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ATTRACTORS

Strange patterns in complex adaptive systems

Steve Trivett

14 April 2024

Living System Metaphors


In mathematics there is a group of patterns referred to as “attractors”.  They represent different types of complex systems, patterns of behaviour that can evolve over time, based on the system’s initial conditions.


POINT ATTRACTORS

The are “point” attractors that emerge when activity in a system moves toward a common ending point. For example when student are taken through a set course of study, or a number of railway tracks converge on one station. That shared end point sets conditions for the evaluating similarities and differences that exist at the start of the journey and along the route. The pattern of movement towards a known end point influences customer expectations. 

PERIODIC ATTRACTORS

There are “periodic” attractors that emerge when all activity in a system recycles in some sort of regular, repeating pattern. In retail sales, for example, types of clothing are available according to seasonal cycles and social trends. Back-to-school cycles occur at the end of a summer break. These periodic attractors of help people to know what to expect.

STRANGE ATTRACTORS

A strange attractor is the type of attractor pattern I find most interesting and useful. These patterns emerge when a system is bound by conditions that allow for infinite variability within a discrete boundary. Think of a social system contained by a set of simple rules and/or shared beliefs such as family, love, and freedom are shared across social groups. They produce similar patters of conversation and responses. 

To demonstrate the idea, suppose that you map the behaviour of a moving pendulum by plotting its angle relative to its equilibrium point on the X axis, and its velocity on the Y axis.

The path of the pendulum would be displayed on the plotting graph as a simple spiral, settling into its final position at the point of origin or its initial condition. It represents the behaviour of dynamical systems such as pendulums, but more complex phase space diagrams can be used to represent the behaviour of more complex systems

Phase space diagram of a pendulum with friction. Courtesy of Frijof Capra

It provides an explanation for why apparently chaotic systems displayed recurrent and recognisable patterns, like weather patterns.

EVEN CHAOTIC SYSTEMS HAVE PATTERNS

It turns out that chaotic systems can form predictable patterns around a strange attractor, but the exact spatial or temporal pathway that they take cannot be predicted.

While Complex Adaptive Systems (CAS) are distinct from chaotic systems, the CAS can be influenced by multiple types of attractors, such as point attractors and strange attractors. A CAS can exhibit similar properties to chaotic systems, such as patterns of “bounded instability”.

What makes CAS different is that they can move towards one or more attractor patterns, and experience radical transformations when novel patterns of organisation emerge.

ATTRACTORS AS METAPHORS

Strange attractors serve as a useful metaphor for a shared vision which drives individual agents’ actions and beliefs towards new patterns of interaction. This offers leaders with a new approach to organisational change when values, goals, theories and leadership itself can be considered as attractors for bringing people together.

An organisation can see itself a network of conversatuions  to change its;s way of being by listening to all its employees, customers and stakeholders.

Seeing people as the experts on their own lives and work, when given the right support, they have the innate wisdom and intelligent ideas needed to improve when relationships and resources are changing or under pressure.

This new vision could be defined by equality and dignity; empathy, care, humility, and active listening, to allow new patterns of behaviour to emerge around this new attractor.

Attractors are the organising principles at work in all living systems. In human systems, attractors can be values, intentions, theories, leadership, etc., that bring people together to share a common cause. They are like the wind that gives a sailing boat it’s energy to go in a given direction. They can combine to influence the direction taken out of many other possibilities required when the wind direction changes.

“I find myself getting into arguments even though I try to avoid them.”

In the Complexity Sciences, an attractor is a model that represents the outcome of a system. it is not a force of attraction or a goal-directed presence, it simply indicates where the system is heading based on the rules that are determining movement.

ATTRACTORS IN ORGANISATIONAL CHANGE

For example, a change of organisational policy or practice can result in a sustainable change to a business or an institution. The marked change in behaviour can be considered a ‘bifurcation’ or ‘phase transition’ in which old behaviours die and new ones emerge. There are four main attractors in the process of organisational change that I have used as my own model, to help organisations transform their ways of working by considering the dynamics of each attractor and the relationship between them. They are:

INSIDE-OUT ATTRACTOR – that promotes mindful change. It is created when individuals in the system know how to think, feel and act coherently with the organisation’s need to adapt to what’s wanted and how to take the right action to achieve it. What does the organisation look like to all those who are noticing what’s going on inside your mind and body?

BOTTOM-UP ATTRACTOR – that promotes local change that emerges from the interactions between individuals in the system and gets the cooperation of the people around you to secure their commitment to aggregate their actions in a consistent way. What does an observer notice when looking at the organisation from the bottom up.

OUTSIDE-IN ATTRACTOR – that promotes contextual change which happens when thoughts and actions are stimulated by, and things are perceived from, the perspective of the situation or the environment. What does an observer notice when looking at the organisation from the outside-in

TOP-DOWN ATTRACTOR – that promotes a holistic change which is often imposed through rule changes and compliance with principles that may not be of the system’s making. It can cause the system to thrive or die. What does the observer notice when viewing the whole organisation from the top-down or across its network?

INITIAL CONDITIONS

When your nervous system creates memory pathways and coupled structures it does not have a purpose. It merely tags on experiences to previous experiences unless we intervene and make a conscious choice to make new connections. For example, we may dress to stand out and separate ourselves from the crowd, but to make friends we may feel the need to position ourselves where we can make connections with people like ourselves. These choices create the ‘initial conditions which are most likely to lead us in the direction we want to go.

A clear goal is a “point attractor” that causes us to consider what conditions and actions will be needed to bring it about. But often situations are more complex where what happens somewhere else can change the local conditions. For example, if the economy slumps, then jobs become scarce. This creates a “closed loop” attractor where one factor is dependent on others. This is why Ontological Coaching is more effective than traditional goal-directed coaching. It seeks to establish the factors that are creating the existing Way of Being that isn’t working and identify the conditions that need to be generated for a new Way of Being to emerge.

ATTRACTORS AS A METAPHOR

Often it is unpredictable events that lead to a breakdown in the normal flow of life. This explains how a small event can create massive emotional reactions and lead us to places we did not intend. This is explained by the “strange attractor” where our behaviour loops and oscillates from one mood state to another until a conscious choice is made to stabilise our nervous system and a new behaviour or habit ‘locks in’.

The idea of attractors can provide us with powerful metaphors to assist our thinking. Notice how one idea or opinion can derail a discussion, which then wanders off to consider another unrelated topic. This is a strange attractor at work. Other ideas can have the opposite effect and pull together other ideas into a coherent and shared objective. This can be a point or closed-loop attractor.

Commitment and leadership can be considered as attractors. Consider what needs to occur for commitment to occur. Energy and information flow towards and around an attractor. The actions generate energy for more actions to create conditions that generate People who have more money can use it to get more money. These attractors emerge from clear intentions, values, principles, successes, etc. Look at leadership as an attractor and see what thoughts it generates.

Look at leadership as an attractor and see what thoughts it generates.

An attractor is also something that holds a system together by maintaining a given pattern of interactions or has the ingredients to propel it into new patterns. They give dynamic systems their stability. Habits are a good example. They act like magnets causing the energy in behaviour to be directed in the same way to achieve a predetermined outcome, goal, purpose, intention, etc. There are different types of attractors. There are Fixed Point Attractors, Periodic Attractors that create a rhythm like your pulse rate and Oscillating Attractors which control the way you breathe in and out.

DYNAMIC INTERACTIONS

Attractors were observed by Edward Lorenz when studying the turbulent flow of liquids. He demonstrated how deterministic systems can give rise to unpredictability. This is because repeated interactions (which is what happens in conversations for example) can give rise to unpredictable behaviour that leads to a mood change and then cannot return to the same conditions that created it.

It is the dynamic balance that shifts between internal capability (inside-out forces) and the external environment (outside-in forces) that create ‘attractors’. So, when the attractors change the behaviour changes. Culture is a good example of a set of attractors (rules, conditions or principles) that impact the behaviour of individuals in an organisation, which is a Complex Adaptive System.

To change a culture or a set of behaviours, the ‘attractors’ have to change. This change is called a bifurcation. A change agent looks for what it would take to create a bifurcation point in order to shift attractors such as habits, language, moods and the sense-making rules used by a client. The result is a shift in the client’s pattern of behaviour. The client then experiences “lock-in” which then creates a new kind of attractor.

For example, a change of organisational policy or practice can result in a sustainable change to a business or an institution. The marked change in behaviour can be considered a bifurcation or Phase Transition in which old behaviours die allowing new ones to emerge.

ATTRACTORS AND EVOLUTION

A ‘strange attractor’ is a useful metaphor for explaining the conditions for continuous improvement or evolution. In organisations, it seeks new distinctions to create a new awarenessof what’s possible or an awareness of the unity of all current feelings and behaviours, or new connections between the self and the environment, even relationships with partners and those in authority.

Craig Renolds who developed a computer simulation of birds flocking discovered simple rules that birds seem to obey no matter what size the flock was. This characteristic is known as scalar invariance. This enables you to see the whole by observing small parts.

ATTRACTORS AND PERSONAL CHANGE

The dynamics of system attractors suggest that attempts to locate blame for the system’s failure on one individual, whilst it may be emotionally satisfying, is largely unhelpful. This is because the patterns of interaction take place between individuals. Consequently, no one individual can achieve a successful outcome by themselves. Yet the boss often gets the credit and the bonuses.

It is clear that behaviour emerges from the many complex interactions in the human system that it is part of. Therefore, changing behaviour is not something that can be tackled in isolation of its context. Individuals can impact a system, but not without impacting other agents and on themselves. Always look at the wider system or “global” influences that are impacting individual behaviour within the system. These might be beliefs that also drive behaviour. The rules that affect local conditions (inside-out perspective) and the global context (outside-in perspective) should be explored in terms of the impact they have on each other.

As human systems evolve they tend to have developmental stages or levels. For example, as people grow from children into adolescents and adults. Groups tend to storm, norm and perform. These stages have limited sets of behaviours, tasks, characteristics, thinking patterns, emotional issues, etc. (inside-out influences). This determines how we as humans are likely to function – for example, within set conditions (outside-in influences), local interactions (bottom-up influences) or when complying with a given set of rules (top-down influences).

ATTRACTORS AND LEADERSHIP

Narcissistic leaders who fail to acknowledge the contributions of others can impact negatively on a team. It weakens morale and commitment and can lead to resentment and resignation which then threatens the viability of the system. A coach is interested in exploring the potential of the individual to contribute to positive interaction and resist the pull of any destructive attractors, such as mental models, personalities, habitual behaviours and emotions.

Coaching from a systems perspective does not see a separation between an individual and the team. Changes in one will inevitably impact the other. Almost all coaching interventions are multilayered in that they can have an impact on many levels. For example, the ‘Logical Levels’ indicated below – each one represents a system within a system, each with its own attractor.

Gareth Morgan uses the image of strange attractors in the context of organisational change. He argues that the creation of new contexts is required in order to break the hold of dominant attractors and bring about transformational change. However, there is no possibility of determining the outcomes through control here as these are unpredictable. However, the conditions for a change can be created. If the existing attractor is too strong then the change will not be significant. At the heart of a strange attractor, we find discontinuity, perpetual novelty and ever-changing elements.

The dynamic balance between internal capability and the external environment creates ‘attractors’. When the attractors change the behaviour changes. Culture is a good example of a set of attractors (conditions or principles) that impact the behaviour of individuals in an organisation’s complex adaptive system.

READING

The Collapse of Chaos by Ian Stewart & Jack Cohen. Penguin 2000

The Intelligence Advantage by Michael McMaster. Butterworth-Heinemann 1996

Complexity by Michael Waldrop. Penguin 1994

The Collapse of Chaos by Jack Cohen & Ian Stewart. Penguin 199