This one is a totally different caterpillar to those I had everywhere the other week (post is here). Those ones were hairy fellas and weren't confined to a food source like these guys are. It must be caterpillar season at my place!
So...ID is not easy (is it ever for me?) but maybe it's these (page of info here) - a caterpillar species of Spodoptera picta.
These are pests in Sydney garden that love 'lilies' of varying types - and the first plant they ate was one of those before they moved across to the begonia. They eat right down into the crown (which the varmints did), and they're about 5 cm long (which they are).
They do turn into quite a pretty fluffy moth (you can see it here), so maybe I won't mind too much - so long as my plants grow again!
Have you had lots of caterpillars this year? Or have I just been lucky that conditions here suit them?
PS Cool that these guys love you, Miss Lily! :)