Fractals

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Geometric Fractals

Want to learn more about geometric fractals, such as the von Koch snowflake we discuss below?

Algebraic Fractals

Want to learn more about algebraic fractals, which are formed by repeating a equation?

What's that art above?

Good question! It's something called a fractal. For example, this can be a fractal:

This is one of the only fractals that can be drawn, at least roughly, by hand. You can try drawing it by taking a straight line segment, and dividing it into three pieces. Remove the middle piece, and replacing it with the two slanting sides of a triangle. This results in 4 pieces, with which the same process is applied to. Of course, you can try what the picture depicts, which is...more complicated.

This is known as the von Koch snowflake, which was studied by Helge von Koch(1870-1904) in 1906. It's actually made of three smaller fractals, known as von Koch curves. This is known as a fractal because:

It exhibits self-similarity. When you zoom in, you can see smaller copies.
It has fine structure, meaning it's details can ideally still be observed the more you zoom in or out. Compare this to a circle, where if you zoom in on it's perimeter, it seems to be a straight line.
Construction of it is recursive. Basically, you can repeat the same steps over and over again to form a von Koch curve, which are then combined to form a von Koch snowflake.

These are the most important properties a fractal has. Therefore, anything with these properties can usually be considered a fractal.

⨍ractals

Geometric Fractals

Algebraic Fractals

What's that art above?

©Fractals

The information on this page is actual information about fractals.

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