Disk-stacking models for stem development have recently emerged as an excellent compromise between mathematical simplicity and biological relevance. Because disk-stacking models allow lattice solutions, the van Iterson paradigm remains a powerful organising principle for their dynamics, and it is by now well established that disk-stacking models can indeed demonstrate Fibonacci structure (Golé et al. in Acta Soc Bot Pol 85(4), 2016). Moreover, as the van Iterson paradigm suggests, there are parameter regions in which strict Fibonacci patterns are lost but patterns remain closely ordered with either Lucas numbers or double-Fibonacci pair counts occurring (Golé et al.; Yonekura et al., PLOS Comput Biol 15(6), 2019). Disk-stacking models have now been shown to exhibit further empirical phenomena in ways no other models have yet achieved or seem likely to (Swinton, arXiv: 2407.05857). However there remain many open questions, both mathematical and biological about the dynamics of this interesting class of models.