Artistic box trees

This short note describes a development of the traditional Pythagorean tree fractal to produce interesting three-dimensional structures based on cubes rather than squares. Adding a 90˚rotation at each bifurcation encourages three-dimensional growth, creating increasingly artistic shapes as the branching angle decreases. 1. Pythagorean box trees The Pythagorean tree is a plane fractal constructed with squares, such that each triplet of touching squares encloses a right-angled triangle [1]. The tree shown in Figure 1 is described as P45 as the smallest internal angle of each such triangle is θ =45.