NetLogo Models Library:
How are groups of bees able to build their honeycombs out of perfect hexagons? This model illustrates one hypothesis for a possible mechanism.
Each bee moves in a clockwise circle, spreading a chemical pheromone behind it. Over time, the pheromone diffuses and eventually evaporates. The pheromone affects the behavior of the bees crawling over it as follows: the bees move faster when there is more pheromone, but they also decrease their turn radius. The effects of these two rules balance each other, leaving the size of the loops roughly constant.
Press SETUP to create some bees, and press GO to start them on their rounds. If you want the model to run faster, make the bees invisible with the HIDE BEES button. Turn off the display through the view controls to make the model run even faster.
Initially, the bees draw a big mess of irregular loops. But over time, the loops sort themselves out into a loose grid. As more time passes, the grid becomes more and more regular, approaching a perfect hexagonal lattice, which is the optimal arrangement for maximizing the number of circles that fit on a surface.
Experiment with the effect of varying the number of bees.
There are a lot of arbitrarily chosen numbers in the Code tab. Experiment with the effect of varying them.
In this version of the models, the bees wrap around the edges of the world. Try modifying the model so the bees are clustered near the center of the world, to prevent wrapping. What happens?
Also, try having the bees all start from a central location. Does this still produce the hexagonal lattice throughout the entire world?
It takes time to diffuse and evaporate the chemical across every patch in the world, so instead of doing it every turtle step, we do it every 10 turtle steps. This speeds up the model a lot without noticeably altering the behavior.
Slime and Ants are other models that use pheromones to coordinate the behavior of individuals into an interesting overall effect.
The rules for this model were invented by David Little in 1995. The NetLogo code is adapted from his original MacStarLogo code. On the starlogo-users list, he wrote:
> During a visit to Tilff, in the Belgian Ardennes this summer, I was amazed to watch live beehives that had been built with glass walls, in the Bee Museum there. You could see into the hive, and observe the bees' activity (safely!). As if by magic, the regular architecture of the hive emerges from the seemingly random motions of the workers: the famous hexagonal array, constructed on both sides of plates hung vertically, and evenly spaced apart. The million-dollar question is, how do they do it? Is the beehive determined by their genes? How is it that different sized bees make cells all exactly the same size?
> That the piling up of round objects easily ends up as a hexagonal array, I already knew: it takes up the least amount of space. Being almost totally ignorant of entomology, nevertheless, I made an amateur hypothesis: maybe the hive is the result of a few simple behavioral rules, and there is no hive 'blueprint' in the bees' genes. The apparent random motion of the bees is perhaps in fact highly organised into feedback loops: a bee's next move must depend on what she and the others have done and built before.
> I don't claim that real bees work with the same rules, but I've proved my hypothesis anyway!
Researchers have extensively studied honeycomb formation. Here are some references to consult for further information:
Camazine, S., et al., Self-organization in biological systems. 2001, Princeton, NJ: Princeton University Press. 538. (ch.16)
Camazine, 1990 -- SO pattern formation in the combs of honey bee colonies.
Pratt, Stephen. 1998. Condition-dependent timing of comb construction by honey bee colonies, animal behaviour, 56, 603-610
Theraulaz, G. & Bonabeau, E. (1995) Modelling the collective building of complex architectures in social insects with lattice swarms. Journal of theoretical Biology 177, 381-400.
Theraulaz and Eric Bonabeau. Coordination in distributed building. Science, 269(4):686--688, 1995.
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For the model itself:
Please cite the NetLogo software as:
Copyright 2003 Uri Wilensky.
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License. To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.
Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at firstname.lastname@example.org.
This model was created as part of the projects: PARTICIPATORY SIMULATIONS: NETWORK-BASED DESIGN FOR SYSTEMS LEARNING IN CLASSROOMS and/or INTEGRATED SIMULATION AND MODELING ENVIRONMENT. The project gratefully acknowledges the support of the National Science Foundation (REPP & ROLE programs) -- grant numbers REC #9814682 and REC-0126227.