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Snail shell
The logarithmic spiral, which gets ever tighter towards its center, is found throughout nature, from snail shells to tropical cyclones to spiral galaxies. It is a self-similar shape: as you zoom in towards the center, the spiral always looks the same.
Aabeele, Shutterstock.com
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Wasp on a nest
Some wasps build nests out of chewed-up wood fibers in which the cells have perfectly hexagonal cross-sections. They have inherited instincts for making this geometrical pattern, which packs the cells together with the minimum of wall area.
Anest, Shutterstock.com
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Sand dune
Sand dunes take many forms, but all arise from the spontaneous self-organization of wind-blown sand. These undulating forms are called seif dunes.
Denis Burdin, Shutterstock.com
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Cracks in molten material
Cracks in a molten material appear as the top layer cools, solidifies and contracts, creating stresses in the hard layer. As the cracks relieve stress, they join up into a network that, while not perfectly orderly, obeys certain geometric rules about how cracks intersect.
Clearviewstock, Shutterstock.com
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Mollusk shell
The spiral shells of mollusks are really just a way of growing an ever larger chamber at the shell mouth for the soft organism to live in, without having to change the chamber’s basic shape.
Chris Hill, Shutterstock.com
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Closeup of a butterfly wing
The colored markings on butterfly wings are made up of thousands of individual scales with distinct colors. Common pattern elements, like stripes and eyespots, are reshuffled in different species with seemingly endless variety and invention.
AppStock, Shutterstock.com
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Millipede
The logarithmic spiral can also be considered to be a kind of rolled-up cone, like the gently tapering body towards the tail end of a millipede.
Khritthithat Weerasirirut, shutterstock.com
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Bubbles
In a normal foam, not all bubbles have the same size and shape, nor do they all have the same number of polygonal sides. But there are geometrical rules that govern bubble intersections: in particular, three bubble walls meet at angles of about 120 degrees, like the Mercedes sign.
Shebeko, Shutterstock.com
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Water drops on a leaf
Surface tension is one of nature’s form-creating agents. Here it pulls water droplets into almost spherical beads as they sit on the waxy, water-repellent surface of a leaf.
Olgysha, Shutterstock.com
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Compound eye
The compound eyes of flies look like a raft of bubbles floating on the water surface: both are arrays of tightly packed hexagons.
Heiti Paves, Shutterstock.com
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Butterfly wing microscopic view
Seen close up, the scales of butterfly wings are themselves delicately patterned with microscopic grooves and channels. Light reflected from these tiny structures undergoes wave interference, which picks out some colors at the expense of others and gives the wings an iridescent hue.
Nikola Rahme, Shutterstock.com
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Mineral dendrites
So-called mineral dendrites—dark branching patterns in rocks—look like fossil plants, and have sometimes been mistaken for them. But they are non-living crystals that have grown into this shape through a delicate balance of spreading and precipitation of the chemical ingredients.
Vangert, Shutterstock.com
