the landscape allows more species to exist in a particular area and in the landscape as a whole;
however, extremely high fractal dimensions cause fewer species to coexist on the landscape scale
(Palmer 1992).
Although many ecologists have found fractal geometry to be an extremely useful tool, not all concur.
Even scientists who have used fractal geometry in their research point out some of its shortcomings.
For example, Scheuring and Riedi (1994) state that “the weakness of fractal and multifractal
methods in ecological studies is the fact that real objects or their abstract projections (e.g.,
vegetation maps) contain many different kinds of points, while fractal theory assumes that the natural
(or abstract) objects are represented by points of the same kind.”
Many scientists agree with Mandelbrot when he said that fractal geometry is the geometry of nature
(Voss 1988), while other scientists think fractal geometry has no place outside a computer simulation
(Shenker 1994). In 1987, Simberloff et al. argued that fractal geometry is useless for ecology
because ecological patterns are not fractals. In a paper called “Fractal Geometry Is Not the
Geometry of Nature,” Shenker says that Mandelbrot’s theory of fractal geometry is invalid in the
spatial realm because natural objects are not self-similar (1994). Further, Shenker states that
Mandelbrot’s theory is based on wishing and has no scientific basis at all. He conceded however that
fractal geometry may work in the temporal region (Shenker 1994). The criticism that fractal
geometry is only applicable to exactly self-similar objects is addressed by Palmer (1982). Palmer
(1982) points out that Mandelbrot’s early definition (Mandelbrot 1977) does not mention
self-similarity and therefore allows objects that exhibit any sort of variation or irregularity on all
spatial scales of interest to be considered fractals.
According to Shenker, fractals are endless geometric processes, and not geometrical forms (1994),
and are therefore useless in describing natural objects. This view is akin to saying that we can’t use
Newtonian physics to model the path of a projectile because the projectile’s exact mass and velocity
are impossible to know at the same time. Mass and velocity, like fractals, are abstractions that allow
us to understand and manipulate the natural and physical world. Even though they are “just”
abstractions, they work quite well.
The value of critics such as Shenker and Simberloff is that they force scientists to clearly understand
their ideas and assumptions about fractal geometry, but the critics go too far in demanding precision
in an imprecise world.
With all the new insights and new knowledge that have been gained through the appropriate
application of fractal geometry to natural sciences, it is clear that is a useful and valid tool.
The new insights gained from the application of fractal geometry to ecology include: understanding
the importance of spatial and temporal scales; the relationship between landscape structure and
movement pathways; an increased understanding of landscape structures; and the ability to more
accurately model landscapes and ecosystems.
One of the most valuable aspects of fractal geometry, however, is the way that it bridges the gap
between ecologists of differing fields. By providing a common language, fractal geometry allows
ecologists to communicate and share ideas and concepts.
As the information and computer age progress, with better and faster computers, fractal geometry
will become an even more important tool for ecologists and biologists. Some future applications of
fractal geometry to ecology include climate modeling, weather prediction, land management, and the
creation of artificial habitats.
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