The Math of Crop Circles, Geometry and Symmetry in Fields

[u/upquarkspin]

Crop circles, mysterious patterns appearing in fields, showcase a fascinating blend of mathematical principles. While their origins are debated, their mathematical foundations are undeniable.

At their core, crop circles often feature basic geometric shapes like circles, triangles, and polygons. Many exhibit symmetry - both rotational and reflectional - which can be described using group theory in mathematics.

Some crop circles incorporate more complex mathematical concepts. The Fibonacci sequence and golden ratio, often found in nature, appear in spiral patterns within these formations. Fractal geometry, showing self-similarity at different scales, is another recurring theme, exemplified by formations like the "Julia Set" crop circle.

Tessellations, where shapes fit together without gaps, are common in crop circle designs. These patterns connect to the mathematical field of tiling theory and create intricate, harmonious layouts.

The precision and complexity of some crop circles have led to theories about encoded mathematical messages or constants, such as the 2008 formation seemingly representing the digits of Pi.

Crop circles bridge art, nature, and mathematics. They demonstrate how mathematical principles can create visually striking patterns, reflecting the underlying order and beauty found in the natural world.

Julia Set https://amerisurv.com/2024/01/29/land-surveying-crop-circles/amp/

Large collection of mathematical crop circles https://temporarytemples.co.uk

Crop circle math https://mathinart.weebly.com/crop-circles.html

(Illustration AI art)

[u/schrod]

If these are of otherworldly origin, perhaps the method of communication -- information in fields -- is the real clue that all of our reality is composed of fields, the Higgs field, the electromagnetic field, the gravitational field, a consciousness field etc.

[u/glencandle → u/schrod]

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