It is well established that topographical features modulate cell behaviour, including cell morphology, proliferation and differentiation. To define the effects of topography on human induced pluripotent stem cells (iPSC), we plated cells on a topographical library containing over 1000 different features in medium lacking animal products (xeno-free). Using high content imaging, we determined the effect of each topography on cell proliferation and expression of the pluripotency marker Oct4 24 h after seeding. Features that maintained Oct4 expression also supported proliferation and cell-cell adhesion at 24 h, and by 4 days colonies of Oct4-positive, Sox2-positive cells had formed. Computational analysis revealed that small feature size was the most important determinant of pluripotency, followed by high wave number and high feature density. Using this information we correctly predicted whether any given topography within our library would support the pluripotent state at 24 h. This approach not only facilitates the design of substrates for optimal human iPSC expansion, but also, potentially, identification of topographies with other desirable characteristics, such as promoting differentiation.