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dynsys [2021/09/06 01:14]
trinh 		dynsys [2021/09/06 01:22]
trinh
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 ====== The mathematics of patterns ====== ====== The mathematics of patterns ======
  
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 If you look around to your surroundings, you will see patterns every which way. Maybe you will see a patterns in the alternating dark and light grain of your wooden desk or chair. Or if you are reading this while sitting outside, you might see pattern in the way tree branches, on the organization of the leaves, or on the design of a snail's shell. Beautiful and intricate patterns arise not only in nature, but also in the geometric patterns of man-made art, such as in a woven rug or a tiled mosaic.  If you look around to your surroundings, you will see patterns every which way. Maybe you will see a patterns in the alternating dark and light grain of your wooden desk or chair. Or if you are reading this while sitting outside, you might see pattern in the way tree branches, on the organization of the leaves, or on the design of a snail's shell. Beautiful and intricate patterns arise not only in nature, but also in the geometric patterns of man-made art, such as in a woven rug or a tiled mosaic. 
  
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 These notes are intended to introduce you to the mathematics behind pattern formation. The first section is just a brief discussion of why we might be interested in understanding patterns in biological systems (e.g. developmental biology). The second section talks about the basic partial differential equations from which we can build many of the patterns we encounter in nature. The next sections will talk about pattern formation itself, and we will work through some interesting examples that can be applied to animal coat patterns. These notes are intended to introduce you to the mathematics behind pattern formation. The first section is just a brief discussion of why we might be interested in understanding patterns in biological systems (e.g. developmental biology). The second section talks about the basic partial differential equations from which we can build many of the patterns we encounter in nature. The next sections will talk about pattern formation itself, and we will work through some interesting examples that can be applied to animal coat patterns.
Last modified: 2021/09/06 01:50