  We consider several distances between two sets of points, which are
modifications of the Hausdorff metric, and apply them to describe some fractals
such as $\delta$-quasi-self-similar sets, and some other geometric notions in
Euclidean space, such as tilings with quasi-prototiles and patterns with
quasi-motifs. For the $\delta$-quasi-self-similar sets satisfying the open set
condition we obtain the same result as a classical theorem due to P. A. P.
Moran. In this paper we try to gaze on fractals in an aspect of their "form"
and suggest a few of related questions. Finally, we attempt to inquire an issue
-- what nature and behavior do non-crystalline solids that approximate to
crystals show?
