Comment on the lichen photographs </P>
Fungi growing under uniform lawns of grass (e.g., I first saw this from
the clock tower of Salisbury Cathedral in 1973: page 243 of The
Geometry of Biological Time) often make richer green contours like
prairie fires consuming and exhausting accessible nutrients on a very
long time scale (many years). In 1981 while backpacking Kauai and in 1984
in Iceland I noticed that
lichens often grow in a similar way in the surface of weathered
rocks. Sometimes the initially circular front of the expanding placque is
broken and its exposed ends curl up like spiral waves in excitable
media. On a trip to Glasgow I discussed this with Prof. Arthur Burgess,
who had noticed the same on village cottage walls. He photographed them
in <A href = "graphics/lichen.84.gif"> 1984 </A>. Finding that old print
among yellowing files recently, I contacted Prof. Burgess to enquire
whether the same cottage wall still stands and maybe had not been
wire-brushed or painted. His <A href = "graphics/lichen.96.gif"> 1996 </A>
follow-up photo shows the same 15-inch long, 9.5-inch high rock after 12 years of
presumably uninterrupted growth. (Fine striations suggest a dozen
annual increments). Overlaid transparencies show the 1984 fronts
uniformly advanced by about 2.5 cm while the "spirals" 
turned about one half rotation. Time lapse movies might present a
fascinating spectacle, if anyone has the patience...
</P>

Footnote 15 Jan 98:  I went back to Kauai after 17 years. Plenty of
  coiled lichen patterns, but none recognizeably related to my 
  ancient photos. I guess it all happens lots faster in that climate
  than in Glasgow. I notice similar things on the big statues of Easter
  Island, that get photographed every day since decades ago: I bet a
  complete history could be assembled from innumerable tourist photos.
</P>

There seems no conceptual foundation for treating lichen growth as an excitable
"reaction-diffusion" process, except the vague idea that weathered nutrients
diffuse into the leading edge of the growth front, turning into lichen
by sudden biochemical reactions which maybe are then satiated for years
before seeking more nutrients (??!). But if one did it anyway, the spiral's period
would be expected to be about 100x the characteristic time for weathering
nutrient into lichen, which we would then have to estimate as 24/100 years
or 3 months to break down rock. And the front "propagation" speed (about
2.5 cm/12 years = 5 x 10^-9 cm/sec) would be expected to be around 
sqrt(diffusion coefficient/that time), which estimates the pertinent
diffusion time (of what? insoluble minerals? ions inside cells?
exchange between alga and fungus?) below 10^-9 cm^2/sec, which seems 
pretty small. The "refractory period" of this "excitability"
would have to be a substantial fraction of the 24-year rotation period.
This is sounding pretty nutty....