Since the start of January, I have expected snow to come because the first snow is usually around this time period. However, it is already halfway through January and rain- snow is the closest I have seen. While looking at a paper decoration of the snowflake model, I had noticed some self – similarity and difference at the same time. Then a question popped into my head: Is snowflake a fractal?

#### What is a fractal?

Fractal is a geometric pattern which is self – similar and the pattern continues on forever. So if you zoom in to a part of the pattern, it will be a “smaller” version of its original self. Also, another trait of the fractal is a non – integer dimension. Dimension is the amount of axis it has. For example a dot has 0 dimension, a line has 1 dimension(length), a shape has 2 dimension(length*width), an object has 3 dimension (length*width*height). All of the examples are integer dimension. Depending on the type of fractal, the dimension will vary such as dragon curves(1-2 D) because of a “shape” composed by lines and landscape images(2-3 D) because some part of it has the “texture” which is more inclined towards 3D.

#### Yes or no

Depending on the type of snowflake, the answer is going to be different.

There is a famous fractal pattern called the Koch snowflake. It is a fractal because it has the pattern of dividing a side into 3 equal segments and draw an equilateral triangle in the center segment. This way when you “zoom in” to each side it has the same pattern. However, Koch snowflake isn’t a real snowflake. In a real snowflake, each of the branches contains some self- similarity but the pattern doesn’t continue on forever. So it isn’t a fractal but it has fractal geometry in it.

#### Conclusion

Snowflake isn’t a fractal because it has a limit to how many times itself repeats and every snowflake is slightly different from each other. Since all of the main branches are self – similar to another, it has the fractal component. Also, a fractal model snowflake can have a 95% or 99% similar to an actual snowflake. However, the Koch snowflake is a fractal but it isn’t a tangible snowflake.

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