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"Morphodynamics", the local dynamics of form, studies the dynamics of causal processes that integrate geometry, mechanics, and local information processing to generate a functional physical object. Computational morphodynamics joins morphodynamic modeling with other computational tools such as microscope image analysis to solve problems, notably those arising in the study of biological development where geometry, biomechanics, and biomolecular informationprocessing are combined in flexible and intricate ways to generate a functional organism from a genetically encoded program. At the molecular level, both equilibrium and nonequilibrium statistical mechanics are needed for quantitative modeling. In this way computational morphodynamics aims to become central to the study of plant and animal development and also instructive to many other scientific and technological disciplines. To simulate such heterogeneous morphodynamic processes on a computer, in pursuit of improved predictive power and enhanced biological understanding, is much easier using powerful modeling software with a clear mathematical foundation. I propose that the mathematical and computational objects that are fundamentally involved follow a natural hierarchy of increasing size, from potentially stochastic dynamical systems on multisets and labeled graphs, to informationprocessing dynamics on infinite limits of graphs that include geometrical manifolds and nonmanifold geometries at several scales. Dynamics of and on such objects are naturally and generally expressed in terms of operator algebras. The result will be a modeling language and a geometry lively and rich enough to underlie the computational exploration of morphodynamics for biology and engineering. Host: William Hlavacek, T6, 6651355 