Fractal structure produces fractal electrons with fractal energies

Fractals
are a source
of
endless fascination
to me. Life itself relies on many of the
concepts of fractals: trees are fractal, as are feathers, coast
lines, and many other things in nature. Indeed, it was the
realization that landscapes are fractal that made modern animated
films possible.

But, what about fractional dimensions in quantum mechanics? It
turns out that electrons in a
Sierpiński gasket
are also fractal, and that has some pretty
cool consequences.

A fractal is a weird beast. A line is 1D, a square is 2D, and a
cube is 3D: dimensions come in integer quantities. Except they
don’t. For instance, it is possible to create a shape that has a
finite area, but a perimeter that is infinitely long (the
construction of such a shape is pictured below). A shape with these
properties does not behave like a 2D object, but it’s not a 3D
object. Instead, it is a two-and-a-bit-D object. That is a
fractal.

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Source: FS – All – Science – News
Fractal structure produces fractal electrons with fractal energies