Topological structure and the creation of visual complexity

What does it mean for something to be complex? Fundamentally, complexity is a cue that something is less easily represented by our minds. With this fact in view, complexity becomes a tool: By understanding the factors that lead to various impressions of complexity of a given object, we can effectively "reverse engineer" the underlying form of the mental representation of that object. Here, we use this tool to explore the ways that topological structure relates to perceived complexity - and, thus, whether, or in what way, topological structure may be part of the representation of objects. In two experiments, we give participants the opportunity to modify simple block-like objects in order to evaluate the topological features that are implicated in their sense of complexity. In a final experiment, using insights gleaned from the previous two, we test specific predictions about topological structure and visual complexity. Altogether, we show that topological structure is clearly implicated in judgments of complexity, including in some key ways that expand existing theories of visual complexity.