It's a neat design. You can cut all the strips from one piece of 8.5" x 11" paper.
Here's my version! It's a little wonky because I needed to cut slots where the pieces join, not just slits.
The instructions are kind of "quick and dirty", so you'll have to click through to the PDF rather than seeing them here.
See this tutorial for a simplified sliceform tree from paper strips.
Extreme Cards and Papercrafting: pop up cards, movable and mechanical cards, digital crafts and unusual papercrafts.