I was so excited when the bathroom lino arrived on this massive cardboard tube, and the plan emerged to create a cat tree for Lyra. Then I got a second tube, slightly slimmer, that had carpet edging strip in.
I made a base using the last of the shelves we had taken down from Tish's room and the living room, and played around the how the whole thing might fit together and support itself. I cut slots (with the saw, the cardboard was too think for just the stanley knife) so that the landing stages could wedge into the neighbouring tube.
Monkey's young man suggested a block of wood screwed in place to provide stability for the tallest tube, I just shaved the corners from a chunk of scrap wood and it fits nice and snugly, and it worked really well. Other than that everything is fastened in place with the hot glue gun:
The only money I spent was on wood glue and three packs of jute rope to make the scratching post (though Lyra has yet to figure this out and is still using the sofa)
We used some paint sample pots to paint the tubes and the base, added fabric covering to each of the landing stages, steps to get up to the top (which she has figured out) and some dangling toys, and voila! We coaxed her up a few times but now she seems to get the idea.