home | resilience library | models | Fractals



A fractal is a geometrical shape that can be split into parts, where each part is a smaller replica of the whole. Examples of fractals from nature are the fern leaf and the snowflake. These shapes often seem very beautiful to us, suggesting that humans are tuned to the symmetry and order combined with variety that a fractal reveals. The splendour of much traditional architecture, such as cathedrals, derives from its fractal nature. This is reflected in the miraculous quality of the Mandelbrot set, which generates infinitely complex shapes from a simple repeated mathematical equation.

In design, fractals can provide economy of design effort, in that an underlying pattern is designed once and replicated. To specify the shape of a fern, for example, it is much simpler to define the underlying pattern than it is to repetitively detail every frond and leaf segment. It is not just geometrical shapes that can be fractals – software applications can have a fractal organization, which makes them quicker to develop and more intuitive to use.

In essence a fractal design is one that solves a problem once and then reapplies that solution over and over again, at higher or lower scales. This is the opposite of “reinventing the wheel”. There have been attempts to create “fractal organizations” where organizational structure is replicated from the lowest to highest scales. In a sense the combat units of an army tend to be organized this way, with the command structure of divisions and brigades being reproduced at smaller scales in companies, platoons and sections. However this is only part of the story, as the fighting units of an army do not carry out all the functions of a business - they need to be supported by a bureaucracy, such as the Ministry of Defence in the UK, which handles supply, procurement and interacts with government. This model is unlikely to be suitable for most growing businesses.

A more comprehensive model of fractal organization, which has been tested in various business settings by its creator Stafford Beer, is the Viable System Model. This model is based on human physiology, and has the flexibility to be applied all the way from the smallest business unit up to national economies. The Scrum system for teams can be used in a fractal way, and our Resilient Teams Model is intended to be used as a fractal.