The fundamental nature of transcriptional regulation has been much studied by both biologists and now by physicists over decades. Nevertheless, much remains to be learned about how transcription is quantitatively controlled and whether such regulation is significantly noisy. Here, I will present recent results on this topic from a highly focused study of a single gene, the floral repressor FLC in Arabidopsis, using mathematical modelling, genetics and single cell imaging. FLC is an attractive target for study as it combines several modes of regulation that are environmentally regulated by temperature. I will show that FLC transcription can be modulated in either an analogue, continuously varying fashion or in a digital, on/off mode. For analogue regulation, transcription appears at first sight to be highly noisy. However, this appearance is illusory: once cell size is factored in, transcriptional dynamics become almost entirely Poissonian. For digital regulation, I will present simple models for how such on/off states can be established and maintained locally in the chromatin, showing that an all-or-nothing nature is vital for long-term (epigenetic) memory storage. I will also show results from experimental tests of the digital model for FLC, confirming the presence of chromatin-based digital epigenetic memory, but revealing that there must be additional factors responsible for epigenetic memory storage beyond histone modifications.