Fractal structures: Why failed states and failed armies are two sides of the same (European) coin

In the previous posts I explained the patterns that can be identified in the war dynamics of the System during the period 1495-1945: The frequency and amplitudes of the four cycles that can be identified increased with the same factor towards ‘infinity’, while at the same time the robustness, fragility and stability of relatively stable periods reached ‘maximal’ values. As a consequence, the (European) anarchistic System collapsed in 1939.

These dynamics and the patterns they produce are closely related and coherent; ‘they do make sense’, and are a result of the accelerating production of tensions in the System, during that period of time.

I assume that these tensions – energy – is a product of the increasing connectivity (related to population growth) in the System. For a full explanation I refer to the study itself.


In the previous article I also explained that the ‘physical’ stability – the size and shape of states in the System – reached a maximum ‘condition’ shortly before the Systems collapse in 1939, and the outbreak of the fourth systemic war (The Second World War, 1939-1945).

During the period 1495-1939, the System (Europe) developed from circa 300 divers and loosely connected ‘units’ with a total population of 83 million (1495), to a ‘coherent’ and optimised anarchistic System of circa 25 highly connected and standardised state structures, with a total population of 544 million (1939).

I argue that the physical and organisational stability of successive international orders (relatively stable periods) are also closely related: During the four successive cycles, the number of Great Power status changes decreased (about linearly) to ‘zero’, while at the same time, the number and size of border adjustments also decreased (Tilly, see study). The growth dynamics of the System can be considered a ‘crystallisation process’.

Eventually – that is in 1939 – the European System collapsed: the high and still growing tensions (energy levels) could not be absorbed and regulated any longer, or being used ‘sensibly’ to implement a next upgraded anarchistic order, without avoiding collective self-destruction. Anarchistic Europe had reached its so called critical connectivity threshold in 1939, produced infinite amount of tensions, and as a consequence collapsed; a phase transition had become unavoidable.

In this article I discuss fractals, self-similar structures that can also be identified in the System. In case of fractals, parts of the System have identical structures as the ‘whole’. Typically, in case of fractal structures, the size-distribution of these structures can be best described with a power-law.

It is not always clear what ‘mechanisms’ produce fractals, however, in a number of cases there is optimisation of distribution processes (trees, but also river systems have fractal structures).

Fractal structures and dynamics in the System.

In a number of cases the properties of war dynamics – for example the size distribution of wars, and of the number of (military) casualties during wars – can be best described with power-laws, pointing to fractal structures.

However more fractal structures can be identified in the System: (1) military organisations and capabilities have fractal structures (a division consist of three brigades, a brigade consists of three battalions, a battalion consist of three companies, etc. parts of the military organisations have similar structures as other levels of organisation), (2) war activity (campaigns, battles, fire-fights, etc. the activity of just mentioned organisations) during systemic wars, and (3) the physical structures of states. The size-distribution of states can also be best described with a power-law. Is this just a coincidence, or is there any consistency?


I assume that these (three) fractal structures are closely related, and together – through an interactive growth process – ‘crystallised’ during the period 1495-1945. I assume that these structures reached their maximal level of ‘structuring’ (crystallisation) in 1939, shortly before the (as a consequence) unavoidable collapse of the System (Europe).

Military organisations are responsible for the distribution – the deployment – of destructive energy. Military organisations optimise their activities, and must – besides the deployment of maximum amounts of destructive energy (at the right time and place) – ensure their own survival on the battle field. In case of military organisations there is optimisation of the distribution of destructive energy.


Figure 1: Schematic representation of a ‘fractal’ military organisation.

I assume that the System is critical during systemic wars; that systemic wars are manifestations of criticality (see study). At a critical point, systems typically have fractal structures. Due to a lack of data I am not able to prove this. The size-distribution of war activities during for example the Second World War (the fourth systemic war, 1939-1945) is not available. However, all other indicators (as I discuss in the study) point to criticality of the System during systemic wars.

I assume that through fractal structures and their dynamics, the release of tensions in the System (that have built up during preceding relatively stable periods) during systemic wars is optimised.


Figure 2: Schematic depiction of the (fractal) structures of a system in a critical condition.

Typically, the most significant and enduring border changes – changes in the sizes and forms of states during the period 1495-1945 (apart from the integration of ‘units’) – took place during systemic wars. During the period 1495-1945, the ‘corrections’ decreased in number in size (see also Tilly).

In the anarchistic System, borders define sovereign states. An important function of borders is demarcation. Borders (can) contribute to stability, and establish positions of power and spheres of influence. For the same reason borders often become flashpoints.


Figure 3: The size distribution of states can be best described with a power-law, intrinsic to fractal state structures.

The reduction in the ‘border’ and Great Power status dynamics – the crystallisation of the organisational (Great Power status hierarchy) and physical structures – also are closely related dynamics. As I mentioned, state structures in Europe (shortly before the System’s collapse in 1939) can be best described with a power-law: in other words, state structures are fractal structures.

Process of crystallisation.

It is possible to depict the forming of Europa during the anarchistic period 1495-1945 as a crystallisation process that was ‘fed’ by population growth. Populations consist of individuals – that can be considered molecules in this metaphor – that had to find a ‘place’ in these structures to ensure their survival. This process required periodic re-ordering and ‘upscaling’ (integration in larger units).

States (and their predecessors) organised military capabilities that were increasingly organised in fractal (organisation) structures, which – as an integral component of the critical dynamics of the anarchistic System – carved out fractal state structures. This was a long-term (1495-1939) growth process.

In 1939 these structures were fully crystallised and optimised, and as a consequence could no longer absorb and regulate the still growing tensions: In 1939 Europe ‘fractured’. In the meantime, Europe had developed itself into the core of a (still) globalising international System.


Figure 4: Above figure schematically shows the above described relationships and consistency of the System: “Increasingly fractal state structures mobilise and organise increasingly fractal military capabilities which by means of systemic wars carve out increasingly fractal state structures in the System”. This was a long term growth, crystallisation and optimisation process that reached its optimal and maximal achievable (anarchistic) condition in 1939. In 1939 the System (Europe) fractured as a consequence of its inability to absorb and regulate the still growing tensions in the System. At that point the effects of a physical law became visible: the tensions (energy) that was released (1939-1945)  was used by the System to implement an upgraded order – through a phase transition in this particular case – that would allow (at least temporarily) for a lower energy state, and relative stability. As a consequence of the unavoidable phase transition, Europe transformed from an anarchistic into a non-anarchistic System.It is difficult to imagine (and maybe to accept) that physical laws apply to social processes; laws that we must obey. Our autonomy is (much) more restricted than we until now assumed.However, this can also be viewed from a different and more positive perspective. We now can (and must) be ‘smarter’: we also ‘mastered’ gravity: we fly to the moon (and back), and we build ingenious structures that do not collapse. Better understanding of the physical laws that apply to social systems and their processes (finally) allow us to design and ‘build’ international orders, that do not unavoidably collapse, with a lot of noise and destruction.

‘Failed states’ and ‘failed armies’.

It is important to notice that the state (as an organisation), the (state) structure of Europe and military organisations and capabilities are European ‘products’; the outcome of a very specific European context and dynamic during the period 1495-1945.

The phenomenon of ‘failed states’ (states that turn out not to be viable), and what I call ‘failed armies’ (Western armies that are consistently ineffective, as was/is the case in Vietnam, Afghanistan and Iraq (2003)) are a consequence of this fact. Armies also are European inventions, designed to fight in a European context that is now largely outdated.

Failed states typically fall back on more basic social structures (as far as they are still functional) and try to re-group on the basis of different (often religious) concepts and organising principles. Survival also is the driver of this dynamic.

Typically, in reaction to their failing performance, failed armies intensify the deployment of destructive energy – a reflex from the period 1495-1945 – and literally and figuratively dig in even deeper.

Failed states and failed armies are two sides of the same (European) coin.