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Showing posts from April, 2012

### Fractal Koch Snowflake Spiral

The Koch Snowflake Spiral 2024: last year, I published, using the following, an interpretation of Quantum Mechanics. https://www.fractalnomics.com/2023/05/fractal%20foundational%20quantum%20theory%20published%20.html International Journal of Quantum Foundations, Speculations. The Fractal Corresponds with Light and Foundational Quantum Problems   Experiment on Inverted Fractal Corresponds with Cosmological Observations and Conjectures On route to understanding if  fractals have a 'wavy' like nature , I finally put pencil to paper and drew what I'd been thinking. I have been pondering what effect a 'mutation' or change to one triangle - a dot at the apex of the triangle as shown below - would have or show on the  iterating  Koch Snowflake. I envisaged that it would spiral to infinity, as shown below. By tracing a smooth curve through the (red) 'dots' series of iterated mutant triangles, I would develop - what looks like - a kind of logarithmic sp

### Fractal: Multiplier

Development and growth of the fractal demonstrate the ( money and Keynesian) Multiplier. The (Keynesian) Multiplier shows how an initial injection of expenditure into an economic system creates more income. This is because added expenditure sets off additional rounds of expenditure with each and every hand or round this income passes. This principle of 'multiplying' the initial injection can be demonstrated by using the fractal. In the diagram below, income is represented by each triangle's area, and the spending rounds by every iteration of the rule.     The initial injection (iteration 1) is represented by the first triangle, which has an arbitrary area of 1. The next round adds 3 extra triangles, increasing the total area of the snowflake. This (principle) process continues until the changes in the area of the triangle—after each iteration—no longer change the total area of the snowflake. In the diagram above, the total area reaches 1.6  at around the 12t