Plant roots are remarkably diverse in size and shape. It is not fully understood how the diversity in root architecture contributes to crop yields or plant biomass in part because roots are buried underground and difficult to study. This research takes a quantitative approach to analyze the wide diversity of root architectures. Bean roots grown under experimental conditions will be imaged and the resulting data will be used to create new mathematical and computational tools to discern causes of root variability. Combined with genomic information, the analytical tools will identify genetic elements underlying root shapes in response to environmental and genetic variation. The research will point to new opportunities for breeding targets in crops such as bean and extended to maize. The research also couples with an education program that integrates computation with plant research, thus addressing the critical national need for a computationally trained plant science workforce. The novel tools will be publicly available and deployed using national cyberinfrastructure: further the technologies will be integrated into two courses that enable basic science and computational biology within an experiential learning environment. A new student award is implemented through the Plant Center and the Georgia Informatics Institute to highlight advances attained by working at the computational and plant science interface. Together, the integration of science and education sets forth a path for fast dissemination of results into breeding programs. After decades of research on plant roots it is still a mystery how and why root architecture arises in seemingly endless variations of shapes. The research introduces the phenotypic spectrum as a new quantitative theory that extends the established concept of plasticity by a new dimension. The phenotypic spectrum of one genotype consists of distinct root architecture types, each of which is hypothesized to be associated with a different plasticity curve across environments. Theoretically, the phenotypic spectrum emerges for a population of one genotype if all elementary geometric measurements at all locations within each individual root system are taken and each individual is summarized by a whole root descriptor. Descriptors with similar characteristics correspond to one architecture type. Hence, the spectrum is not observable with current phenotyping tools that capture only one location in a root system per trait. Quantifying the phenotypic spectrum demands the development of unprecedented whole root descriptors and simulation techniques to capture the differences in the 3D spatial organization of the whole root architecture. In doing so, a new combination of differential geometry and imaging approaches as well as a newly developed statistical analysis is proposed. The experiments will provide an understanding of how to describe and evaluate the interplay of different root architecture types in the greenhouse and the field by linking both with the developed descriptors. The educational goal is to increase the number of researchers at the interface of computational and plant sciences through two courses using the developed tools. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.