The features have to stop eventually. There is a limit to how far nature can keep repeating these features. Atoms will be left when we are through with the continuous magnification. At this time, the fractal would no longer exist because atoms would then be identified and differentiate from the original fractal. Another example of mistaken fractals is in leaves and flowers.
Fractals do appear to exist and the patterns the plants display seem never ending.
In reality, though, self-similarity has to stop and the object is then seen more precisely, like with the atom. After visiting numerous websites, we have learned that although fractals are odd but interesting patterns in the world, they can be useful in many ways. Earlier, we had also believed that fractals appear everywhere, but later found out that fractals do not exist everywhere such as nature. Fractals, therefore, rarely exist in nature, but exist in mathematics. It is these fractals that aid us with items ranging from tracking hurricanes to the making of movie backgrounds.