I was watching this video by 3blue1brown and he discusses the idea of fractal dimensions. He notes that fractals can have non-integer number of dimensions. For example, the Sierpinski triangle has a dimension of 1.5849.
+Itai Efrat asked the question in the comments section "In physics the idea of dimension is usually expressed as the number of degrees of freedom needed to describe the movement of a particle. Is there a sense in which a particle moving in a fractal has a non integer number of degrees of freedom?"
Unsurprisingly, the combined intelligence of the Youtube comments section (including myself) was unable to come to a conclusion.
So, does a particle moving in a fractal have a non integer number of degrees of freedom?