[2] Varela et al. (1974)
  uses the term ``component'' rather than ``particle'';
  I prefer the latter term, because at any given time
  these entities may or may not be
  ``components'' of a higher level (autopoietic?)
  structure. Calling them ``components'' seems to me to
  obscure or prejudge this issue of the formation of
  higher level structures.
[3] Formally,
  ``holes'' could be equally regarded as another
  ``element''; in which case we would say that every
  lattice position is always occupied by exactly one
[4] Again, formally, particle movement
  might be regarded as a special degenerate kind of
  ``reaction'', in which all reactants are
[5] It might have been preferable to
    term links ``monomers''.
[6] This is a particularly counter-intuitive,
  or unnatural aspect of this model; I speculate that
  this limitation was stipulated primarily in order to
  simplify the computer realisation of the model.
[7] That is, it seems
    that 1.31 and 1.32 are not to be interpreted as a
    sequential refinements of 1.3, but rather as
    concurrent qualifications or constraints on it.
[8] I conjecture that part of the
    explanation of this, and some other related
    peculiarities of the algorithm, may be that the
    algorithm was actually derived from a functional
    implementation (and thus inherited artifacts from
    it), rather than the algorithm having been written
    first and used as the specification of the
    implementation.  However, this is of only
    historical interest at most.
[9] Only three
  directions arise here, since one direction is already
  accounted for by the free L particle we are
  attempting to move at the higher level of the
[10] Steps 1.2 and 1.3, or 2.2 and 2.3, or
    3.2 and 3.3.
[11] Note
  that, with the specified initial condition of the
  space-holding only K and S particles,
  then, by conservation rules, there would always be
  guaranteed to be a hole available somewhere in
  the space, given that an L is being disintegrated;
  but if that initial constraint were relaxed, it would
  be possible that a hole might not be available at
[12] Indeed, since the
  algorithm makes no stipulations at all about how this
  is to be done, locality could be completely
  ignored-for example by saying that the extra 
  S particle should be put in a hole simply chosen
  uniformly from all holes in the space, without any
  regard to proximity to the disintegration site.
[13] Note that L and K particle
    movements come before production in the
    algorithm; so produced L particles cannot separate
    from the K particle within a single iteration
    of the algorithm.
[14] There is
    one L initially produced by EXP29.FOR that
    is still processed for bonding; but it is
    isolated from the other L particles and thus
    cannot bond in practise within that first timestep.
    In any case, that particular L particle does
    not appear in figure 5, indicating
    either an error in redrawing, or some detailed
    discrepancy between the code of EXP29.FOR and that
    actually used to generate this diagram.
[15] Milan Zeleny, personal communication.
[19] peterw/latex/harvard/
[20] peterw/index.html
[21] I am
  indebted to Ms. Marita Prandoni of the Santa Fe
  Institute for her assistance in making this
[22] This is also available as a
  standalone source code file-see the 
[23] [Escritura] NOTA: En esta
  busqueda no cuenta las veces en que encuentra
  elementos M en las fases + & * en la neuva
  ubicatión.  Esto sultimo lo hace moverse
  preferentemente a lo largo de canales de M.
[24] [Handwritten] Note: In this
    search, the times when an M particle in the + or *
    state is encountered in the new location are not
    counted.  In this way there will be preferential
    movement along channels [?] of M.

Copyright © 1997 All Rights Reserved.
Timestamp: Tue Dec 31 18:43:32 GMT 1996