Monday, July 11, 2011

(Christmas) tree Lorenz Curve

After completing my Lorenz analysis of the Koch Snowflake fractal I set upon analysing a real life fractal and chose a Christmas tree. This has been a side interest from my core fractal work and thinking so I have not written it up as a 'science report'.
I am not sure of the species of tree I selected, but it is typical conifer of Northern hemisphere.

Method
I trimmed all the branches off the tree, counted them, weighed them, recorded results, then ranked the branches from lightest to heaviest; completed a cumulative percentage rank of weight and count table, and finally graphed the results.
Branches everywhere:
Below is the Christmas tree Lorenz Curve in terms of weight. Note that 'cumulative percentage of triangle weight' should read branch rather than triangle.

I found that there were 5 levels of branches.
I will be honest with you, I did not continue counting and weighing the branches in detail after the 3 level - the time cost was just so high and it would not change the shape as they were so light. So, I counted and averaged the final 2 levels (sorry, things to do).


Conclusion and reflection

The conifer tree has a very large Gini coefficient - similar to that of the Koch snowflake (below) and that of the standard wealth distribution.



The question is, is this how an economy is? Is this disribution universal? Yes it is.
Is improving this gini coefficient impossible? Do we see Chrismas trees with branches as big a the trunk? No - the branches will break.
This does make me think of cacti, but I still think the trunk is dominant.





That was fun; I would like to thank my family who promised not to laugh while I counted branches on the floor :)  ..  and to my school math. teacher colleagues for their support, and of course - always - to my students.

Update 2017, I have published/posted.
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. 
 https://www.academia.edu Demonstrating_Lorenz_Wealth_Distribution_and_Increasing_Gini_Coefficient_with_the_Iterating_Koch_Snowflake_Fractal_Attractor



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