This article is adapted from the Introduction of Design in Nature: How the Constructal Law Governs Evolution in Biology, Physics, Technology, and Social Organization, written by Adrian Bejan and J. Peder Zane. This law sweeps the entire mosaic of nature from inanimate rivers to animate designs, such as vascular tissues, locomotion, and social organization. The constructal law tears down the walls that have separated the disciplines of science by providing a new understanding of what it means to be alive. The constructal law defines life in physics terms, and it covers all live-system phenomena. The author believes that the constructal law also challenges another idea that has become dogma since Darwin—that there is no overarching direction to evolution. The constructal law, by contrast, predicts that evolution should occur because of the tendency of all flow systems to generate better and better designs for the currents that flow through them.


This book is about design in nature as a scientific discipline, centered on a physics law of design and evolution: the constructal law. This law sweeps the entire mosaic of nature from inanimate rivers to animate designs, such as vascular tissues, locomotion, and social organization.

Discovering a unifying law of design in nature was not on my to do list when I traveled to Nancy, France, in late September 1995. I was a forty-seven- year-old professor of mechanical engineering at Duke University who had come to deliver a lecture at an international conference on thermodynamics. Giving you a sense of how steeped my career was in mechanical engineering, I remember that I had brought fliers announcing the publication of my seventh book, Entropy Generation Minimization.

My work took a fateful turn during the prebanquet speech delivered by the Belgian Nobel laureate Ilya Prigogine. Echoing the scientificcommunity's conventional wisdom, this famous man asserted that the tree-shaped structures that abound in nature—including river basins and deltas, the air passages in our lungs, and lightning bolts—were aléatoires (the result of throwing the dice,). That is, there is nothing underlying their similar design. It's just a cosmic coincidence.

When he made that statement, something clicked, the penny dropped. I knew that Prigogine, and everyone else, was wrong. They weren’t blind; the similarities among these treelike structures are clear to the naked eye. What they couldn’t see was the scientific principle that governs the design of these diverse phenomena. In a flash, I realized that the world was not formed by random accidents, chance, and fate but that behind the dizzying diversity is a seamless stream of predictable patterns.

As these thoughts began to flow, I started down a long, uncharted, and wondrously exciting path that would allow me to see the world in a new, and better, light. In the sixteen years since, I have shown how a single law of physics shapes the design of all around us. This insight would lead me to challenge many articles of faith held by my scientific colleagues, including the bedrock beliefs that biological creatures like you and me are governed by different principles from the inanimate world of winds and rivers, and the engineered world of airplanes, ships, and automobiles. Over time, I would develop a new understanding of evolutionary phenomena and the oneness of nature that would reveal how design emerges without an intelligent designer. I would also offer a new theory for the history of Earth and what it means to be alive.


Evolution (persistence, life) of an artificial river basin on the laboratory floor. The lower figure shows the evolution of a river basin in a porous layer with uniform resistance to erosion (n is the number of grains removed by the erosion process, that is, the measure of time).

In addition, I and a growing number of scientists around the world would begin finding new ways to make life easier: better ways to design roads and transport systems; to predict the evolution of civilization and science, of cities, universities, sports, and the global use of energy. We would unravel the mysteries of Egypt's pyramids and the genius of the Eiffel Tower while demonstrating how governments are designed like river basins and how businesses are as interdependent as the trees on the forest floor.

All that lay in the future when I boarded the plane for the trip home. High over the Atlantic, I opened my notebook (the old-fashioned kind, with paper) and wrote down the constructal law:

“For a finite-size flow system to persist in time (to live), its configuration must evolve in such a way that provides easier access to the currents that flow through it.”

I was writing in the language of science, but the fundamental idea is this: Everything that moves, whether animate or inanimate, is a flow system. All flow systems generate shape and structure in time in order to facilitate this movement across a landscape filled with resistance (for example, friction). The designs we see in nature are not the result of chance. They arise naturally, spontaneously, because they enhance access to flow in time.

Flow systems have two basic features (properties). There is the current that is flowing (for example, fluid, heat, mass, or information) and the design through which it flows. A lightning bolt, for example, is a flow system for discharging electricity from a cloud. In a flash it creates a brilliant branched structure because this is a very efficient way to move a current (electricity) from a volume (the cloud) to a point (the church steeple). A river basin's evolution produces a similar architecture because it, too, is moving a current (water) from an area (the plain) to a point (the river mouth). We also find a treelike structure in the air passages in lungs (a flow system for oxygen), in the capillaries (a flow system for blood), and the dendrites of neurons in our brains (a flow system for electrical signals and images). This treelike pattern emerges throughout nature because it is an effective design for facilitating point-to-area and area-to-point flows. Indeed, wherever you find such flows, you find a treelike structure.

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. 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. All these designs have arisen—and work together—to allow animals, like raindrops in a river basin, to move more easily across a landscape.

The constructal law tears down the walls that have separated the disciplines of science by providing a new understanding of what it means to be alive. Life is movement and the constant morphing of the design of this movement. To be alive is to keep on flowing and morphing. When a system stops flowing and morphing, it is dead. Thus, river basins configure and reconfigure themselves to persist in time. When they stop flowing and morphing they become dry riverbeds, that is, the fossilized remains of earlier “live” flow systems. The solid, treelike veins of ore found underground today are fossils of the fluid streams, eddies, and meanders that flowed before solidification a long time ago. Biological creatures are alive until all their flows (blood, oxygen, locomotion, and so on) stop, after which they, too, become fossilized remains.

This unifying definition marks an advance because it removes the concept, life, from the specialized domain of biology. It aligns it (or, better, it juxtaposes it) with the physics concept of the dead state, which means “equilibrium with the environment” in thermodynamics: a system that is at the same pressure, the same temperature, and so forth as its surroundings and hence, nothing moves. The constructal law defines life in physics terms, and it covers all live-system phenomena.

On one level, the constructal law can be expressed through the language of mathematics, physics, and engineering. My colleagues and I have published hundreds of articles in leading peer-reviewed journals. My own books for specialists—including Advanced Engineering Thermodynamics; Shape and Structure, from Engineering to Nature; and Design with Constructal Theory—use the constructal law to predict the phenomenon of design configuration. Leading universities, from Paris and Lausanne to Shanghai and Pretoria, have hosted international conferences and courses on the constructal law.

This is the natural phenomenon covered by the constructal law: the generation, ceaseless morphing, and improvement of flow design. This mental viewing enables us to recognize that people, birds, and other animals are flow systems that carry mass on the surface of the globe; that trees and mud cracks are flow systems for moving water from the ground to the air; that universities, newspapers, and books are flow systems for spreading knowledge across the globe.

Consider the snowflake. The prevailing view in science is that the intricate crystals formed by the snowflake have no function. This is wrong. In fact, the snowflake is a flow design for dispersing the heat—called the latent heat of solidification—generated on its surfaces during freezing. As water vapor condenses and freezes it throws off its excess heat. When the ice crystal first forms, its spherical bead is the shape that grows faster than other shapes, the shape that facilitates rapid solidification. When the bead is large enough, needles emerge and enhance solidification (that is, produce ice) faster than the sphere. To facilitate solidification even more, larger snowflakes morph into shapes with more needles that disperse heat. Complexity is finite (modest), and is part of the constructal design that emerges. Complexity is a result, not an objective; not an artist's wish; and, contrary to current dogma based in fractal geometry, it is certainly not “maximized.”


Design unites the animate with the inanimate. The phenomenon of design generation and evolution is exhibited by all flow systems: if we see a pattern, then something is or was flowing. The left side shows the delta of the Lena River in northern Siberia. The right side shows a cast of the human lung (Courtesy of Prof. Ewald Weibel, University of Berne).

As a first principle, the constructal law does not start from observation. It is a pure theory, a purely mental viewing of how things should be. We don’t catalog and measure every river (or bird, tree, lightning bolt, etc.). Instead, we discover mentally just one of them, and one is enough—it is the cat out of the bag; it keeps us awake until we assure ourselves that nature is the way in which the principle painted it for us in the mind, in the dark of the night.

In the sixteen years since the conference in Nancy, I and many other researchers have not found a single flow system that cannot be predicted by the constructal law. Specialists are using it to illuminate a wide range of subjects, including linguistics and sociology, nuclear decontamination, globalization, finance, warfare, patterns of residential segregation, and human mortality. The applications are so numerous that the constructal law is still in its infancy.

If I were to add two words to the constructal law, they would be these: “given freedom.” Constrictions abound in our world, preventing things from organizing themselves in more efficient ways. A dam, for instance, stops the river from flowing; bad ideas make it harder for human beings to thrive.

Rigid governments lacking the ability to change are just one manifestation of the inevitable forms of resistance that obstruct flow. Instead of struggling under dictators or totalitarian governments, flow configurations evolve in one direction in time: to reduce the effects of friction and other brakes that inhibit their flow. Resistance is inevitable and unavoidable. It is why the world will never be a perfect place and why the most flow systems can accomplish is to keep getting better, that is, to be less and less imperfect. Given freedom, flow systems will generate better and better configurations to flow more easily.

In my academic life, I was particularly attuned to this phenomenon—able to see what others had missed—because I had, quite by accident, grappled with the same problem faced by rivers and trees through my research as an engineering professor at Duke University and as a consultant for industry and government. We engineers are rarely thought of as cool, but my specialty is designing smaller, more efficient systems for cooling electronics. In general, the more computational power you generate, the more heat you create. For decades I used mathematics and the laws of physics to develop better designs for guiding that heat through and out of the box.

I noticed but did not think much of the fact that the drawings I was producing corresponded to the treelike flow structures that appear in nature. Before Prigogine's speech in 1995, I had never put two and two together and seen that a universal principle explained why Mother Nature and I were arriving at similar answers. The “click” I experienced that evening made me lift my eyes from my work and consider the shape and structure of everything around me. It made me wonder: What generates all these configurations? Why does this geometry happen?

Design in nature is generating a lot of excitement today over the entire range of science—from geophysics and biology to social dynamics and engineering. The interest is fueled by two trends:

  • 1.

    A voluminous body of knowledge has accumulated, and it shows that features our minds perceive as design (configurations, rhythms, scaling rules) are present in all flow systems in nature.

  • 2.

    Design phenomena are not covered by the existing laws of physics.

The empirical knowledge has far outpaced the theoretical framework that is needed to support it. This kind of mismatch is the ammunition and trigger for scientific revolution. If science is an evolving animal design, then the animal has become too heavy and has no alternative but to develop a larger skeleton for itself.

From the clash between the empirical and the theoretical comes the better science, the larger skeleton that includes a law to support all the phenomena of design and evolution in nature. Many other scientists have offered their own insights into the riddle of design in nature. To varying degrees these include fractal geometry, complexity theory, network theories, chaos theory, power laws (allometric scaling rules), and other “general models” and optimality statements (minimum, maximum, optimum).


Locomotion is the constructal-law design for moving animal mass on the biosphere. The characteristic speeds of all the bodies that fly (insects, birds, human-and-machine species) next to the constructal speed versus body mass raised to the 1/6 power.

My work is not a response to, or critique of, their efforts. In fact, I became acquainted with this vast literature only after discovering the constructal law in 1995. What I did know at the time is thermodynamics, the science of how to convert heat into work and work into heat. Work represents movement and flow against forces that resist. 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.

Not appreciated then was that 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.

It occurred to me that if physics is to cover nature completely, it must be endowed with an additional first principle that accounts for the phenomenon of design generation and evolution everywhere and in everything. The constructal law is this new addition.

Previous attempts to explain design in nature are based on empiricism: observing first, thinking and explaining after. All these attempts articulate conclusions about observations that have accumulated into a body of knowledge. They are backward looking, descriptive, and explanatory, not predictive. They are not theory, even though many authors use the word “theory” to name their work in order to promote it.” Darwin, for example, gathered all his observations about the evolution of biological creatures and created a convincing narrative that fit those known facts. Likewise, fractal geometry is descriptive, not predictive. Proponents of fractal geometry create mathematical algorithms to manufacture images that look like natural images, such as snowflakes, lightning bolts, and trees. The algorithms they devise in order to draw these images are not derived from principle but from trial and error. The algorithm that the mathematician chooses in order to draw the tree in the garden is analogous to the brush and paint that the painter chooses in order to depict the same object. The mathematician shows us only the algorithms and drawing that come out right, not those that look like nothing. The painter does the same.

This fundamental division between physics and biology is false. The remnants of this old worldview aren’t the only things that have hindered understanding. At its best, science encompasses everything—it seeks to provide a rational basis for all that is. However, especially during the last two hundred years, its practitioners have tended to slice and dice the universe into smaller and smaller pieces, all the way to the infinitesimal. This has prevented even those who are aware of the overarching tendencies of design in nature from taking the imaginative leap to see that the broad evolutionary tendencies we observe in living creatures also shape inanimate phenomena that do not possess DNA subject to random mutation, such as rivers, global weather patterns, and everything else that moves.


Animate and inanimate flow systems predicted based on the constructal law. They all facilitate the circuit executed by water in nature: raindrops, tree-shaped river basins and deltas, trees and forests, the flow of animal mass (swimming, running, flying), and turbulent structure.

I took this step in 1996. While writing my second paper on the constructal law for an international journal, I noted:

A lot has been written about natural selection and the impact that thermodynamic efficiency has on survival. In fact, to refer to living systems as complex power plants has become routine. The tendency of living systems to become optimized in every building block and to develop optimal associations of such building blocks has not been explained; it has been abandoned to the notion that it is imprinted in the genetic code of the organism.

If this is so, then what genetic code might be responsible for the development of equivalent structures in such nonliving systems as rivers and lightning?... Whose genetic code is responsible for the societal “trees” that connect us, for all the electronic circuits, telephone lines, air lines [routes], assembly lines, alleys, streets, highways, and elevator shafts in multistory buildings?

I am not disputing the role of genetics in the origin of species-just as I don’t discount the pivotal role of soil erosion in the formation of river basins. But mechanism is not law. It may explain what has happened but not why it should happen.

The constructal law also challenges another idea that has become dogma since Darwin-that there is no overarching direction to evolution. Proponents of that view claim that adaptations make species better able to survive, but they never explain why these changes should occur and what they mean by “better.” The closest they come is through a piece of circular logic that says: A change is better if it aids survival; any change that aids survival is better. The constructal law, by contrast, predicts that evolution should occur because of the tendency of all flow systems to generate better and better designs for the currents that flow through them. It expresses the meaning of “better” in unambiguous physics terms-change that facilitates faster, easier movement. Design evolution never ends.

The constructal law is not about destiny (or optimum, maximum, minimum, most, least, best, worst, etc.). Yet the insights from the eighteenth century suggest one of the powers of the constructal law: It offers a scientific confirmation, a rational, testable basis for our intuition that there is a direction in time to the evolution of all around us, a purpose, a direction toward flow performance in all that goes on around us.

The constructal law teaches us that nothing operates in isolation; every flow system is part of a bigger flow system, shaped by and in service to the world around it. The flow system we call a tree is also part of the larger flow system (that also includes rivers and weather patterns) for moving water from the ground to the air in order achieve an equilibrium of moisture locally and globally. At the end of the day, the tree, like every other flow system, exists in order to facilitate nature's tendency to flow with configuration. Its shape and structure reflect the tendency to generate designs to do this efficiently. This interdependence, born of thermodynamics and the constructal law, is the true source of harmony, balance, and oneness in nature.

I have not only discovered this fact, I’ve lived it. When meat began to disappear from shelves in Romania during the 1960s, my father, a veterinarian, made a statement. He hatched chickens. He had a light box that illuminated the inside of the egg so we could make sure the embryo was developing. As a teenager, I stared in awe and wonder at the growth that unrolled before my eyes each day, as the vasculature grew and spread tightly on the inside surface of the shell. I also noticed that the design I was seeing was the same as that of the river basins on the colored maps I was drawing in school. Where the chicken embryo was evolving on the inside of the sphere, the Danube basin had evolved on the outside of the spherical Earth.

Back then, I considered these similarities cool correspondences, nice ideas. Now I recognize that my father's light box was illuminating the design all around us. I am also able to see that the Earth with its river basins and other river basins-of atmospheric, ocean, and air traffic circulation-is a vasculature woven on top and through another spherical surface of life. So life is flow, life is movement, life is design.

DESIGN IN NATURE by Adrian Bejan and J. Peder Zane.

Copyright © 2012 by Adrian Bejan and J. Peder Zane.

Published by arrangement with Doubleday, an imprint of The Knopf Doubleday Publishing Group, a division of Random House, Inc.