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@imaff.cfmac.csic.es) 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;
at http://www.aip.org/png/2008/297.htm we*ve posted a picture of a
plant tumor provided by the Complex Systems Laboratory at the
Technical University of Madrid. )

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Food for thought. TIme fractals? Hmmmm.


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