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This lecture explores the concept of morphogen gradients in biological systems, focusing on the establishment of spatial patterns through diffusion. It covers the Kolmogorov-Fisher equation, logistic growth, and the formation of fronts in reaction-diffusion systems. The instructor discusses the role of morphogens in creating gene expression domains and provides examples from Drosophila embryos. The lecture also delves into the implications of morphogen gradients in pattern formation and spatial organization, showcasing experimental evidence and mathematical models.