One aspect of intelligence is the ability to restructure your own environment so that the world you live in becomes more beneficial to you. In this paper we investigate how the information-theoretic measure of agent empowerment can provide a task-independent, intrinsic motivation to restructure the world. We show how changes in embodiment and in the environment change the resulting behaviour of the agent and the artefacts left in the world. For this purpose, we introduce an approximation of the established empowerment formalism based on sparse sampling, which is simpler and significantly faster to compute for deterministic dynamics. Sparse sampling also introduces a degree of randomness into the decision making process, which turns out to beneficial for some cases. We then utilize the measure to generate agent behaviour for different agent embodiments in a Minecraft-inspired three dimensional block world. The paradigmatic results demonstrate that empowerment can be used as a suitable generic intrinsic motivation to not only generate actions in given static environments, as shown in the past, but also to modify existing environmental conditions. In doing so, the emerging strategies to modify an agent’s environment turn out to be meaningful to the specific agent capabilities, i.e., de facto to its embodiment.