Wednesday, March 30, 2011

Macro and Micro and the Fractal

Updated 29th Nov 2012

There are many insights - in relation to macro/micro - that can be taken from the fractal .
Firstly, and importantly, when viewing a fractal (in isolation) scale cannot be discerned, the object maybe any size at all, from infinity small to infinitly large; the object shares the fractal charactoristic of being 'same' but 'different' at every scale. What can be discerned is the shape of the object, and from this an attempt can be made to deduce an understanding of the process to produce it.
The object is the 'same', the examples infinitly 'different'.
Examples: income, wealth, trade, selection, reproduction, specialisation and so on.
We see the same but different - at all scales. These principles repeat throughout the universe and are central too to biology, and maybe even chemistry and physics also.

This observation sheds light on whether there is a distinction between micro and macro : the fractal shows us that there maybe no real separation between the micro and the macro - they maybe one and the same. This is not to say shapes repeat exactly, it is to say rules repeat, principles repeat.  The rule is universal, and this rule will be in the micro, the small, as it will be in the macro, the large. 
If there appears to be a separation, it maybe just a matter of perspective, a matter of the point of observation.  The fractal does demonstrate relativity.
Macro micro: supply and demand
Fractality is evident in the supply and demand diagrams we draw.
From a distance, without looking at the labels and such, they look the same. Downward sloping demand, (and both for much the reasons), and upward sloping supply; price and output on the axis.

The fractal demonstrates imergence behaviour: one to many relationships -as shown above in the Koch curve development (or Growth). From one triangle to an infinity of them, and in so doing, creating a new shape. The new shape in the context of economics, is the economy itself, or what every we term it - the ecosystem

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