Compute growth form for substitution tilings when it exists

Develop a general algorithmic method that, given a substitution tiling (specified by its prototiles and inflation/dissection rules) known to possess a growth form, determines that growth form.

Background

Even when a substitution tiling has a growth form, there is no general computational framework analogous to the periodic or regular grid cases for obtaining it. Only isolated examples (e.g., pinwheel, chair, hat) are understood.

The authors explicitly ask for a general method to compute the growth form of substitution tilings, highlighting the gap between existence and effective determination.