[From Bruce Nevin (2002.09.23 17:00 EDT)]
In the November SciAm pp. 116-118 is a description of a cousin of
the Gather demo (f.k.a. Crowd). If I understand correctly, this can be
restated as follows:
The amoeba Dictostelium discoideum (slime mold) generally propagates by
cell division, like most one-celled animals. When it can’t get enough
food (when the population is too dense for the available food supply),
they begin to produce a substance called cyclic AMP in their environment.
They also begin to move toward a higher concentration of cyclic AMP. This
seems a poor choice for survival, since the result is that they clump
together, increasing local population density even more.
Now the variant on the Gather program. As arriving amoebae aggregate
toward a clump, they “sometimes form an elegant spiral.” This
is because the clump slowly rotates. “At some point [the spiral]
breaks up into ‘streaming patterns’ that look like roots or branches
extending from the center. The streams thicken, and as more and more
amoebas try to get to the same place, they pile up in a heap known as a
slug […] The slug is a colony of amoebas, but it moves as if it were a
single organism. Once it finds a dry place, it attaches itself firmly to
the ground and puts up a long stalk. At the top of the stalk is a round
blob called the fruiting body. The amoebas in the fruiting body turn into
spores and blow away on the wind.” If it lands in a nice, moist
spot, it germinates into an amoeba and starts to hunt bacteria and other
food. If there’s enough food, it begins to propagate by cell
division.
Why the rotation? My guess is that the rotation has been going on already
in the individual animals’ search for food and/or cyclic AMP. The
rotation of the clump is an emergent effect, like that of a vortex. From
the illustration it is evident that contiguous spirals are opposite.
I don’t know what happens if the dry spot becomes wet and food again
becomes plentiful. Perhaps the slug and fruiting body devolve into
separate amoebae again; perhaps those in the base and stalk are no longer
viable.
Alan Turing wrote equations that generate these patterns. I wondered if
these equations can be reinterpreted in a model. I found these
references:
“The Chemical Basis of Morphogenesis”, AM Turing,
Philosophical Transactions of the Royal Society B (London), 237,
37-72, 1952.
Morphogenesis: Collected Works of AM Turing, Volume 3, ed PT
Saunders, North-Holland, 1992.
A general description of “the phenomenon” is at
http://homepage.ntlworld.com/j.swinton1/jonathan/Turing/fibonacci.[htm
](http://homepage.ntlworld.com/j.swinton1/jonathan/Turing/fibonacci.htm)http://www.math.smith.edu/~phyllo/
Some related math is at
http://www.swiss.ai.mit.edu/~rauch/turingweb/
This is beyond me. I don’t know whether they’re looking at this as a side
effect of control by a crowd of individual control systems. Google turns
up lots more. Is there an opportunity here?
/Bruce
Nevin