Constructal Theory and the Asynsis Principle

“The designs we see in nature are not chance. They rise naturally, spontaneously,
because they enhance access to flow…” (any flows: information, energy or matter)

Adrian Bejan

The Constructal law explains why nature has a temporal/spatial fractal geometry, and in so doing, how it enhances and facilitates complexifying evolution in both animate and inanimate systems.

So it’s with a sense of some relief and also vindication that the design research work that I’ve previously termed Dynamical Symmetries or more recently, Asynsis (meaning: asymptotic synthesis, asymmetric creation – or simply – ideas realised); regarding the geometries of optimal information, mass and energy flows in nature has also been conducted by others in parallel, over a similar timeframe of 20-odd years.

It’s called the Constructal Law (or Theory, if you prefer), and it explains why the geometry of nature is Fractal.

The author of this research (backed by a very substantial body of empirical data and predictive science, which comes to similar conclusions as my own), is the renowned Professor Adrian Bejan of the Pratt School of Mechanical Engineering at Duke University, NC, USA.

He describes himself as an engineer and thermodynamicist, as elaborated upon here:

The substantial and diverse academic work in the Constructal field is to be found here:

He’s also backed this work up with numerous experimental demonstrations (and is one of the top 100-cited authors of academic articles in his field), so I finally feel that I have an ally in convincing the world of the relevance of this beautiful and elegant, emergent property of nature.

I also feel that our work is highly complementary in that he approached it as an engineer while I did as an architect. It’s also terrific that he had earlier aspirations to be an architect himself, which I think shows in his holistic synthesis of Constructal law, his use of visualisations, diagrams and of geometry to demonstrate its validity.

I see his conclusions (based on his intuitions followed by empirical analyses and demonstrations) and my intuitions (based on reviews of work in numerous fields followed by conjectures relating to geometric and proportion systems and feedback loops and also some direct measurement), as two sides of the same coin in this sense:

If I may, (and to paraphrase): he refers to (information, mass and energy) flows becoming more easy over time, increasing their degrees of freedom, moving from areas to points and vice versa and needing more power over time, as a tendency of nature – while I refer to dynamical systems minimising their energy-waste (entropy production), whilst optimising their complexity over time through reiteration of archetypal feedback processes and oscillation between finite and infinite attractors to explore the widest, most irreducible probability spaces whilst still being an evolving unitary entity.

To quote a recent definition of feedback taken from a US Green Building Council study guide:

“Both positive and negative feedback loops effect a system. Feedback is essentially information or results of the system. This feedback can encourage the system or stop it.

A feedback loop can’t work unless information or results flow in the system.”

We are therefore in my humble opinion, talking about the same thing. We are talking about nature’s supreme economy, about it’s feedback-led optimisation and emergent, analogical complexification imperative. We are exploring why for example, self-organised criticality phenomena have a fractal structure, and why they even occur at all. We do this via thermodynamic behaviours on the Constructal side, and by analogical, recursive and optimal geometries with Asynsis.

Both are inherently dynamical, both describe how Form follows Flow.

From the earliest versions of my work (published in AD magazine in 1994 and since revised and peer-reviewed in 2011 by Professor Emeritus Vera de Spinadel of the University of Buenos Aries and the Nexus Network journal of mathematics and architecture), I have linked this behaviour with the pressing need for the sustainable development of our civilisation in general and specifically for environmentally sustainable design to be an urgent priority in the practice and education of  the architecture and engineering design of our built environment.

This Treehugger article also links Constructal Law with Sustainability:

Essentially, to best preserve nature – we must first truly understand and then properly emulate her.

I think Adrian certainly (and I in my small way), has contributed enormously to articulating Sadi Carnot’s intuitions about these behaviours, as he recently put it – and so I propose that he and I join forces in this regard, to push forward together at every opportunity to promote a sustainable future for society and in the built environment, since construction accounts for such large proportions (30-40%) of global energy use and consequent greenhouse gas emissions.

One of the reasons I connect the archetypal dynamical feedback iterator of the golden ratio (also known as φ – phi, pronounced “fee”), with architecture and sustainability is because its energy-minimising period-two behaviour is manifested as an asymptotic convergence series in the evolution of the Feigenbaum diagram which is a proportion I first measured in 1994-5 whilst studying Fractals, Chaos and Dynamical systems at the Engineering and Computer Science faculty of the University of Westminster, London.

I also found similar proportions in the analogous Julia set associated with the Period 2 disk of the Mandelbrot set.

I realised then that the golden ratio had an important behaviour in time as well as in space and that it was associated with optimal feedback processes and also energy minimisation, that the two were related – and that the analogical geometries that resulted were a manifestation of the principle of least action.
I then proposed that its dynamical, recursive behaviour should therefore become an icon for energy-efficiency and sustainability. To my knowledge, I’m the first architect to describe the golden ratio’s dynamical behaviour over time, rather than as just a static, proportion system – and its profound associations (via optimal, analogical geometries), with sustainability.

All this was still conjecture back in 1991-4, when I wrote my Kingston BA and Westminster Diploma theses, followed by publication in AD magazine in 1994.

So I hope you can imagine my surprise (and later delight), to also find corroborating references to these kinds of signatures in the dynamical systems science literature that I was then researching at the British Library and subsequently over the last two decades – culminating in my being kindly invited to present at the 8th annual Constructal law conference at Nanjing University of Science and Technology in 2013.

A summary review of the work over the last 20 years can be found here on this site in pdf format:

Initial confirmation of my 1994 article conjectures arrived in 2006 in the form of proof of the golden ratio being integral to the evolution of models of chaotic complex dynamical systems – as published here:

Fibonacci order in the period-doubling cascade to chaos

Physics Letters A 359 (2006) 638–639

(Please also see this blog’s Sunday 6 May 2012 entry: Entropy begets Design – QED, which also includes the above article as a pdf.)

As alluded to above, the golden ratio is also found in the locus of the Period Two disk of the Mandelbrot set and when it’s Julia Set dynamics are studied, it’s reiteration oscillates between finite and infinite attractors, analogous to Bejan’s “from points to areas and back again” behaviours.

Period Two is the lowest dynamic period possible, so is inherently also the lowest energy-consuming behaviour.

So in the AD article, I speculated that logically, the golden ratio must exemplify minimal-energy behaviours in nature.

I also note with great interest Bejan’s original study of the golden ratio in relation to optimal fields of human vision and how we favour ideal proportions that correspond to phi as imbedded in that same vision field.

I suspect that he is correct and would just add that I believe on the evidence of the above two examples of the dynamical, archetypally recursive, optimising and complexifying behaviour of the golden ratio that phi is also imbedded in the temporal feedback loops that we see in nature as well.

Another way of expressing this is that phi’s archetypal self-similarity is an emergent property or geometric signature of nature’s innate, dynamical, optimising, analogical, complexity-enhancing, self-organising behaviour.

So in short, I believe that we are largely in accord and that we could complement his definition of Constructal Law with one for the Asynsis Principle:

“Given freedom, 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.”

with an (admittedly less succinct), elaboration to this effect (effectively a 1st – 2nd Thermodynamics laws fusion):

“Open local dynamical systems when pushed further from thermal equilibrium by energy flows, minimise their energy-mass dissipation but also optimise their information and synthetic complexity over time, through the reiteration of archetypal, asymptotic, analogical feedback processes, through emergent synergised simplexity, by doing more for less, and by creating good forms – following true flows.”

In other words:

“Design in nature analogically, optimally emerges  from Entropy”

Together, engineers and architects have achieved great things in the past (my Hong Kong Spin structural engineer is ARUP’s wheel specialist, Pat Dallard), so I hope Adrian Bejan and I can too in promoting Design as (Art bridging to) Science.

For example, Hong Kong Spin is a landmark tower (the world’s first horizontal, habitable Ferris wheel), taking the form of the Greek letter Phi and the Chinese character Zhong in homage to the golden ratio in nature’s architectures and to the success of the “one country – two systems” process in Hong Kong.


I also hope that having some architectural, geometric backup in the form of the legendary golden ratio of Corbusier, Leonardo, Kepler, Fibonacci and Pythagoras will give Adrian Bejan extra resources in his quest to further disseminate and popularise the Constructal Law!

Nigel Anthony Reading BA Dip Arch ARB RIBA 

Paris, Tuesday 17 April, 2012


nigel reading | ba diparch cppa-ucl | arb-uk | riba | design director | ASYNSIS architecture + design 

shanghai-hong kong-london | | | +86 159 0040 4248 | +852 9370 1841



~ by Asynsis on April 17, 2012.

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