Spectral dimension
The spectral dimension is a real-valued quantity that characterizes a spacetime geometry and topology. It characterizes a spread into space over time, e.g. a ink drop diffusing in a water glass or the evolution of a pandemic in a population. Its definition is as follow: if a phenomenon spreads as , with  the time, then the spectral dimension is . The spectral dimension depends on the topology of the space, e.g., the distribution of neighbors in a population, and the diffusion rate. In physics, the concept of spectral dimension is used, among other things, in 
quantum gravity, 
percolation theory, 
superstring theory, or 
quantum field theory. Examples
The diffusion of ink in an isotropic homogeneous medium like still water evolves as , giving a spectral dimension of 3. Ink in a 2D Sierpiński triangle diffuses following a more complicated path and thus more slowly, as , giving a spectral dimension of 1.3652. See also
Dimension
Fractal dimension
Hausdorff dimension

References 

Geometry
Diffusion
Quantum gravity
Power laws