Many patterns in nature are obvious, and others become apparent as one develops a habit of looking. In these patterns we see characteristics of repetition, symmetry, specific shapes and combinations of these aspects.

Some traditions endow such patterns with profound or even sacred significance. The hexagon is one of the geometric shapes found in nature to which esoteric power has been ascribed.

Perhaps the best known natural form of the hexagon is the 6-sided cell of a honeycomb. Honeybees fashion the wax walls of cells that combine to form a honeycomb with amazing precision. The hexagon is an efficient shape for packing identically shaped cells together. By contrast, square or triangular cells packed together have longer wall lengths and so would use up more wax.

Hexagonal packing of a space enables the maximum number of close neighbours and a minimum amount of reinforcement is needed for the shallow corners.

The honeycomb in the photo above was all that remained of a natural hive in a fallen tree abandoned by wild bees, which I came across on a walk in a neighbouring suburb. Small amber-coloured ants were apparently gleaning bits and pieces from the dry honeycomb.

Interestingly a raft of bubbles floating on liquid form hexagon-like shapes when the bubbles are blown together and start adjoining each other. Although some bubbles may have 5 or 7 sides (or even more or less), most have 6 sides. Surface tension causes each bubble to have the least surface area and contributes to the stable arrangement of the mostly hexagonally shaped bubbles. (See http://nautil.us/issue/35/boundaries/why-nature-prefers-hexagons.)

The photo above is of a bubble experiment I performed today using a small bowl of soapy water. I created the bubbles by blowing down a tube inserted into the water.

It has been suggested that perhaps bees make round cells that surface tension pulls into hexagonal shapes, but can surface tension explain the hexagonal shape of cells in the nests of paper wasps? Paper wasps construct their nests from chewed-up fibrous material obtained from plants.

The hexagonal shape of the cells can be seen in this old wasp nest (above), which I found on the ground after a windstorm.

This nest is in use – some of the hatched larvae are visible in the cells of the nest tended by adult wasps. Interestingly the sides of cells that adhere to neighbouring cells are hexagonal, but the outer edges of cells that do not adhere to a neighbour tend more to roundness. This observation suggests the possibility that the insects make similarly sized round cells in a precise pattern, and as adjacent cells adhere to each other they attain the hexagonal shape – but I hasten to add that this is very uninformed speculation!

Another example of hexagons in nature is that the compound eyes of insects are packed hexagonally. Efficient hexagonal packing enables the compound eye of a dragonfly to contain 30000 hexagonal facets.

Only a high level of magnification reveals the hexagonal packing structure of the compound eye of an insect, such as a dragonfly, which is way beyond the capability of my camera. This photo does however show the enormity of dragonfly eyes relative to its size.

Dragonflies have better colour vision than any other animal. For example, the human eye has three types of light-sensitive protein (opsins) and human vision encompasses tri-chromatic vision. We see colour as combinations or red, blue and green. By comparison, the dragonfly eye, depending on the species has at least 11 opsins with some having as many as 30 different kinds of opsins. The vision of dragonflies, which is far superior to ours, is termed ultra-multicolour.  See Vyas (2018) and Brahic (2015).

I was considering digressing to look at the patterns in the segmented wings of dragonflies and other insects, but I have decided instead to see if I could find any visible hexagonal patterns in creatures and plants photographed in our garden.

I have kept a section of shed snake skin that I found in the garden. Snakes have scales of different shapes and sizes on different areas of the body, usually with particularly distinct scales on the head and neck. Scales on the back (dorsal scales) are very different to the scales underneath along the belly (ventral scales) that the snake uses to gain traction when moving. The scales in the photo are dorsal scales. The shape of these scales is hexagonal with two opposite sides being shorter (marked in red and black) than the other four sides (marked only in red).

A few weeks ago we found a complete shed snake skin hanging from the rafters of the roof over our back deck. It is most likely the skin of an Eastern Green Snake, which is a non-venomous snake. I have marked in red representative scales that are hexagonal.

As a matter of interest, I have labelled the clear ‘eyelid’ that covers and protects the snake’s eye. The eye cover is shed as part of the skin.

In this photo of an Eastern Green Snake that was hanging out in the grapevine above our back deck the different shaped scales on the head, neck, back and belly can be seen. The scales on the neck and the dorsal scales can be seen to overlap slightly. I have marked one of the dorsal scales that are hexagonally shape.

One sunny winter’s day a Brown House Snake came out into the open behind our house to bask in the sun. This is the only time I have seen this snake out in the open. The Brown House Snake, a non-venomous constrictor, is a very handsome snake with white stripes running longitudinally from the head down the sides of its body. The dorsal scales, slightly overlapping, are hexagonal with two opposite sides being shorter than the other four sides as in the Eastern Green Snake.

And although seemingly completely different, the segments on pineapple skin are also essentially hexagonal in shape. We grew this pineapple in our vegetable patch from a top we cut off from a bought pineapple.

The segments of the skin of the cone-shaped pineapple are arranged in spirals that follow the Fibonacci sequence – but I think this kind of patterning will be a discussion in another post.

When I started this post, I expected to cover various patterns in nature, such as spirals, and repetitious spots and stripes, but hexagons stole the show. In next week’s post I will highlight other conspicuous patterns in nature.

Sources:

Ball, Philip. 2016. Why Nature Prefers Hexagons: The geometric rules behind fly eyes, honeycombs, and soap bubbles. Nautilus, Issue 035. April 7. http://nautil.us/issue/35/boundaries/why-nature-prefers-hexagons

Brahic, Catherine. 2015. Dragonfly eyes see the world in ultra-multicolour. New Scientist, February 23. https://www.newscientist.com/article/dn27015-dragonfly-eyes-see-the-world-in-ultra-multicolour/#:~:text=Their%20massive%20globular%20eyes%20should,of%20red%2C%20blue%20and%20green.

Vyas, Kashyap. 2018. Why is The Hexagon Everywhere? All About This Seemingly Common Shape. Interesting Engineering, June 10. https://interestingengineering.com/why-is-the-hexagon-everywhere-all-about-this-seemingly-common-shape

Posted by Carol