## Posts

Showing posts from January, 2011

### Fractal equilibrium count

Continuing on from my earlier blog on fractal equilibrium : Koch Curve Animation From a fixed viewpoint: all fractals ('attractors')  form their shape (are at fractal equilibrium) at and around 7 plus or minus 2  iterations - any more than this will come at too high a cost, and with no extra benefit - as shown in the animation of the Koch Snowflake development above. The 5 iterations to develop the fractal Koch snowflake in Fig. 1 (below)—the point where the blue extra (Marginal) area (MA) and green extra (Marginal) cost (MC) intersect—correspond to the point  where the shape of the snowflake is fully developed.  I believe this is not only a demonstration but also an explanation for The Magical Number—Seven, Plus or Minus Two—and is also observable throughout our reality. From any standpoint, there will be around 4,5,6,7, or 8 levels of protrusion. For example, from where I am writing, I can see out my window a park and some buildings. The building is the first pro

### 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 inform

### Marginal Cost - Production of the Fractal

Marginal Cost - derived from the fractal Original Post The fractal demonstrates cost. To demonstrate the increasing cost—in effort and time—at each iteration (see my first blog on marginal analysis and the fractal) to produce the fractal, I used the reciprocal and inverted the Marginal Area, MA. The rationale for this choice is that the more area there is for the snowflake, the more cost. I am sure there are other ways of doing this, but this method is as simple and easy as calculating the MC again; it should be okay. Fig. 2 shows the original MA TA diagram with the MC. Background One thing about computer generated fractals is that they appear to be produced with ease, we simply forget that they would not be viewable if it were not for the memory and processing power of our modern computer. To see how complex and slow they are to draw, one only has to take a pen and paper and have a go at drawing the Koch snowflake progression - step by step. It is easy from the beginnin

### Marginal Utility - derived from the fractal

Marginalism and Marginal Analysis: derived from the fractal. Here, I perform basic marginal analysis on the Koch Snowflake Intro For some time now, I have pondered on how the Koch Snowflake fractal (seen below) demonstrates, uncannily, key features in economic theory. Is it that the economy - as we experience it - is a fractal? or is the fractal an economy? After doing the following basic math, fractal geometry is the foundation of the social science of economics. Koch Snowflake animation: Towards Equilibrium From the outset, the concept of Marginalism and fractals have something in common: They are both about the next unit or iteration. Once a rule, in this case, new triangles, is set in action and allowed to progress (iterate) step by step, it will go on to eventually form a snowflake. After iteration 4, the shape will set and no longer change - at least from the viewers' static perspective. Koch Snowflake development If one were to continue the itera

### Marginal Analysis of the Fractal

Marginalism and Marginal Analysis: derived from the fractal. Here, I perform basic marginal analysis on the Koch Snowflake 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 shall post the Abstract, followed by the original post. I hope to collaborate and 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 geom

### Lorenz Curve of the Koch Snowflake Fractal

Update 2015, I have published/posted. I have found that Lorenz distribution is a fractal phenomenon. The Lorenz Curve and Gini coefficients increase in the fractal models as the fractal grows and develops. The distribution between groups accelerates with growth and development. Lorenz distribution is universal: income and wealth inequality is a scale-invariant aspect of a universal phenomenon.   https://www.academia.edu Demonstrating_Lorenz_Wealth_Distribution_and_Increasing_Gini_Coefficient_with_the_Iterating_Koch_Snowflake_Fractal_Attractor Also see:  Improved Fractal Lorenz Curve Wealth Distribution: a (universal) fractal phenomena  I was teaching income distribution recently, and I thought the (Koch Curve) fractal may demonstrate the Lorenz Curve . After doing this entry I analysed a (Xmas) tree for Lorenz distribution. Click to see. I could not make any obvious connection between the Lorenz Curve's income distribution and the Koch snowflake development: maybe because