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A fractal is by definition a curve whose complexity changes with measurement scale. Whereas approximations of a smooth curve get closer and closer to a single value as measurement precision increases, the measured value of fractals may change wildly. The length of a "true fractal" always diverges to infinity. However, this figure relies on the assumption that space can be subdivided indefinitely. The truth value of this assumption—which underlies Euclidean geometry and serves as a useful model in everyday measurement—is a matter of philosophical speculation, and may or may not reflect the changing realities of 'space' and 'distance' on the atomic level.

Koch Like a Koch Snowflake,coastlines have fractal properties. This is a phenomenon called the coastline paradox. Because of this, the perimeter of a coastline depends solely on the method used to measure it and is practically infinite as more accurate methods are used. Derek Muller's cool YouTube show Veritasium gives a better explanation of it. Check out the video here .