This paper has presented our ideas of computing geographical reality with animated map language. Inherently, geographical reality is considered as an integration of physical, cognitive, and computational geographical worlds. An animated map is the result of animated mapping of time-varying geographic phenomena. Alternatively, the animated map is a computational reality of geographical world or an augmented part of existing geographical reality. More, the animated map results from the interaction of humans and the computers on geographical world. Again, the animated map is a visual medium of geographical spatio-temporal information communication between map makers and map users. In terms of valid time involvement, we distinguish two types of animated maps, i.e., temporal and atemporal animated maps. We consider an animated map as a composite map symbol of atomic map symbols. The design of dynamic map symbols is grounded on the theory of visual variables. The syntax of animated map language is a group of rules of visual variables applied to geographical data. To some extent, the organization rules of map symbols are projections of geographical spatio-temporal data structural relationships. In particular, an experiment of population change mapping is used to exemplify our ideas of animated map design.