Thematic mappings offer many insights into individual phenomena seen over space. Multivariate extensions are often messy, to the extent they are cartographically possible at all. It can be unclear what advantages such maps may have, in theory or in practice, to small multiples of lower (one- or two-) dimensional traditional thematic mappings. Here, we explore a set of multivariate cartographic approaches that we refer to as woven or tiled maps. These maps, inspired by weaving and mathematical tiling, are not limited to two or three variables, but depending on circumstance, may be capable of offering insights into how substantially more types of phenomena are juxtaposed differently in what often appear to be regions arising within space. We move from thematic mapping as a tool well-suited to reductionist analysis to one portraying landscapes emerging from synthesis and the visual confluence of diverse phenomena. We offer examples and introduce a prototype code library (in Python, entitled 'weavingspace') and a web-based interface ( http://dosull.github.io/mapweaver/app/ ) useful in making such maps.