http://www.aip.org/pnu/2008/split/857-1.html
Number 857 #1, February 28, 2008 by Phil Schewe
Fractals Through Time
A new theoretical study looks at what fractal things look like not just
when you magnify them in space (they are scale invariant: they look the
same even at finer and finer size scales) but also when you magnify them
in time---that is, when you look at them over finer and finer time
intervals. Fractals are those geometrical shapes so tortuously indented
as to take on extra dimensionality. For example, a nominally
one-dimensional curve can, with enough switchbacks, begin to be
characterized by a dimension somewhere between 1 and 2. In other words
the curve starts to take on the properties of a surface. Similarly a two
dimensional surface can be so dimpled as to acquire some “volume.” This
fractal geometry is especially interesting to consider for minerals and
for certain living things (such as tumors) where highly non-Euclidean
interfaces are important.
In a new paper, Carlos Escudero of the Institute for Mathematics and
Fundamental Physics in Madrid performs calculations of the dynamic
scaling (how a surface changes in space and over time at several
different scales) of growing structures, such as the kind of
semiconductor films used in the microchip industry where, even under the
most carefully controlled of conditions, rough (non-Euclidean)
geometries can exist. He found that the moment-by-moment behavior of the
surfaces are strongly effected by the fractal geometry. Escudero (34-
915616800, cel@[EMAIL PROTECTED]
) will soon be testing his theories
with colleagues in several practical areas of research, including the
growth of tumor-like tissues in plants and the growth of semiconductor
films. ( Physical Review Letters upcoming article)
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