top of page



"Scientists from the University of Chile published a paper in the journal "Physical Review E. “With our work, we believe that the foundations are laid to study complex localized patterns. In particular, we show that the phenomenon is robust, that is, that it appears in different natural systems and that it is a consequence of the coexistence between a disordered pattern state and a homogeneous state”, explained one of them"...

Nature works under complex structures. We (Humans) as part of that sometimes seem chaotic, but our ages always converge via ADN@+ over time.

Here is the translation of the local note published in Chile:

In nature, there are patterns, forms that are repeated until a great structure is generated, which can be simple as rolls in clouds and sand dunes, hexagons in bee panels and pineapple shells; even labyrinthine forms in the self-organization of trees and in the skin of some fish. Understanding how this organization is produced is the objective of a team of physicists from the University of Chile, who have found a new discovery that allows them to understand this phenomenon.

“These complex structures generate labyrinth-like forms, which generally occupy the entire space, the entire skin of the fish, for example. We have discovered that these patterns can exist localized, not dominate the entire space, something like a complex, disordered stain, such as the stains in some animals”, indicates Marcel Clerc, a physicist at the University of Chile.

Until now, the possibility of the existence of a localized pattern with non-trivial symmetries had not been discussed.

“With our work, we believe that the foundations are laid to study complex localized patterns. In particular, we show that the phenomenon is robust, that is, that it appears in different natural systems, and that it is a consequence of the coexistence between a disordered pattern state and a homogeneous state”, adds Clerc.


With this, they hope to be able to understand complex phenomena, for example, in vegetation, it is important to understand the emergence of patterns because it can be an indicator of the degree of desertification of the ecosystem, this is because plants often self-organize to take more advantage of water, forming structures.

“That is to say, we can see a completely green zone, but also spots, certain arid zones, creating a disorder”, adds Sebastián Echeverría-Alar, a physicist at the University of Chile, co-author of this research.

There are also labyrinthine structures and focused patterns in our brain, with the network formed by neurons, our intestines, or skin diseases. So the understanding of these systems can have multiple applications.

“What are the environmental conditions that favor the appearance of localized and non-extended complex patterns. Answering this question could help to know the state of self-organization of trees and shrubs in arid and semi-arid systems?” adds Echeverría-Alar.


From a theoretical point of view, this work opens a new path in the numerical analysis of localized structures in pattern-type equations. The methods that exist so far rely heavily on the symmetries of the system. “Localized mazes lack trivial symmetries and require new methodologies to be fully analyzed. This motivates us to link our work with mathematicians who can develop new theories to understand the emergence of these intriguing solutions”, explains Clerc.

To reach these conclusions, Clerc and Echeverría-Alar worked together with Mustapha Tlidi of the Université libre de Bruxelles. During that time they carried out numerical simulations of two-dimensional and three-dimensional models of pattern formation to obtain different localized labyrinths in optical, chemical, and vegetation systems.

For the same reason, they now plan to continue with research in this field “the complexity of the labyrinth-type patterns is determined by the presence of defects within the structure. These defects bridge the different orientations allowed in the maze (paths). We want to investigate the role played by the interaction between these defects in the location of this type of patterns”, concludes Clerc.

The results of the research appeared in the article "Localized states with non-trivial symmetries: localized labyrinthine patterns" in the journal Physical Review E.


Water is life. If nature is converging to physical structures in order to make the best use of it, our question in Hexagon Group since research performed in 2015 is: Human Societies, like bees, can adopt a Hexagonal approach in order to make the best use of water, and other scarce resources, and create agreements, new governance, and accelerate development, projects, and investments?

During 2015 research we had the opportunity to use Hexagon Toolkit (R) for testing that hypothesis during an assignment hired by the National Secretariat of Water of Ecuador.

Our tool convened policies for water usage by engaging six kinds of players in games organized for creating a route map for accelerating investments in water infrastructure, and more important: creating a set of socially-accepted tariffs for covering the costs of water "as a right".

The methodology was qualitative in essence, in order to understand different complexities of water usage (water is economically and environmentally a good and service at the same time; it is also a human and nature´s right in the constitutional framework of Ecuador).

Our research mixed the results under a pattern that was able to organize, under a pricing mechanism, based not only on the usual long-run marginal cost of provision but also (and mainly) through a more "modern approach" of "long-run marginal benefits of water as a protected right for humans and nature".

For that, we had the opportunity of convoking 30 leaders on average (5 per each side of our "Hexagon") in the 34 most-conflictive zones in the map of water supply and demand. With those near 1000 observations included in our Hexagon Toolkit, we recovered an econometric model that allowed us to find patterns of supply and demand parameters, willingness to pay, and more important: capacities to pay after receiving the long-run marginal benefits, but bringing that to a "present-value" in time zero, under the expectations of policies and projects raised among the 1000 leaders convoked by the national government over the whole country.

In order to test the results, we also run a survey on households in the same locations where the leaders represented the needs of the locals.

We had the opportunity of running the same models with the other local data and found the same patterns among hexagonal leaders and family/homes leaders.

That way, we had the chance of applying a double set of data that was able to add the answers of leaders and families, getting to a model of prices that created a "quasi-market" of water as a public resource (water is not privatized in Ecuador), generating a financial mechanism (different to taxation) for covering the costs of supply, by estimating the marginal value of water as a demanded good and service.

The Hexagon model was key for adding structure to the complex governance scenario in water conflict zones. The agreements reached via Hexagon Toolkit between 1) state authorities, 2) private investors, 3) NGOs, 4) academia and networks, 5) communities, and 6) international players on policies and projects was key for granting water price per cubic meter (and not by a cubic meter per second, as previous tariffs were imposed).

The research was presented to national authorities, and the society in general and reached consensus, creating new legislation, and making viable the principles in the new constitution.

If water is key for life, and the hexagon shape is key for granting it in society, we can probably find new ways of agreements that are less public vs private ones, and more complex (more hexagonal, in a way).

It is only a matter of Structuring It!

Before closing this short article, please think about this final question:

Why does water form a hexagonal pattern?

"Water molecules in the solid-state, such as in ice and snow, form weak bonds (called hydrogen bonds) to one another. These ordered arrangements result in the basic symmetrical, hexagonal shape of the snowflake. ... As a result, the water molecules arrange themselves in predetermined spaces and in a specific arrangement. Dec 25, 2006"

149 visualizaciones0 comentarios


bottom of page