Fractal: Equilibrium Perfect Knowledge and Output

Fractal Equilibrium:
This entry follows on from 'production of the fractal'.
Here, I suggest that equilibrium - in any sense - is fundamental to the fractal.

Koch Snowflake development: source, Wikipedia

The above animation shows the development of the fractal; at iteration 5 or 6, fractal equilibrium is reached - where the shape (of the snowflake) is made or where benefit production is equal to the cost of production.

Fig. 2b below, shows a closeup analysis of the fractal equilibrium, at least from a static point of view.  MC  intersects, or is equal to MA, at iteration 5 where the Area is equal to 1, due to the reciprocal of 1 itself being equal 1.

Equilibrium - Perfect Knowledge*
http://en.wikipedia.org/wiki/Perfect_information
Any iteration less than fractal equilibrium will result in an imperfect (snowflake) shape or incomplete knowledge or information.
Any iteration point with greater fractal equilibrium will result with little added gain in information or shape and come at a great cost.
Perfect knowledge, or the perfect shape, is gained where MA =MC.  This, taken directly from economics theory, resembles where allocative efficiency is maximized - at the equilibrium point in market theory. Competition gives the best shape or knowledge, unlike a monopolist that would produce or output somewhere left of equilibrium.
Notice that total knowledge will never be gained - the cost is too high.
*I am aware that the fractal demonstrates infinity and thus shows the infinity of knowledge - of the rule. To say perfect information may well be a relative statement, said in context or in a paradigm.

A theory of knowing?
Development of the Little Man is my attempt at understanding how we know: check out my theory of mind

http://www.fractalnomics.com/2011/09/paradigm-fractal.html

Equilibrium Output (quantity)

Of course, the iteration number is not the output or quantity ( as in classical economics). So, what then is it?

It is the number of triangles - that are added after each iteration.

In the diagrams below (fig.3 and 3b), the increase in the quantity of triangles after each iteration is shown in orange. I recently learned that this curve is exponential.

 Equilibrium quantity or output at fractal equilibrium is  ..... triangles or point 'a', on the diagram.
Update May 2017
This is by far my best idea; I have written it up in a working paper at my academia.edu and vixra, and named it:  Quantum Mechanics, Information and Knowledge, all Aspects of Fractal Geometry and Revealed in an Understanding of Marginal Economics.
I will post the abstract, followed by the original post and then the paper. I hope to have some collaborators review my work in time.

Abstract

Fractal geometry is found universally and is said to be one of the best descriptions of our reality – from clouds and trees to market price behaviour. As a fractal structure emerges – repeating a simple rule – it appears to share direct properties familiar to classical economics, including production, consumption, and equilibrium. This paper investigated whether the mathematical principles behind ‘the market’ – marginalism – is an aspect or manifestation of a fractal geometry or attractor. Total and marginal areas (assumed to stand for utility) and the cost of production were graphed as the fractal grew and compared to a classical interpretation of diminishing marginal utility theory and the market supply and demand. PED and PES were also calculated and analysed with respect to (iteration) time and decay.  It was found that the fractal attractor demonstrates properties and best models classical economic theory, and from this, it was deduced that the market is a fractal attractor phenomenon where all properties are inextricably linked. The fractal, at equilibrium, appears to be a convergent – zeta function – series, able to be described by Fourier analysis and involves Pi, i, e, 0, and 1 (of Euler’s identity) in one model. It also demonstrated growth, development, evolution and Say’s Law – production before consumption. Insights from the fractal on knowledge and knowing are also revealed, with implications on the question of what exactly is ‘science’ – and what is ‘art’? A connection between reality and quantum mechanics was identified. It was concluded marginal classical economics is an aspect of fractal geometry.  

 Keywords

Marginal, Fractal, Elasticity, Utility, Cost, Production, Price, Growth and Development, Say’s Law