Constructal theory

Design in nature is flow. The two sides of the constructal law: we predict the occurrence of design in nature, and we design devices for human use.

The constructal law puts forth the idea that the generation of design (configuration, pattern, geometry) in nature is a physics phenomenon that unites all animate and inanimate systems, and that this phenomenon is covered by the Constructal Law. The constructal law was stated by Adrian Bejan in 1996 as follows: "For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it." [1]

The tree is the natural design for achieving flow access between one point and a volume. Alternating trees achieve flow access between two planes. Natural porous media exhibit multi-scale flow structures consistent with the multiple scales and performance of alternating trees.


Design in Nature

Design in nature is attracting interest across the entire range of science, from biology and geophysics to social dynamics and engineering. The interest is fueled by two trends:

  • An increasing body of knowledge showing that “design” features (patterns, rhythms, configurations, scaling rules) are present in all flow systems in nature, and
  • The fact that design phenomena are not covered by existing laws.

These trends meet head on, and the result of their collision is a better science: a new set of laws, which includes a law that accounts for all design phenomena in nature.

Constructal Law

The constructal law was stated by Bejan in 1996 as follows: "For a finite-size system to persist in time (to live), it must evolve in such a way that it provides easier access to the imposed currents that flow through it."

"Constructal" is a word coined by Adrian Bejan, coming from the Latin verb construere, to construct, in order to designate the natural tendency of flow system (rivers, trees and branches, lungs and also the engineered forms) to morph in a constructal evolutionary process toward greater and greater flow access in time.

The constructal law was proposed in 1996 as a summary of all design generation and evolution phenomena in nature. The constructal law represents three steps toward making “design in nature” a concept and law-based domain in science:

  1. Life is flow: all flow systems are live systems, the animate and the inanimate.
  2. Design generation and evolution is a phenomenon of physics.
  3. Designs have the universal tendency to evolve in a certain direction in time.[2]

The constructal law is a first principle of physics that accounts for all design and evolution in nature. It holds that shape and structure arises to facilitate flow. The designs that arise spontaneously in nature reflect this tendency: they allow entities to flow more easily – to measurably move more current farther and faster for less unit of useful energy consumed.[3] Rain drops, for example, coalesce and move together, generating rivulets, streams and the mighty river basins of the world because this design allows them to move more easily. The constructal law asks the question: Why does this design arise at all? Why can't the water just seep through the ground? The constructal law provides this answer: Because the water flows better with design. The constructal law covers the tendency of nature to generate designs to facilitate flow.

The constructal law proclaims that this is why we find a similar tree-like structure in all designs that move a current from a point to an area or an area to a point. The lightning bolts that flash across the sky generate a tree-like structure because this is a good design for moving a current (electricity) from an area (the cloud) to a point (a church steeple or another cloud). The circulatory and nervous systems of biological creatures generate a similar tree-like design because they too are moving currents from a point to an area and from an area to a point.[4]

Although treelike structures are a very common design in nature, they are only one manifestation of the constructal law. In a simple example, logs floating on a lake or icebergs at sea orient themselves perpendicular to the wind in order to facilitate the transfer of motion from the moving air body to the water body. A more complex example is the design of animals that have evolved to move mass better and better (to cover more distance per unit of useful energy) across the landscape. [5]

This includes the seemingly “characteristic” sizes of organs, the shape of bones, the rhythm of breathing lungs and beating hearts, of undulating tails, running legs, and flapping wings. The constructal law proclaims that all these designs have arisen—and work together—to allow animals, like raindrops in a river basin, to move more easily across a landscape. [6] Because human beings are not separate from but a part of nature, their designs are also governed by the constructal law. [7]

The constructal law defines the time direction of all evolutionary design phenomena. It states that designs should evolve, acquiring better and better configurations to provide more access for the currents that flow through them. It defines in physics terms what it means to be “fittest”, to “survive”, and to be efficient. Not all changes are improvements, but those that stick measurably enhance flow. [8] The constructal law states that design generation and evolution are macroscopic physics phenomena that arise naturally to provide better and better flow access to the currents that run through them. This occurs at every scale. Each component of an evolving flow system—each rivulet, each tree, each road—acquires evolving designs to facilitate flow access. As these elements coalesce into larger and larger structures (into evolving river basins, forests and transport networks), a hierarchy emerges such that the varying sized components work together so that everything flows more easily. This is seen in the shape and structure of the neural networks in the brain, of the alveoli in the lung, the size and distribution of vegetation in the forest and of human settlements on the map. [9]

In the big picture, all the mating and morphing flows on the largest system that surrounds us, the Earth itself, evolve to enhance global flow. For example, trees and other forms of vegetation that move moisture from the ground to the air are components of the larger global system, including forests, river basins and weather patterns, that have the tendency to equilibrate all the moisture on Earth.[10] The constructal law states that every flow system is destined to remain imperfect. The direction of design evolution is toward distributing the imperfections of the system, such that the “whole” flows easier (e.g., river basin, animal body, human vehicle). Evolution never ends. Optimality statements (minimum, maximum, optimum, end design, destiny), have no place in constructal theory. Nature does not move toward an optimal end design. The natural phenomena is not the elimination but the distribution (better and better over time) of imperfection. The distribution of imperfection generates the geometry (shape, structure) of the system.[11]

For example, in point-area and point-volume flows, constructal theory predicts tree architectures, such flows displaying at least two regimes: one highly resistive and one with lower resistivity. The constructal-law tendency manifests itself at every scale.

Some domains of application
Application What flows Tree channels: Low Resistivity Interstitial spaces: High Resistivity
Packages of electronics Heat High-conductivity inserts (blades, needles) Low conductivity substrate
Urban traffic People Low-resistance street car traffic Street walking in urban structure
River basins Water Low-resistance rivulet and rivers Darcy flow through porous media
Lungs Air Low-resistance airways, bronchial passages diffusion in alveoli tissues
Circulatory system Blood Low-resistance blood vessels, capillaries, arteries, veins diffusion in capillaries tissues

The constructal law provides a unifying theory of evolution. It holds that inanimate and animate phenomena generate evolving configurations to move more easily. The constructal law also provides a new definition of what it means to be alive. It states that life means flow and the free generation of design. If the flows stop, the system is dead (in thermodynamic equilibrium). The constructal law is the physics law of life and evolution. [12]

Constructal Thermodynamics

Thermodynamics rests on two laws. Both are first principles: The first law commands the conservation of energy, and the second law summarizes the tendency of all currents to flow from high (temperature, pressure) to low. These two laws are about systems in the most general sense, viewed as black boxes, without shape and structure.

The two laws of thermodynamics do not account for nature completely. Nature is not made of black boxes. Nature’s boxes are filled with configurations—even the fact that they have names (rivers, blood vessels) is due to their appearance, pattern, or design. Where the second law commands that things should flow from high to low, the constructal law commands that they should flow in configurations that flow more and more easily over time. [13]

Classical thermodynamics versus constructal thermodynamics
Thermodynamics Constructal theory
State Flow architecture (flow structure)
Process Change of structure (design change)
Properties Global objective and global constraints
Equilibrium state Equilibrium flow architecture
Fundamental relation Fundamental relation
Constrained equilibrium states Nonequilibrium architectures
Removal of constraints Increased freedom to morph
Energy minimum principle Evolution toward greater flow access

In contrast to fractal models of observed objects in nature, the constructal law is predictive and thus can be tested experimentally. Many natural designs, animate and inanimate, have been explained and unified by the constructal law, for example:

  • Global circulation and climate
  • River basin design: Horton's rules of stream numbers (~4) and lengths (~2), and all the other scaling rules (e.g., Melton, Hack) of river basins all over the world.
  • The distribution of city sizes and numbers, i.e. the "Zipf" line of log (size) versus log (rank).
  • The distribution of tree sizes and numbers on the forest floor, which is also a Zipf line of log (size) versus log (rank).
  • The flow of education as a morphing vasculature on the globe, and the rigidity of university rankings.
  • Vision, cognition, and the "golden ratio" phenomenon.
  • The entire architecture of vegetation: roots, trunks, canopies, branches, leaves, and the forest, including the prediction of Leonardo da Vinci's rule, Huber's rule, and the Fibonacci sequence.
  • Pedestrian movement, speeds, and patterns
  • The emergence of urban traffic design
  • The entire morphogenesis of dendritic crystals (e.g., snowflakes), as a flow structure that facilitates the flow of the heat of solidification
  • The scaling law of all animal locomotion (running, flying, swimming): speeds, frequencies, forces and the work spent per unit of mass moved and distance traveled.
  • The evolution of speed in sports.
  • Kleiber's law, the relationship between metabolic rate and body size
  • the relationship between breathing and heart beating times and body size
  • the relationship between the mass transfer contact area and body mass
  • The human bronchial tree with 23 levels of bifurcation.
  • the dimensions of the alveolar sac,
  • the total length of the airways,
  • the total alveolar surface area,
  • the total resistance to oxygen transport in the respiratory tree.

External links

  • Constructal Law web portal: publications, events, links, etc.
  • Unified Physics Theory Explains Animals' Running, Flying And Swimming: Duke University article.
  • Is Einstein the last genius? [1]
  • Tree branching key to efficient flow in nature and novel materials, [2]
  • Unifying The Animate And Inanimate Designs Of Nature, [3]
  • The bigger they get, the faster they go, The Guardian, UK, [4]
  • Size matters: bigger athletes dwarf efforts of smaller rivals [5]
  • ABC News, Are giants taking over sports? [6]
  • Why the golden ratio pleases the eye, The Guardian, UK, [7]
  • Le secret de la beaute demystifiee, Le Devoir, Montreal, [8]
  • Behind the NFL's Touchdown Binge, The Wall Street Journal, [9]
  • Collaboration of soloists makes the best science, [10]


  1. ^ Bejan, Adrian (1997). “Advanced Engineering Thermodynamics,” (2nd ed.). New York: Wiley.
  2. ^ Bejan, A; Lorente, Sylvie (2010). “The Constructal Law of Design and Evolution in Nature.” Philosophical Transactions of the Royal Society B, Vol. 365: 1335-1347.
  3. ^ Bejan, A; Lorente, S (2006). “Constructal Theory of Generation of Configuration in Nature and Engineering.” Journal of Applied Physics. Vol. 100: 041301.
  4. ^ Bejan, A (2000). “Shape and Structure, from Engineering to Nature.” Cambridge: Cambridge University Press.
  5. ^ Bejan, A; Marden, James H. (2006). Constructing Animal Locomotion from New Thermodynamics Theory. American Scientist, July-August, Volume 94, Number 4
  6. ^ Bejan, A (2010). The Constructal Law Origin of the Wheel, Size, and Skeleton in Animal Design. American Journal of Physics, Vol. 78, No. 7: 692-699
  7. ^ Bejan, A; Merkx, Gilbert A, eds. (2007). "Constructal Theory of Social Dynamics." New York: Springer.
  8. ^ Bejan, A (2005). The Constructal Law of Organization in Nature: Tree-shaped Flows and Body Size. Journal of Experimental Biology. Vol. 208, No. 9: 1677-1686.
  9. ^ Lorente, S; Bejan, A (2010). Few Large and Many Small: Hierarchy in Movement on Earth. International Journal of Design & Nature and Ecodynamics. Vol. 5, No. 3: 1–14.
  10. ^ Bejan, A; Lorente, S; Lee, J (2008). Unifying Constructal Theory of Tree Roots, Canopies and Forests. Journal of Theoretical Biology 254: 529–540.
  11. ^ Bejan, A; Lorente, S (2008). “Design with Constructal Theory,” Hoboken: Wiley.
  12. ^ Bejan, A. The Golden Ratio Predicted: Vision, Cognition and Locomotion as a Single Design in Nature. International Journal of Design & Nature and Ecodynamics. Vol. 4, No. 2: 97–104.
  13. ^ Bejan, A; Lorente, S (2004). The Constructal Law and the Thermodynamics of Flow Systems with Configuration. International Journal of Heat and Mass Transfer 47: 3203–3214

Popular literature

  • Maggie Wittlin, "A Finger on the Pulse of the World", SEED Magazine, January 13, 2006.
  • A. Bejan and J. H. Marden, “Constructing animal locomotion from new thermodynamics theory, Am. Sci., 94, 2006b, pp. 343-349. (doi:10.1511/2006.60.1000)
  • H. Poirier, Une théorie explique l’intelligence de la nature, Science & Vie, 1034, 2003, pp. 44-63.
  • You Tube, A new "constructal" law of nature? [11]
  • Video: Design in Nature, [12]
  • Video: Constructal Theory explains why a river looks like a tree, [13]
  • Natural Design with Constructal Theory, Mechanical Engineering magazine, [14]
  • The many and the few, Mechanical Engineering magazine, [15]
  • Laufen = Fliegen = Schwimmen, [16]

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