I have found; Lorenz distribution is a fractal phenomenon; the fractal models the Lorenz Curve; Gini coefficients increase as the fractal grows and develops; and the distribution between groups accelerates with growth and development. Lorenz distribution is universal: income and wealth inequality one aspect of a universal phenomenon, and is scale invariant.
Wealth Distribution: a (universal) fractal phenomena
I was teaching income distribution recently, and I thought maybe the (Koch Curve) fractal demonstrates 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 showflake development: maybe because income is a flow concept and the Koch snowflake doesn't seem to demonstrate this. So I thought: what distribution does it demonstrate? I turned my attention to the concept of wealth distribution. I assumed that Wealth corresponds better with the Area - reasoning that both are a 'stock' concept.
I did the calculations (taken from the area calculation table in my first blog 1.1 seen below) : percent of number of triangles, and percent of area for each triangle -and then corrected the results so as to view like the original Lorenz Curve.
|Koch Snowflake (fractal) development|
|Analysis of the Koch Snowflake|
|Lorenz Curve calculation|
|Lorenz Curve for the Koch Snowflake|
|Lorenz Curve from Book: Economics, Micheal Parkin, Addison-Wesley 1990|
Discussions and Conclusions