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. an ink drop diffusing in a water glass or the evolution of a pandemic in a population.
The spectral dimension depends on the topology of the space, e.g., the distribution of neighbors in a population, and the diffusion rate.
[7] The diffusion of ink in an isotropic homogeneous medium like still water evolves as
Ink in a 2D Sierpiński triangle diffuses following a more complicated path and thus more slowly, as