Interestingly it seems to be misnamed, the drawers are a Fibbonocci sequence, not a fractal.
http://www.tmiyakawadesign.com/fractal-2.html
http://www.tmiyakawadesign.com/fractal-2.html
Is it not fractal? It does seem to be self-similar at diminishing scales, which is what I think of as the heart of fractal-ness...
I think of the essence as being "scale symmetric", that is it looks the same as one zooms in. The two boxes at the top of the left side, the 1-1 that starts Fibonacci, means that zooming in things change.