Week 8: Fractals!

I was introduced to the fractals the first time in my life last week. It was fascinating because I have never applied or had a term to describe the chaotic yet patterned shapes. After learning it more, anything that appears random and irregular can be a fractal. Fractals are the patterns that left behind by the movement of chaos.

  TreeSilS  EarthquakeSRiversS

The fractals can be found in the branching of the trees, earthquakes, river, lightenings, clouds or the stock market, etc.

LightningSCloudsSfinance1

Fractals draw a chaotic behavior yet if we look closely enough, we can always find the self- similarity within a fractal. Fractals provide a new perspective. Thus, more and more scientists have been studied the fractals for they can describe real world better than traditional mathematics and physics.

In astronomy, fractals change the whole perspective of how scientists look at the universe. It was assumed that matter is spread uniformly across the space but observations show that it was not true. The assumption can be only applied on a small scale but on a bigger scale, the scientists found that the galaxy correlations are fractals and not homogeneous. As the result, the galaxy structures are highly irregular and self- similar. Though it still needs more data to prove that we are living in a fractal universe, fractals gave the scientist a new perspective that can further their research

.timeline    Timeline of the universe.

   In nature, when we study a tree and pick a section of the tree, to chaologist, the tree, the branch and the leaves are identical. To a lot of us, chaos means randomness but after knowing fractal, every randomness might just be a section of a very organized system that comes with a pattern. For example, the weather is so unpredictable; the forecasts are just the prediction because the minor disturbance in airflow could make a big change. In fractal study, the minor disturbance would make a change that will increase geometrically with time. Thus, it builds up the unpredictableness that is hard for human to fetcher.  By using fractal geometry, we can now visually model the coastlines and mountains in the Mother Nature.

MountainsSPCoastlineS

It would be cool if we would be able to see the “big picture” and figure out the fractal someday. Fractal is a hard concept to grasp but it is a notion that can change a lot of perspective. For example, looking at the bigger picture when solving an unsolvable problem.

SierpMtn1SThis is drawn by a forth grader, Stephanie Davis, after her babysitter taught her the idea of fractals. Though fractal geometry can be complicated and difficult, the concept is fundamental and neat.

Sources:

http://kluge.in-chemnitz.de/documents/fractal/node2.html

http://classes.yale.edu/fractals/

-Wei- Yin (Annie) , Cheng

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