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Patterns appear everywhere around us, from vast galaxies, or intricate shapes of snowflakes, to coffee stains on paper, ripples on sand dunes, or stripes on a zebra, and even spreading of a virus in a community. These patterns emerge spontaneously at all levels, through self-organization in nature. Many of them are universal: spirals, spots, branches, honeycombs, stripes. In this course we will explore how patterns and organized complexity of form can be created by simple physical laws—how simplicity creates complexity. Among other topics, we will cover bubbles, waves, branches, fractals, grains, and breakdowns.


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