  This work is an analytical and numerical study of the composition of several
fractals into one and of the relation between the composite dimension and the
dimensions of the component fractals. In the case of composition of standard
IFS with segments of equal size, the composite dimension can be expressed as a
function of the component dimensions. But in the case of the compositions
including component multifractals, the composite dimension cannot be expressed
as explicit function of component dimensions and can only be solved
numerically. An application of fractal composition to a physics problem within
the incomplete statistics is discussed.
