Scale invariance
When some geometry is scaled up/down by a certain constant factor then it maps to a geometry that is indistinguishable form the original geometry.
This is similar to translational symmetry in the sense that logarithmic mapping of the geometry leads to translational symmerty.
See: Log polar mapping
Fractal self similarity across scales can (but may not) be a weaker property.
Like the Mandelbrot set is not scale invariant in the stringent sense stated above.
Scale invariance needs to hold only for the local limit with more or less of the surroundings.
There are truly scale invariant fractals with branching that goes beyond what's possible in layers in 3D.
(wiki-TODO: Add an example and explain why layers are a more natural baseline model fro productive nanosystems.)
In advanced productive nanosystems like gem-gum factories there may be some limited form of cale invariance.
Especially when organized in assembly layers. An especially for the upper end of the Convergent assembly.
Bottom layers must feature heavy deviations from scale invariant geometry due to a number of factors.
Some explained on page: Convergent assembly.
