Coastlines aren't really fractal in the mathematical sense because they do not scale predictably with dimension the way that true fractals do (except perhaps truly complicated ones). However, coastlines do share the property with fractals that the irregularity of the edge of a landmass exists at all scales, making the actual length of a coastline impossible to actually measure or even define.

Now, this said, there are computer programs that have generated, using fractals, realistic-looking landscapes, using simple, deterministic (i.e. fractal) rules, and simply observe them at such a small portion of the fractal design that the entire shape of the fractal is not obvious. However, the real world is not a mathematical construct, and coastlines and their formation is not mathematically predictable the way that a true fractal is.

At the beach, waves come in, and if you stand up close, the water and the sand make a wavy line, where the water comes a few inches farther onto the beach in some places and a few inches less far onto the beach in other places.

If you stand a little bit away from the water, you can see there are places where the water comes a few feet farther up the beach and places where the water comes a few feet less far onto the beach.

If you stand away from the water even more, you can see places where the waves come a few yards farther up the beach and places where the water comes a few yards less far onto the beach.

If you go up in an airplane and fly along the coast, you can see places where the water comes a few miles farther in at the edge of the land and you can see places where the water is a few miles farther away, because the land sticks out into the ocean.