  A central notion of physics is the rate of change. While mathematically the
concept of derivative represents an idealization of the linear growth, power
law types of non-linearities even in noiseless physical signals cause
derivative divergence. As a way to characterize change of strongly nonlinear
signals, this work introduces the concepts of scale space embedding and
scale-space velocity operators. Parallels with the scale relativity theory and
fractional calculus are discussed. The approach is exemplified by an
application to De Rham's function. It is demonstrated how scale space embedding
presents a simple way of characterizing the growth of functions defined by
means of iterative function systems.

Classical Analysis and ODEs