Complexity theory and planning: examining 'fractals' for organising policy domains in planning practice

This article examines selected methodological insights that complexity theory might provide for planning. In particular, it focuses on the concept of fractals and, through this concept, how ways of organising policy domains across scales might have particular causal impacts. The aim of this article is therefore twofold: (a) to position complexity theory within social science through a ‘generalised discourse’, thereby orienting it to particular ontological and epistemological biases and (b) to reintroduce a comparatively new concept – fractals – from complexity theory in a way that is consistent with the ontological and epistemological biases argued for, and expand on the contribution that this might make to planning. Complexity theory is theoretically positioned as a neo-systems theory with reasons elaborated. Fractal systems from complexity theory are systems that exhibit self-similarity across scales. This concept (as previously introduced by the author in ‘Fractal spaces in planning and governance’) is further developed in this article to (a) illustrate the ontological and epistemological claims for complexity theory, and to (b) draw attention to ways of organising policy systems across scales to emphasise certain characteristics of the systems – certain distinctions. These distinctions when repeated across scales reinforce associated processes/values/end goals resulting in particular policy outcomes. Finally, empirical insights from two case studies in two different policy domains are presented and compared to illustrate the workings of fractals in planning practice.

Causes of the apparent scale independence of fractal indices associated with forest fragmentation in Bolivia

In a recent investigation, Landsat TM and ETM+ data were used to simulate different resolutions of remotely-sensed images (from 30 to 1100 m) and to analyze the effect of resolution on a range of landscape metrics associated with spatial patterns of forest fragmentation in Chapare, Bolivia since the mid-1980s. Whereas most metrics were found to be highly dependent on pixel size, several fractal metrics (DLFD, MPFD, and AWMPFD) were apparently independent of image resolution, in contradiction with a sizeable body of literature indicating that fractal dimensions of natural objects depend strongly on image characteristics. The present re-analysis of the Chapare images, using two alternative algorithms routinely used for the evaluation of fractal dimensions, shows that the values of the box-counting and information fractal dimensions are systematically larger, sometimes by as much as 85%, than the "fractal" indices DLFD, MPFD, and AWMFD for the same images. In addition, the geometrical fractal features of the forest and non-forest patches in the Chapare region strongly depend on the resolution of images used in the analysis. The largest dependency on resolution occurs for the box-counting fractal dimension in the case of the non-forest patches in 1993, where the difference between the 30 and I 100 m-resolution images corresponds to 24% of the full theoretical range (1.0 to 2.0) of the mass fractal dimension. The observation that the indices DLFD, MPFD, and AWMPFD, unlike the classical fractal dimensions, appear relatively unaffected by resolution in the case of the Chapare images seems due essentially to the fact that these indices are based on a heuristic, "non-geometric" approach to fractals. Because of their lack of a foundation in fractal geometry, nothing guarantees that these indices will be resolution-independent in general. (C) 2006 International Society for Photogrammetry and Remote Sensing, Inc. (ISPRS). Published by Elsevier B.V. All rights reserved.

Global exponential periodicity of a class of neural networks with recent-history distributed delays

In this paper, we propose to study a class of neural networks with recent-history distributed delays. A sufficient condition is derived for the global exponential periodicity of the proposed neural networks, which has the advantage that it assumes neither the differentiability nor monotonicity of the activation function of each neuron nor the symmetry of the feedback matrix or delayed feedback matrix. Our criterion is shown to be valid by applying it to an illustrative system. (c) 2005 Elsevier Ltd. All rights reserved.

Dynamical complexity in a mean-field model of human EEG

A recently proposed mean-field theory of mammalian cortex rhythmogenesis describes the salient features of electrical activity in the cerebral macrocolumn, with the use of inhibitory and excitatory neuronal populations (Liley et al 2002). This model is capable of producing a range of important human EEG (electroencephalogram) features such as the alpha rhythm, the 40 Hz activity thought to be associated with conscious awareness (Bojak & Liley 2007) and the changes in EEG spectral power associated with general anesthetic effect (Bojak & Liley 2005). From the point of view of nonlinear dynamics, the model entails a vast parameter space within which multistability, pseudoperiodic regimes, various routes to chaos, fat fractals and rich bifurcation scenarios occur for physiologically relevant parameter values (van Veen & Liley 2006). The origin and the character of this complex behaviour, and its relevance for EEG activity will be illustrated. The existence of short-lived unstable brain states will also be discussed in terms of the available theoretical and experimental results. A perspective on future analysis will conclude the presentation.

Fractal spatialities

This paper argues for the use of ‘fractals’ in theorising sociospatial relations. From a realist position, a nonmathematical but nonmetaphoric and descriptive view of ‘fractals’ is advanced. Insights from the natural sciences are combined with insights on the position of the observer from Luhmann and notions of assemblages and repetitions from Deleuze. It is argued that the notion of ‘fractals’ can augment current understanding of sociospatialities in three ways. First, it can pose questions about the scalar position of the observer or the grain of observation; second, as a signifier of particular attributes, it prompts observation and description of particular structuring processes; and third, the epistemic access afforded by the concept can open up possibilities for transformative interventions and thereby inform the same. The theoretical usefulness of the concept is demonstrated by discussing the territory, place, scale, and networks (TPSN) model for theorising sociospatial relations advanced by B Jessop, N Brenner, and M Jones in their 2008 paper “Theorizing sociospatial relations”, published in this journal (volume 26, pages 389–401). It is suggested that a heuristic arising from a ‘fractal’ ontology can contribute to a polymorphous, as opposed to polyvalent, understanding of sociospatial relations.

Fractal spaces in planning and governance

This paper discusses concepts of space within the planning literature, the issues they give rise to and the gaps they reveal. It then introduces the notion of 'fractals' borrowed from complexity theory and illustrates how it unconsciously appears in planning practice. It then moves on to abstract the core dynamics through which fractals can be consciously applied and illustrates their working through a reinterpretation of the People's Planning Campaign of Kerala, India. Finally it highlights the key contribution of the fractal concept and the advantages that this conceptualisation brings to planning.