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  1. Recommended for you
  2. The Sierpinski Gasket
  3. How the Mathematics of Fractals Can Help Predict Stock Markets Shifts
  4. Modelling nature with fractals
  5. Fractal -- from Wolfram MathWorld

How could two measurements for one and the same object be completely different?

This was the birth of the coastline paradox. It was named this way because the same effect can be noted when comparing different measurements of coastlines. The coastline paradox is best explained visually. Let us consider an island that is completely surrounded by water.

Lecture - 14 Introduction to Fractals

But as we can see, the ruler is rather large for the coastline with many different edges, nooks, and crannies. Now that we have two measurements for the same object, the coastline of the island, we are able to compare them. When considering Figure 2 and Figure 3 we realize that the measured length of the coastline increases as we decrease the length of the measuring tool.

Recommended for you

We have just described the coastline paradox that Richardson stumbled upon with his research:. The length of a coastline depends on the length of the measurement tool.


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Renew my subscription Give a Gift Manage my subscription. Fractals in nature. Explore fractals. Michael Lucy is features editor of Cosmos. Looking for more science? Click here to see our subscription options. Click here to see our gift options. Popular Today. Spiders fly using electricity, not wind News.

The Sierpinski Gasket

Mars up close and personal Image of the Day. Animals, science, behaviour and ethics News. Coastlines, of course, are not true fractals. While the self-similarity of a coastline extends pretty far, at the end of the day, coastlines are made up of atoms, and so the infinite levels of recursion that are possible in mathematical abstractions like the Koch snowflake are impossible with actual physical objects.

Some of the most interesting developments in math come out of the interplay between abstract concepts and actual physical things that exist in the real world.

How the Mathematics of Fractals Can Help Predict Stock Markets Shifts

Fractals like the Mandelbrot set or the Koch snowflake are artifacts of pure geometry, but it took a strange attribute of coastlines to jump-start the study of this beautiful branch of math. World globe An icon of the world globe, indicating different international options. Search icon A magnifying glass. It indicates, "Click to perform a search".

Modelling nature with fractals

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Fractal -- from Wolfram MathWorld

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