Rotational symmetry $\leftrightarrow$ isotropy, dilation symmetry $\leftrightarrow$ ________?

Symmetries correspond to specific properties of the space in question.

• translation symmetry $$\leftrightarrow$$ homogeneity,
• rotational symmetry $$\leftrightarrow$$ isotropy

What property is related to invariance under dilatations?

• dilatation symmetry $$\leftrightarrow$$ scale invariant.