Natural phenomena Incorporating the Secret of Synchronization

 

 
 Tacoma Narrows Bridge moving in resonance with the wind
 



YouTube Introduction to complexity: Fractal Dimension Part 4 7 minute video - https://m.youtube.com/watch?v=t-_VPRCtiUg

.https://youtu.be/CKx-OAKN-2U

The idea of non integer dimensions is motivated to study non standard geometric figures.

A poignant example would be the Koch curve. 
For the Koch curve _/\_

r is     1 2 3
            ___

           _/\_
N is   1234

r=3 length, N=4 number of divisions

r=3, N=4
D=log 4/log 3 ~ 1.26

Therefore, the fractal dimension of the Koch curve is ~1.26.

Indices - Law of Indices - An Introduction
https://mathematics.laerd.com/maths/indices-intro.php

D is dimension. D can be intuitively said to be the "density of detail" of an object. Fractal dimension qualifies how much detail you can see at all scales.

Further reference: Tacoma Narrows Bridge Collapse With Sound Rare - YouTube
https://m.youtube.com/watch?v=3XE5qU0c5qU

The Secret of Synchronization - YouTube
https://m.youtube.com/watch?v=t-_VPRCtiUg


AN INFINITE HIERARCHY OF EXPONENTS TO DESCRIBE GROWTH PHENOMENA - ScienceDirect

 

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