- Exact self-similarity: identical at all scales; e.g. Koch snowflake
- Quasi self-similarity: approximates the same pattern at different scales; may contain small copies of the entire fractal in distorted and degenerate forms; e.g., the Mandelbrot set’s satellites are approximations of the entire set, but not exact copies.
- Statistical self-similarity: repeats a pattern stochastically so numerical or statistical measures are preserved across scales; e.g., randomly generated fractals; the well-known example of the coastline of Britain, for which one would not expect to find a segment scaled and repeated as neatly as the repeated unit that defines, for example, the Koch snowflake
- Qualitative self-similarity: as in a time series
- Multifractal scaling: characterized by more than one fractal dimension or scaling rule
+ a new definition of shapestacking-similarity, in which the previous zoompath stores itself