It is hard to know whether there are likely to be any surprising new developments in automata theory, in order to be able to predict them. To judge from past experience, each technological episode which has produced substantial new computing power has brought with it some new development in automata theory. The industrial revolution allowed Babbage to envision a mechanism which transcended dolls having the style of a Swiss music box operated by cams, levers, and gear wheels; even so, inadequacies of technology and project management kept a functioning machine from becoming a reality.
A century later, the first completely electronic computer inspired von Neumann to speculate about the possibilities of automatic factories, leaving a huge gap between his mathematical symbolism and the ability to design specific cellular automata, much less their translation into performing mechanisms. Greatly improved computers, interactively operable, permitted following up his original designs and simplifying them. Still further advances, in the form of symbolic programming languages and visual displays, were waiting when Conway's discoveries attracted attention. Finally, Wolfram's forays into one dimensional automata would seem to have coincided with the advent of a generation of widely accessible computers, endowed with ample memory and rapid operation.
When circuits become available, for which large numbers of cells with large numbers of states can rapidly evolve in parallel according to programmable rules, there is no doubt that new insights will be found, very likely through empirical observation. In the meantime it is always possible to say that more details could be filled in with respect to any of the facets of the theory which have already been studied. So the problem is to take some feature which seems to show promise, to see which of its aspects make it interesting, anticipate what results are expected, and try to find the best way to go about establishing them.