Investigating Fractals Through Time 

March 25, 2008

A new study looks at something surprising: what fractals look like over extended time intervals. 

Fractals are geometrical shapes so tortuously indented that they can take on extradimensionality. For example, a one-dimensional curve can, with enough switchbacks, be characterized by a dimension between one and two and the curve can take on the properties of a surface. Similarly, a two-dimensional surface could be so dimpled that it acquires some "volume."

Theorizing about fractals this way can have relevance when working with certain minerals and living things where highly non-Euclidean interfaces are important. Carlos Escudero (Institute for Mathematics and Fundamental Physics, in Madrid) has performed calculations of the dynamic scaling--how a surface changes in space and over time at several different scales--of growing structures.

One area of his research involves the kind of semiconductor films used in the microchip industry where, even under the most controlled conditions, non-Euclidean geometries exist. Escudero found that the moment-by-moment behavior of such surfaces is strongly affected by fractal geometry.

Escudero will be also test his fractal theory on the growth of tumor-like tissues in plants and publish his findings in Physical Review Letters.

Source: American Institute of Physics