The focus of my work is on a deeper understanding of natural pattern and structural formation. I am specifically interested in the spontaneous creation of order and pattern in nature; where fundamental universal laws defining how energy is distributed throughout the universe intuitively suggests a natural tendency towards irregularity and disorder, rather than the order and patterning we see.
From researching a diverse variety of different cellular honeycomb structures; radiolarian skeletons to dragonfly wings, beehives to bubble and foam arrangements; it is clear that the governing, emergent principles defining their form and creation are indistinguishable. The repeating patterns and structures arise directly from an optimal use and organization of energy by all systems in the universe.
This project is concerned with further understand and researching the mechanisms by which energy is used, distributed and organized in natural systems and the built environment. I am interested in the notion of how seemingly unconnected systems organize and distribute energy/information in remarkably similar ways despite their physical differences. The fractal nature of energy and information distribution in all types of systems, from metabolic rates, to the structural of the web, to cosmological forces, points towards an underlying structural logic to the universe. Logic I feel that if  understood will redefine the way we think about our ever expanding cities and the role we play in shaping its future. 
To start to gain a better understanding about the structuring of natural systems and in what ways they are all connected and interrelated; I would like to begin with examining the surprisingly simple scaling patterns that determine the development of all life on earth.
Allometric power laws can describe all aspects of an organism’s physiology; heart rates, brain size, life span all are proportional to the mass of the organism. Max Kleiber’s first observed this scaling phenomenon in 1947 from a detailed analysis of metabolic rates of a wide variety of different organisms. 
Metabolic rate can be understood as the proportional relationship between its heat generating mass and its total surface area (the area by which heat is transferred away from the body). As an organism grows, its surface area increases in two dimensions whilst its body mass grows in three dimensions; meaning the rate at which an organism burns energy and produces heat, cannot exceed the rate at which its surface area can transfer the same heat away.
This proportional relationship between mass and metabolic is quantified by Kleiber’s negative quarter power scaling law.Negative quarter power scaling states that the metabolic rate for any organism, scales to the negative ¾ power of the organism’s entire mass. The same law holds for all types of organism of every scale; therefore in terms of energy distribution and consumption by way of an analogy, a mouse is identical in every way to a blue whale, as is a sunflower to a giant redwood. Moreover, because the relationship between mass and metabolic rate is sub-linear (negative), a blue whale, roughly 10,000 larger than a mouse, will only need 3160 times more energy (10,000 to the negative ¾ power). There is an economy in biological scaling, whereby larger organisms require less energy per capita than smaller organisms. This can also be understood by saying that as any organism grows bigger, life gets increasingly slower.

It at first seems illogical to begin to think that all life on the planet could evolve the exact same relationship between mass and metabolism. How could it be possible for the same allometric laws to extend to all organisms, from plants down to bacterial and single cell organisms, to the largest mammals as well as entire ecosystems like rainforests and coral reefs? Yet negative quarter power scaling can be found in all types of life across the whole planet, regardless of evolutionary paths; whenever a biological organism has to expend and distribute energy throughout its body, quarter power scaling governs its patterns of development.

“Life is easily the most complex of complex systems, but in spite of this, it has this absurdly simple scaling law. Everything around us is scale dependent; It’s woven into the fabric of the universe.” – Geoffrey West
Geoffrey West’s metabolic theory of ecology takes Kleiber’s law even further applying the theory to one the largest creations of all; the man made city. Gathering an immense range of data on many different sized cities around the world. West was looking to see if even the designed and planned infrastructure of our cities mimics in any way the negative quarter power scaling law seen in biological systems. Is the metaphor of a cities metabolism just that, a metaphor, or is there any empirical mathematical truth to support the assertion.
West found that negative quarter power scaling regulates all consumption and distribution of energy and transportation within the city. The number of petrol stations, petrol sales, road surface area, the length of electrical cables etc – all follow the exact same power law that governs the speed with which energy in expended in biological organisms. A city that is 10 times larger than another will not required 10 times more infrastructure, but only 3.16 times more; again highlighting the economy of largeness in sub-linear scaling. 
This economy in largeness has been proposed as the reason why large corporations seem to merge into even larger corporations or why cities worldwide are facing mass expansion in the face of an exponentially increasing population. If a blue whale is a scaled up mouse in terms of energy, then on the same graphical trajectory, a city is a scaled up ecosystem like a coral reef. Moreover the data studied was collected from cities in countries all over the world and every city fit the correlation. This last point highlights the underlying, universal reason for sub-linear city scaling as the correlation occurred regardless of any cultural, geographical or economical variations. Something is happening globally in all cities suggesting a common connection. That connection between all cities, West suggests is us. The city is a physical manifestation of human interaction and the dense clustering of those interactions; it is these dynamic and complex social networks that shape the cities ever-evolving form.


“All structure is a manifestation of underlying process.” – Fritjof Capra
The cause of the sub-linear correlation between mass and metabolism, across the entire spectrum of life and the built environment is therefore found within the architecture and structure of its governing networks. “Scaling emerges from the geometrical and statistical properties of the internal networks organisms and cities use to distribute nutrients, energy and information” – West. If our interactions are the complex networks defining the evolution of our cities, what then do the complex governing networks of biological systems look like? 
They are the familiar fractal forms that can be seen in the structures of neural networks, circulatory systems, river formations, lung trachea, tree branches, food webs and even entire ecosystems. They are the self-similar networks that evolution has favoured in every context to efficiently distribute nutrients, information and energy around any given system. In human social networks these network architectures are the reason behind the ultimate paradox of human connectivity; that even though we move in very small and tight social circles in comparison to 6.9 billion possible people we could know, we are still bound to every single person within six steps or less. 
It is the structure of complex networks that science has over looked in the past, and which has recently formed a new branch of science; network theory. Beginning with an explanation of small world networks defined by the work of Steven Strogatz and Duncan Watts in 1998, I wish to then take the analogy between reef and the city even further to describe another apparent natural scaling phenomenon; super-linear scaling.
“Small world networks is a unifying feature of diverse networks found in nature and technology, if a day should come that we understand how life emerges from a dance of lifeless chemical or how consciousness arises from billions of unconscious neurons, that understanding will surely rest on a deep theory of complex networks”. – Steven Strogatz
The size and topology of most complex networks you can imagine are incredibly vast; 30000 genes in the human genome, millions of species across the planet, billions of people, web pages and interactions, 50 trillion cells to fuel in your body including the most complex of all know networks, the human brain; 100 billion neurons with on average 1000 connections to other neurons, equalling 100 trillion distinct connections. Moreover even with a complete wiring diagram for all these examples, it is still very difficult to fully comprehend their mechanics due to the shear amount of computation required. This is where network theory is concerned; with simple organizing principles defining the relationships between individuals in a network and the patterns of their interactions.
To be able to study the pure mechanics of a network, network scientists tend to focus on pure connectivity, bare nodes and the links between them. The ambiguous relationships of human social circles for instance would simply be too much to comprehend at once so the individual in most cases is suppressed in order to uncover deeper understandings and laws. It is from these towering heights that many different networks look identical and start to reveal new insights into their functioning.
To understand the topology of small world networks, their structure and characteristics, it is important to look at the two extremes of how any system could possibly be connected; completely regular or completely random. Imagine 1000 nodes arranged around a wide circle, each node connected to 4 neighbours either side of itself. This is an example of a completely regular network where the statistical likelihood that your friends will know each other- is very high. The regular network displays high clustering but low connectivity, as it would take many intermediate steps to join a single node to another node on the opposite side of the network. A completely random network on the other hand (where a single node is connected to 8 other nodes randomly chosen from the 999 possible connections) would exhibit the exact opposite, very low levels of clustering (low possibility that your friends will know each other) but very high connectivity (you know 8 people, who know 64 people, who know 512 etc.) binding the whole network together in a very few steps.


Either of these types of network structures clearly is not suitable in describing, for example the paradoxical phenomenon of the six degrees of separation. In the regular world you could only ever know your immediate locality and would be widely disconnected from the rest of the network. Alternatively in the random network your entire social links would be distributed over the entire plant and it would statistically be very unlikely that you would know the person immediately next to you.
A small world network on the other hand combines both high levels of clustering and connectivity into one network architecture. Taking the regularly connected network and incrementally replacing the small local connections with completely random connections creates the dual natured small world network. The random connections join parts of the network that would otherwise have been completely separated. Moreover, converting just 10% of the small local connections into random connections, the network still exhibits high levels of local clustering whilst also having connectivity identical to that of the random network. As mentioned previously, this is clearly a very abstract way of describing any network. The model is a stripped back version of any network that might occur in nature; simple, featureless nodes and connections ignoring any other possible influences or other possible level of connectivity. 

However, small world networks define a type of network structure that is most revealing and eerily representative of many diverse networks found in nature and man made constructions. Lying somewhere between complete order and complete chaos, small world networks seem to be able to help explain a broad range of complex network systems; systems so diverse and different that it might seem ridiculous at first to compare them at all. These include; the six degrees of separation, the structure of neural networks, electrical grid infrastructure, the structure of the web, the communication of the10000 pacemaker cells in the hearts sinoatrial node, the worldwide spread of diseases like AIDS and even the synchronous behaviour of thousands of firefly’s flashing in unison.  Since their formulation in the late 90s, small world networks practically launched the science of complex networks and have had a profound affect upon almost all areas of scientific thought.

The interchangeable description previously made between the manmade city and the natural reef, can now be taken even further with the idea of small world networks architecture and also the areas where Geoffrey West’s city data didn’t in fact fit with negative power scaling law. 

West’s data that involved creativity and innovation – creative professions, patents, R&D budgets, inventors, etc. didn’t actually follow the negative quarter power scale law it was supposed to. A city 10 times larger than another wasn’t just 3.16 times more creative, nor was it 10 times more creative; it is 17 times more. A scaling law is still at work but this time is positive not negative; super-liner scaling rather than sub-linear scaling. City’s cover 2% of the earth surface, are currently home to 50% of the world population and provide the vast majority of innovative movements and social progression. The data was showing that the dense networks of larger cities worldwide provide an environment where the levels of creativity and innovation are far greater than that of lesser-populated areas.

“Great cities are not like towns only larger” – Jane Jacobs
The idea of super-linear creative scaling also explains the paradox proposed by Charles Darwin as he stood on fringe of the atoll reefs of the Keeling Islands in 1836. Surrounded by hundreds of miles of sparsely inhabited, nutrient poor open waters, Darwin wondered how it was possible for there to be so many species occupying an incredible variety of different ecological positions in such a comparably small space. The diversity displayed in the coral ecosystems points to super-linear scaling in relation to the harbouring and nurturing of evolution. Coral reefs in fact make up one tenth of 1% of the earth’s surface, yet account for a quarter of all known marine life. The dense interconnected network of the complex ecosystem much like the city itself provides an environment where evolution can exponentially flourish.

The city and reef ecosystem therefore can not only be described as identical in their use of and distribution of energy but also related in their harbouring and nurturing of innovation and evolution. Seeing all this from the small world network perspective also reveals that Darwin’s paradox isn’t a paradox at all; the dense connections and interactions between individuals, enable the biological and man made metropolis to create possibilities and connections that would otherwise have been impossible. They open doors and possibilities into what theoretical biologist Stuart Kauffman elegantly calls the ‘adjacent possible’.

“The adjacent possible is a kind of shadow future, hovering on the edges of the present state of things, a map of all the ways the present can reinvent itself.” – Steven Johnson

Unfortunately, the reef/city comparison can only go so far for now. Superliner scaling not only affects creativity and innovation, but also every other socioeconomic activity of the city that has no analogy in the natural reef that follows the same patterns; Wealth, crime, pollution, AIDS cases all follow the same superliner scaling. 

As a city gets bigger there is an economy and negative scaling in infrastructure, but everything else in life increasingly is forced to get faster and faster. This is most glaringly true in our economic paradigm, where companies need constant growth in order to survive at all. Thankfully our cities have a duel nature and are a huge resource of innovative ideas and creative responses; yet these virtues are forced to lie upon the same trajectory of the economy, constant acceleration, and the question is whether they can keep up? Collapse and depression it seems are therefore inevitable and in a way an intrinsic part of the modern cities ecosystem under our current paradigm of thought.

To put the role of the city in perspective and to quantify why a complete shift in current mentality is needed; every week until 2050 it is predicted that more than a million people will be added to the global city population. Cities all over the world are already facing the problems of mass expansion and ultimately the negative affects of super linear scaling and exponential growth. Moreover the population of urban slums over the next 30 years in predicted to double from the one billion it is now.

Our cities are historically the epicenters of all human interaction and their future survival and evolution will paradoxically come from the innovative environments they inherently harbor. This is where I feel the lessons of biology and the natural reef can not only help inform a new type of urbanism based upon intelligent small world networking and natural scaling laws, but also a whole new paradigm of thought about the city and the individuals role in shaping a sustainable future.


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