Just did an easy form of the tree growing for a customer for Nutcracker.  (Remember that the nutcracker tree is a Christmas Tree).  We used Chameleon Scrim material in Green cut to a Triangle shape.  Initially most of the material is folded on the ground underneath the small hanging portion, which has a fishing line tied to the top.  As the tree grows the line is pulled simultaneously lifting and unfolding the portion on the ground, so the full tree is created to be 20 times the little tree.  This would work best for a conifer or a tree with a conical shape.  The tree could be printed (costs less for printed scenery on Chameleon than people think) or painted on the scrim material.  Part of the reason that Chameleon Scrim was used was because it--unlike most other fabrics--was light enough to use this way.