Wednesday, July 20, 2011

The credit card effect

The credit card effect (as opposed to 'the butterfly effect') - one persons (credit card) debt could bankrupt a country - or even the world's economy.

This is the perfect economic fractal example where dangerous massive debt burdens have migrated from the small scale (individual) to the large scale (country);  the principle or idea (of debt) is the same, the scale is irrelevant.
I explained the world's economic problems to my 10 year old daughter by reducing the problem to her scale - it was very easy.

Today - through the mechanism of (moral hazard) bank bail-outs - it is countries that are getting burdened.

Where to next?

This is the perfect storm.'

Thursday, July 14, 2011

Object: transformation, formation, creation

From a triangle, to the formation of a snowflake, this is a (universal) demonstration of creation: this is transformation, the creation of an object. Many to make one. Emergence

Q. Is the original triangle the big bang?

Animation of Koch Snowflake development

Monday, July 11, 2011

Fractal Elasticity along the straight line curve.

Fractal Elasticity - along the straight line curve.
Click to see most recent developements that complement this entry.

After discovering in my early blog that the elasticity of the Koch Snowflake fractal is constant, I have since pondered on what is the meaning of all this?
Economic theory suggests that all objects have this constant elasticity or are logarithmic in nature. The next thing to to is to straighten out the fractal curves.
I produced the following diagrams to do just that and to demonstrate the change in fractal elasticity as the fractal developments. The above diagram shows constant elasticity, and the below variable elasticity along the straight (log) curve.

(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.

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. Demonstrating_Lorenz_Wealth_Distribution_and_Increasing_Gini_Coefficient_with_the_Iterating_Koch_Snowflake_Fractal_Attractor