
-- George Washington