This article describes an interactive visualization tool, LinMap, for exploring the structure of complexity gradients in evolutionary landscapes. LinMap is a computationally efficient and intuitive tool for visualizing and exploring multidimensional parameter spaces. An artificial cell lineage model is presented that allows complexity to be quantified according to several different developmental and phenotypic metrics. LinMap is applied to the evolutionary landscapes generated by this model to demonstrate that different definitions of complexity produce different gradients across the same landscape; that landscapes are characterized by a phase transition between proliferating and quiescent cell lineages where both complexity and diversity are maximized; and that landscapes defined by adaptive fitness and complexity can display different topographical features.

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