This paper presents a working prototype of a mobile, programmable set of construction kit elements for children. SmartTiles are small, lightweight, independently programmable tile objects that can be combined to cover various sorts of planar surfaces; each touch-sensitive tile contains its own computer and LED, and communicates with its neighboring tiles when placed on an appropriate background material. Collectively, the tiles enact usercustomizable cellular automaton programs and thus display complex and fascinating dynamical patterns of light. In this paper, we discuss the implementation of SmartTiles and explore their potential use as an instance of mobile computation for children. We also discuss the way in which the tiles can be programmed wirelessly via a PDA interface, and discuss the implications of this sort of programming for educational computing more generally.