19 March 2005 | Draft

Imagination, Resolution, Emergence, Realization and Embodiment

iterative comprehension ordered via the dynamics of the Mandelbrot set

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Annex 3 to Sustainability through the Dynamics of Strategic Dilemmas
in the light of the coherence and visual form of the Mandelbrot set


Introduction
Progressive "embodiment" of M-set through iteration
Resolution and emergence of features through iteration
Differentiating features within the M-set by colour
Iterative comprehension of the M-set as an ordering template


Introduction

The concern in this Annex to Sustainability through the Dynamics of Strategic Dilemmas is to indicate features associated with the Mandelbrot set (hereafter the M-set) in order to point to their significance in configuring complex experience -- rather than in describing natural phenomena, as is normally the case. The assumption is that the features offer templates for innovative thinking in response to highly divisive strategic and value dilemmas. An assumption is also made that the mind is uniquely capable of undertaking operations that explore the features of complex spaces such as those with which the M-set is associated. Note that contextual arguments and references are provided in the main paper.

Progressive "embodiment" of M-set through iteration

The determination of the points defining membership of the M-set is based on a selected number of iterations. Normally this number may be at 100 to view the set as a whole. Much higher numbers of iterations are required to bring out the detail in the representation -- into which one can zoom. There is therefore a marked contrast in the detail obtained with the following iterations 32, 64, 128, 256, 512, 1024, 2048 and 1000000 [more]. The following table (based on a selection of iterations from 1 to 23) gives a sense of the degree of resolution of the M-set as its overall form "emerges". A particular colouring convention is used to highlight the progressive differentiation of the form and its features.

The sequence is reminiscent of the embryology of cell division -- but may be of greater relevance here to cognitive ontology. As explored in the Annex, it is also worth reflecting on the implications of an iteration understood as: a day, a year, a generation, a life, a budget cycle, etc -- and the memorability (or sustainability) of the different "body" that emerges. It is of course relevant to iterative revision of a paper!

Figure 4: Progressive emergence of M-set through succession of iterations
Emergence of Mandelbrot set through succession of iterations (Iteration 0) Emergence of Mandelbrot set through succession of iterations (Iteration 1)
Iteration 0 Iteration 1
Emergence of Mandelbrot set through succession of iterations (Iteration 3) Emergence of Mandelbrot set through succession of iterations (Iyeration 4)
Iteration 3 Iteration 4
Emergence of Mandelbrot set through succession of iterations (Iteration 6) Emergence of Mandelbrot set through succession of iterations (Iteration 7)
Iteration 6 Iteration 7
Emergence of Mandelbrot set through succession of iterations (Iteration 9) Emergence of Mandelbrot set through succession of iterations (Iteration 10)
Iteration 9 Iteration 10
Emergence of Mandelbrot set through succession of iterations (Iteration 12) Emergence of Mandelbrot set through succession of iterations (Iteration 13)
Iteration 12 Iteration 13
Emergence of Mandelbrot set through succession of iterations (Iyeration 15) Emergence of Mandelbrot set through succession of iterations (Iteration 16)
Iteration 15 Iteration 16
Emergence of Mandelbrot set through succession of iterations (Iteration 18) Emergence of Mandelbrot set through succession of iterations (Iteration 19)
Iteration 18 Iteration 19
Emergence of Mandelbrot set through succession of iterations (Iteration 21) Emergence of Mandelbrot set through succession of iterations (Iteration 22)
Iteration 21 Iteration 22

Differentiating features within the M-set by colour

*** in progress

Figure 5: Illustration of different colouring conventions inside the M-set
Contrasting colouring conventions in renderings of Mandelbrot set Contrasting colouring conventions in renderings of Mandelbrot set
Contrasting colouring conventions in renderings of Mandelbrot set Contrasting colouring conventions in renderings of Mandelbrot set
Contrasting colouring conventions in renderings of Mandelbrot set Contrasting colouring conventions in renderings of Mandelbrot set
Contrasting colouring conventions in renderings of Mandelbrot set Contrasting colouring conventions in renderings of Mandelbrot set
Contrasting colouring conventions in renderings of Mandelbrot set Contrasting colouring conventions in renderings of Mandelbrot set

Iterative comprehension of the M-set as an ordering template

**** in progress


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