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Chaos: Geographers and The Butterfly Effect

In chaos theory, the Butterfly Effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic non-linear system can result in large differences in a later state.

As geographers, we observe spatial and temporal variation at the most enormous scale range and handle the data we acquire by tying it to the Earth’s surface – Lat / Long, Easting, Northing, Grid Coordinate.

Every little change on the Earth’s surface today can amplify and deliver a totally new paradigm in time and space which could be immediate and dramatic, such as a sudden violent storm or volcano erupting, or subtler and slower, felt over a millennium, such as wind erosion or tectonic movement.

We should feel honoured that one of the most complex and challenging areas of mathematics and computer modelling relies on the use of geographic imaging to convey its core principle. With so many examples of this butterfly and its cataclysmic impact on the earth, beating its wings in Argentina, Brazil and Mexico impacts the Western side of the Pacific with hurricanes and tornados. It is fascinating to witness how the power of geographic visualisation allows the end user, those of us without doctorate in mathematics and physics, to grasp the true impact of chaos.

As Ray Bradbury, in “A Sound like Thunder” stated, ‘Step on a mouse and you leave your print, like a Grand Canyon, across Eternity. Queen Elizabeth might never be born, Washington may never have crossed the Delaware, and the United States may never have existed…”

Indeed, the community of chaos and mathematics has produced some of the most wonderful visual representations; even held up as art, with a wonderful aesthetic beauty. For example, the Lorenz attractor, a set of chaotic solutions of the Lorenz system which, when plotted, resemble a butterfly or figure of eight.

Visualizing the way things were, are today and could be, will always influence our own actions and decisions. It is reasonable to say that change, when it happens, can be sudden and dramatic, or subtle and take a millennium to understand its consequences. 

Working now in the field of business analytics powered by geography, we [Sterling Geo] have the wonderful opportunity and responsibility to present that bigger picture, or in our case the ‘bigger map’.

Dynamic data, even if it is turbulent and chaotic, can be represented and understood in maps and through intuitive visualisation techniques allowing us to reach the broadest cross-section of society. Also, with the now constant inflow of remote sensed data we can continually update or ‘nudge’ the visualization on through a smarter map to represent what ‘was’, what currently ‘is’ and potentially what ‘could be’ in a dynamic and highly informative manner.

Improvements in our arena of satellite imagery provision, from providers like Planet, imaging the earth every day, or Urthecast transmitting a 24/7 imagery feed from the International Space Station allow us to feed the map, we then witness the Butterfly Effect across the Earth’s surface dynamically.

With the growing power of cloud computing the opportunity to crunch massive datasets and produce simple information can now swiftly inform our decision-making and can allow simple lightweight applications to be created rapidly.

To illustrate just how chaos impacts us and can be represented, I have pulled together some simple images.

This wonderful representation from Earth Wind Map, showing the turbulence and flow of wind data. This dynamic environment only comes to life when portrayed as a map. Through the effective use of colour, over the basic outline of the United Kingdom, a viewer can understand what is essentially an extraordinarily complex, turbulent and chaotic system.

Prediction has a long tradition of manifesting itself in the mapping world, and we have certainly come some distance in our technology and accuracy in a short time, yet the fundamentals of Visualisation have only truly been updated by graphic design creating a more dynamic experience for the end user.


Weather prediction graphics in 1980's (left) compared to weather forecasting graphics today (right)

So why should we really care about this butterfly, and why now? The sheer volume of data now available allows us to consider the ‘predictive analytics’ of the future and, with the business analytics tools, certainly representation of data is simple but it’s the predictive analytics, the result of butterfly wings that we should consider next whilst Chaos is alive and well, whilst we have Geography we can at least see where it is!

Phil Cooper

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