Alexander's Horned Sphere fractal changes how we define inside and outside

Alexander's Horned Sphere fractal changes how we define inside and outside: Other fractals occupy decimal dimensions or are seemingly solid shapes that are actually all surface area - this fractal can divide the world into one single spherical 'inside' but more than one 'outside.'

Getting just a little crazier, this is only even conceptually possible in a three dimensional universe. The Jordan Curve Theorem, showed that there is no single, enclosed curve that cannot carve a two-dimensional plane into an inside and an outside that mirror each other. It's only in the universe that we perceive that things can get more complicated than that. It's only in our reality that one spherical inside creating more than one outsides is possible.