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Perhaps the most magnificent animal building structure is the bee wax comb-a double-sided, nearly horizontal hexagonal cell. These units are built on both sides of a common backplane, which forms a foundation for the units on both sides. This usually highly regular structure has been proven to be mathematically optimal, maximizing storage space and stability while minimizing building materials (1). However, Smith et al. (2) It shows that honeybees also build cells of various shapes and sizes, such as when combining separate honeycomb structures. This raises the question of whether the innate behavior library of bees contains multiple different routines for each shape, whether bees plan to insert the best shape in advance, or whether the diversity of this structure can be explained by simple rules.
The hexagonal grid structure of the honeycomb is constructed by a leaderless collective composed of hundreds of bees, which makes people guess that it must be robots and repeated innate behavior routines at work. An analogy is to build a brick wall, where each layer is built by adding new bricks in a staggered, one-to-two pattern. This can be effectively achieved by robots without the supervision of an architect (3). This concept—the features of the existing structure are used to add the next element of the structure through a simple rule—is called stigmergy (4, 5). The analogy between insect cells and bricks has led some social insect researchers to model comb-like structures as a simple process of installing new, complete comb-like cells onto existing structures (5).
However, the hexagonal unit is not an externally supplied prefabricated unit. In contrast, honeybees use small wax dots to build cells, which are chewed, deposited, and carved into the wall (6) to form a hexagon with equal length sides with an internal angle of 120°. This is not the only challenge to the failure of the bricklaying robot analogy.
Bee hives are usually built downwards, attached to the underside of supporting structures, such as branches, rock outcrops (in open nesting bee species) or the upper surface of hollow trees (in hollow trees)-nesting species, such as familiar Western honeybee, Apis mellifera, the species studied here), and these natural surfaces are not flat and smooth (7). Therefore, the behavior must be flexible enough to deal with additional complexities such as slopes, protrusions, and cracks. One might assume that once the foundation is laid, the bees can turn to simple rules to construct repeating hexagons that are the same size as the worker's body-but they must also build a hexagonal drone that is 1.2 times larger than the worker's cell unit. The transition (change from one size to another) requires the assumption of further complexity of the building rules. Finally, honeycomb blades usually start with a few individual teardrop-shaped tongues (8) (Figure 1). When they stretch, they touch, so bees must adjust the cell structure to incorporate cell structures of different sizes, directions, and offsets. Smith et al. (2) Explore how bees respond to these challenges, and ask whether the bees that construct combs can be regarded as automata or architects.
The regularity and irregularity of the hive. (Top) Discrete tongue starting from five positions. (Bottom) An example of three tongues merging, the fourth gap is closing but not yet touching. There are irregular cell areas in the merge location (the highlighted examples are heptagons, pentagons, and irregular hexagons). In the middle of the second tongue, there is a transition from the working cell to the drone cell. The second and third tongues show varying degrees of tilt.
The author obtained measurements of regular and irregular cells. This is achieved by combining image processing methods for edge detection, allowing their software to locate cell walls. Then, further software performs geometric calculations to locate cell centers and vertices and extract cell metrics, such as area and wall length. Combining the advantages of manual processing and automatic processing, the typical inaccuracies in automatic image processing are subsequently eliminated by manual editing. Automation allows the authors to measure more than 12,000 cells and study the adaptations and compromises that bees make when they need to change or unify discrete parts of the honeycomb. Research areas of interest include the transition from the worker unit to the drone unit and the merging of parts involving the alignment, inclination (direction of the vertices of the hexagon) and size (worker and drone) of different units. These manually defined areas are arranged to span 30 mm (five or six cells) on both sides of the interface (transition or merge) to sample both regular and irregular cell formation. A huge diversity of cell shapes was discovered: pentagons and heptagons are the most common non-hexagonal shapes, but there are also quadrilateral, octagonal, and nine-sided cells.
Smith et al. (2) Shows that the adaptation between the cell areas of different tilts requires smaller adjustments, where the cells are more closely aligned, so the gradual change in tilt to match the other should result in reduced irregularities and fewer non-hexagons cell. Although the wall length in the interface area and the number of walls per cell vary more, the distribution is still bimodal, which is very consistent with the typical values of drones or working cells (2). The most common non-hexagonal cells (pentagons and heptagons) are usually found in pairs or triplets, where one cell with extra faces is adjacent to another cell with fewer faces. It seems that even if the bee cannot construct a perfect specimen, it will deviate as little as possible from the ideal state.
The interface between the worker and the drone unit can be created by the transition or merging of two construction sites, both of which introduce irregular units with different areas and wall lengths. Analysis (2) shows the difference between the controlled transition between the worker and the drone comb, compared to the less coordinated merger between the two tongues of the downward-growing comb. In the former case, it was found that the cells in the interface gradually changed from one size to another, resulting in few cells that were too small, while the merged area contained a wider range of sizes and many were not very usable Of smaller cells. This shows that when things are under their control, bees are more successful in adjusting cell size than using two separate hives.
For each type of merger (changes in size, displacement, and rotational misalignment), the author shows the degree of irregularity in the location of the intersection. Most of the irregular cells are concentrated in a distance of 15-20mm, or two or three cells. The author points out that this range, the distance over which adaptation occurs, is smaller than the bee’s foot-to-foot span. Therefore, the comb builder will be able to perceive the walls and corners of the cells on both sides of the adaptive area, so she can detect the arrangement of combs she will construct and the arrangement of the desired results. With inputs from both arrangements, balancing any deviation from the ideal length, the angle to others, and the distance from the opposite cell wall, she can find a cell vertex on each side of the gap to be connected by a suitable wall.
Research by Smith et al. Provide useful input to the question of how much complexity a simple rule can achieve, and the extent to which these may have to be paired with some form of blueprint of the desired result to generate a functional structure.
Therefore, bees seem to have a series of technologies. By default, they will build regular cells of a fixed size, but they can also build regular cells of different sizes, gradual from one size to another, merge unmatched cells, and deal with it. Regular cell basis, and a curved structure is generated through lateral asymmetry (9, 10). In addition, it seems that the technology chosen for a particular adaptation is well suited for this task, as the cells produced are rarely distorted to the point of being unusable (2). Cells that are not the correct size or are not hexagonal are rarely used for brooding, but are used to store food, so they are not wasted.
What can explain the diversity of seemingly intelligent solutions to such diverse geometric architectural challenges? One possibility is to combine stigma with a highly rich library of behaviors-each cell type has a pre-programmed rule (hexagonal cells, heptagons, pentagons, etc. for workers and drones). It can then be assumed that each routine is triggered by a geometric constellation of existing wax structures. However, a properly complete set of instructions becomes a bit onerous, as Donald Griffin (11) put it: “Environmental conditions vary so much that the animal’s brain must be the best in all situations. Behavioral programming specifications require a manual that cannot be lengthy."
A cognitive explanation for the observed diversity of solutions is that bees may have some form of mental template for constructing expected results (9, 10), evaluate existing geometric shapes, and then decide whether to construct an irregular shape The hexagon, or possibly a pentagon or heptagon as a compromise, is the optimal solution. Smith and others hinted at this kind of forward-looking planning. (2) In the transition from standard workers to larger drone units: The author observes that in the process of preparing for the construction of full-scale drone units, workers will build medium-sized units—as if they knew they were building And take preemptive steps to facilitate the transition. However, it seems that the medium-sized unit may also come from a simple rule-if the three sides of the structure are formed by comb units, then adding the three sides of the typical UAV unit size will generate a medium-sized unit.
So maybe we shouldn't get rid of the concept of stigma right now-we just need to check it at a finer-grained level than adding the entire comb unit shape (the bricklaying robot analogy above). Assuming that stigmergy is a mechanism that causes social insects such as bees to work without a guiding ideology but collectively work towards architectural goals, then the next step will be to characterize the entire content of the basic task, that is, to build a wall relative to the best direction. Existing cell walls, and have the required length. The structure of the cell is the emergent attribute of these actions, and the cell is the result of building a set of walls. If the walls of the existing structure are perfectly built, then the perfect unit can be easily added to the structure. If the requirements are roughly the same, the rule may just be to build a standard-sized wall at 120°.
If the current state is irregular, or the desired result is different from the current form, then the task will be slightly different, possibly a parametric version of the basic building of the 120° building wall. Regardless of how the vertices of adjacent cells are connected to the new wall, the misaligned walls of two adjacent construction sites will inevitably lead to irregular cells. Considering that building a wall is a basic task, bees do not need to have the specific ability to build hexagonal honeycombs, one with five sides and one with seven sides. In addition, knowing how to build walls of approximately the right size does not require knowing how to build worker-sized cells, drone-sized cells, and medium-sized cells.
Stigmergy originated from the study of social insects (4, 12), but recently it has been accepted by roboticists and space engineers (13, 14). The latter believes that stigma can help design alien construction systems in orbit or elsewhere. Due to the long distance, communication delay eliminates the possibility of direct control from the ground, so local decision-making is desirable. Distributed processing enhances overall reliability because it reduces the possibility of a single point of failure. Although there is no master controller, members of the robot labor force can be implemented as autonomous units, and each robot has possible actions. The specific operation will be selected based on whatever needs to be done and the current state of the construction/artifact. However, it is essential to use a form of branding that is smarter than the simple bricklaying method: a large group of bricklaying robots released on an alien planet will fail on the obstacle of bricklaying. Even with these, and the basic one-to-two rules for building brick walls, they might build impressive but not necessarily useful buildings. Research by Smith et al. (2) Provide useful input to the question of how much complexity a simple rule can achieve, and the extent to which these may have to be paired with some form of blueprint for expected results to generate a functional structure.
Author's contribution: VG and LC wrote this paper.
The author declares no competing interests.
See the accompanying article "Imperfect comb structure reveals the building ability of bees", 10.1073/pnas.2103605118.
This open access article is distributed under the Creative Commons Attribution-Non-Commercial-No Derivative License 4.0 (CC BY-NC-ND).
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