The research I am doing under the umbrella concept of 'Fractal Agility' is just complexity science by another name. So what is 'complexity science'? It is really just another attempt to re-draw the map of different specialisms, using both new mathematical methods, computer simulation and computer science, and also a philosophy about how subjects are really related. The approach I have taken, for example, involves seeking to establish a strong mathematical connection between organisational economics and molecular biology.
The motivating idea for all complexity scientists is that, in some sense, the way we look at research problems today still resembles the way that biologists looked at biology before the discovery of DNA. We are unable to say which problems are really related to which because we don't understand which problems share the same 'DNA' (i.e. are truly closely related). By analogy, we now know by genetic analysis that what we call wasps (yellow and black striped insects that live together in hives) are part of a genetic family, the vast majority of which, look just like flies, are solitary and parisitic. The same thing may be true of the family of problems we study called organisational economics, economics generally and problems of cell differentiation in biology. I don't mean that economists are actually parisitic wasps, of course ;) but just that domains which don't resemble each other are actually closely related. If you disagree, you may perhaps believe the way that we have classified these two different domains is correct. In this case, you are making the opposite 'bet' which is that we already understand the 'DNA' of these two domains pretty well. Perhaps how you feel about this sort of bet depends on your intuition. I like intuition by the way - I don't think science = counter-intuitive; instead, to paraphrase Jordan Ellenberg author of 'How Not to be Wrong', mathematics is just common-sense but it is common-sense with a super-powered prosthesis.
The idea of 'fractal agility' is derived from both current thinking in software development culture (the school of thinking known as the 'Agile' movement) and ideas from complexity science. While 'fractals' have a reasonably precise definition in terms of Benoit Mandlbrot's ideas the concept of 'fractals' are also used more broadly by researchers in complexity science to draw new connections between certain kinds of phenomena.
Fractals are just one example of means by which mathematicians often find new connections between seemingly disparate fields of study. In the case of 'fractal agility', I use the concept of fractals to convey the idea that insights from the 'Agile' movement in software development (which is part of problems in organisational economics) may also apply to problems of differentiation of cells and cell behaviour, i.e. problems of modelling phenomena in molecular biology. This is becuase fractals are one way people are familiar with of relating patterns in objects of very different scales to each other. I also use concepts from fractal mathematics to model complex phenomenon of agents performing complex tasks. I develop agent-based simulations by encoding insights from game theory, information theory and computer theory. I also like to draw comparisons between the mathematics of physical agility, e.g. the ability for a cheetah to suddenly change direction while pursuing a gazelle, and the design of systems that can tolerate a high level of uncertainty and unreliable information whatever the scale of the system we are studying. I think that cell behaviour and software development problems both come under the same class of phenomenon that need to be 'agile' when described the right way. I couldn't think of a catchier name for this though.
Complexity science and art
'Complexity science' is a relatively recent discipline that seeks to approach existing domains of research from a different philosophical position. This philosophy is generally to try to re-draw the map of relationships between different domains in a 'holistic' way. As part of this approach I am very interested in the Art and Science movement and I also work with James Robert White whose website www.jamesrobertwhiteart.com hosts my previous blog. My work with James has allowed me to focus on the problems of modelling creativity, novelty and innovation.
Re-drawing the map
This approach of trying to 're-draw the map' is actually very old in terms of academia, but, historically, has often involved re-drawing something inside the boundaries of the scientific domain that was considered entirely outside the realm of science. A great example was the study of chance which was considered outside the realm of mathematics in the 16th and 17th century but gradually became part of mathematics, and so science. Another example is the study of philosophy which was circumscribed once the scientific method was established in the 17th century and then became further diminished when the social sciences of psychology, economics and sociology were established. One may argue that we are now seeing a reversal of this long historical trend as philosophy is currently expanding on its connections to practical science, e.g. AI, X-phi, philosophy of physics, philosophy of complexity, etc. If so, the academic map is being re-drawn in a way that is expanding the territory and prominence of philosophy after centuries of retreat.