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Spiral beehives have a lot in common with crystals

Spiral beehives have a lot in common with crystals

The fundamental laws that govern everything in the Universe, including thermodynamics, apply to both crystal formation and bee combs. However, there is plenty of room for other phenomena to occur under the principles of thermodynamics, which is why the cosmos can be as complicated as it is. Crystal formation and bee comb construction are two mechanisms that operate in quite distinct fields of research. So what leads to similar structures?

When scientists utilized mathematical models to analyze patterns seen in beehives, they discovered that they resembled crystal formation. Tetragonula stingless bees build a three-dimensional brood comb with a spiral or target pattern architecture.

(a) Combs of two species of the stingless bee Tetragonula showing structures of (a) target patterns (Tetragonula carbonaria), (b) spirals (Tetragonula carbonaria), (c) double spirals (Tetragonula carbonaria) and (d) more disordered terraces (Tetragonula hockingsi). Images courtesy of (a) Elke Haege; (bd) Tim Heard.
Figure 2.
(a) The open structure is like a multi-storey car park or, in this case of a spiral ramp, like the Guggenheim museum in New York (T. carbonaria). (b) Worker bees are observed to spend time clustered at the growing edges of terraces (T. carbonaria). Images courtesy of Tim Heard.

On the molecular level, crystals exhibit the same patterns. Because the same excitable-medium dynamics drive both crystal nucleation and development, as well as comb construction, a minimum coupled-map lattice model based on crystal growth explains how these bees generate the patterns visible in their bee combs.

The researchers utilized a few of factors to represent the shaped honeycomb when modeling how this type of structure arises. The first is the R value, which indicates that distinct patterns emerge based on the radius of one layer of beehive cells. Then there’s the –, which generates a random probability distribution. This is produced by imperfections in crystal development, and it is caused by how flat the bees can construct a layer in honeycomb building. The greater the R, the larger each layer of the bullseye or spiral, with fewer layers altogether. The larger, the more ‘disordered’ the terraces will become.

Figure 5.
Regime diagram of 1/R versus α. By increasing the randomizing factor α, the regime changes from flat terraces (target patterns) to steep terraces (spiral patterns) and eventually disordered terraces at higher values of α. The radius R influences the separation between terraces.

Although the principle is being understood, it does not explain why bees create such amazing designs instead of simply building normal honeycomb layers. The team believes it is a set of behavioral norms that force bees to build these buildings rather than a master plan. “When we humans build, we normally employ an architect who makes a plan of the whole structure. That’s global information,” Cartwright explains.

Crystals, slime moulds, the brain, the heart, chemical oscillators, forest fires and many other systems can function as excitable media. And, in this instance, bees making their combs too. So what the mathematics tells us is that the processes that drive atoms or molecules to aggregate as a crystal have the same mathematical structure as the processes that drive bees when making their bee comb.

See Also

The bee Tetragonula builds its comb like a crystal, Silvana S. S. Cardoso, Julyan H. E. Cartwright, Antonio G. Checa, Bruno Escribano, Antonio J. Osuna-Mascaró and C. Ignacio Sainz-Díaz

Published:22 July 2020
https://doi.org/10.1098/rsif.2020.0187

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