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This is a picture of a succulent plant that I found at the Devonian Gardens, an extension of the University of Alberta. It is a beautiful, tranquil place with collections of all manner of plants: medicinal herbs, Orchids, and many others.
Plants, of course, are part of the organic world that seems to be so full of patterns. The Devonian gardens also has a wonderful butterfly room stocked with butterflies from all over the world -- just another example of amazing the patterns in the organic world...
The inorganic world, rocks and such, struggle to keep up with plants and animals when it comes to patterns. Sure there are agates and waves on water, but non-living things do not seem to have anywhere near the variety of patterns displayed by living things. Think of the nearly infinite patterns that seashells have, no one would mistake them for rocks.
A seedling grows the most from the tip of its shoot. The cells that are formed there move off to the edges. This natural process of growth creates the spiral pattern which is seen in many plants. This shape evenly spaces the plant's leaves and prevents nearby leaves from overshadowing each other, thus favoring the optimal growth of the plant. Apparently, a similar pattern of growth creates the patterns found on seashells. Those fairly simple natural processes create the mathematically elegant forms that amaze us.
See a few other pattern photographs here.
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