Tubular Cluster Algebras II: Exponential growth
  Among the mutation finite cluster algebras the tubular ones are a particularly interesting class. We show that all tubular (simply laced) cluster algebras are of exponential growth by two different methods: first by studying the automorphism group of the corresponding cluster category and second by giving explicit sequences of mutations. 
Michael Barot, Christof Geiss and Gustavo Jasso
math.RT