Measuring growth of shape in stony corals -- the fractal problem

[John McManus]

In response to an inquiry about paint precision:

A thin latex paint covers the surfaces fairly evenly - enough to contrast
surface areas of major life forms. However, precision in this case would
raise interesting questions. The surface of a coral is highly fractal. The
coastline of the UK  (or any geographic body) has no specific length - only
a length as measured by a particular set of tools (photo scales, etc.) and a
fractal index. Similarly, the surface area one measures on a coral skeleton
is dependent on the tool - in this case, the viscosity and other properties
of the paint. If one used an extremely fine single molecule paint, the
surface area would be huge! The paint would then sink into pores wrap around
spines and ridges, etc. Differences in area tend to be in squares
(difference in one dimension times another), so the differences in surface
area measure among various surface measuring devices and techniques could be
more than those found among coastline estimations (which typically vary by
50% to 200%). Note that though the "flat" area (the integral) within a
fractal body is often fairly constant despite the measuring approach used to
estimate the perimeter, that does not apply to convoluted 3D surfaces.

I mention this because the principle would apply no matter how one measured
the surface (by photos, lasers, etc), even if you are talking about live
corals with tissue spread out over tentacles, pores, etc. There will be no
"correct" answer. One has to restrict comparisons to objects measured the
same way.


John

_________________________________________________________

John W. McManus, PhD
Director, National Center for Caribbean Coral Reef Research (NCORE)
Rosenstiel School of Marine and Atmospheric Sciences (RSMAS)
University of Miami, 4600 Rickenbacker Causeway
Miami, Florida 33149.
jmcmanus at rsmas.miami.edu
Tel. (305) 361-4814
Fax (305) 361-4600
www.ncoremiami.org



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