On exponential growth in Lindenmayer systems

AbstractAn explicit formula is derived for the growth function of a DOL-system. This yields an algorithm for deciding whether the growth is (i) exponential independently of the axiom, (ii) polynomial independently of the axiom, or (iii) exponential for some axioms and polynomial for others. Such an algorithm is obtained also by an elementary combinatorial argument. Some comparisons are made with context-dependent Lindenmayer systems