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An Evolvable Artificial Chemistry
Featuring Continuous Physics and Discrete Reactions
Thomas E. Portegys
Illinois State University
Campus Box 5150
Normal, Illinois, USA 61790-5150
portegys@ilstu.edu
Abstract
This paper describes an artificial chemistry featuring atoms
and molecules moving and colliding in a continuous manner
in a viscous fluid filling a 2D cellular space. Chemical
reactions are mappings of discrete cellular configurations to
parameterized actions on atoms. Actions allow atom creation
and destruction, bonding and unbonding to make and break
molecules, orientation, type change, and propulsion. Actions
are easily added in this extensible model. An example
involving a complex “foraging” reaction is provided as a
demonstration of the capabilities of the framework. The
reaction rules can be evolved by a genetic algorithm to exhibit
a desired set of reactions. A portion of the foraging reaction
was evolved to demonstrate this.
Introduction
This work was done in the spirit of the growing belief that
artificial life requires a sufficiently rich physics and
chemistry in which to develop (Bedau et al. 2000, Dittrich
et al. 2001). The attempt here is to combine a simple
continuous Newtonian particle physics with the well-
known and readily computable cellular automaton (CA)
model as a chemistry implementation. There are two
additional purposes for using a CA: (1) the chemistry of
real organic molecules, involving complex foldings and
bondings, is computationally infeasible (Zagrovic et al.
2002); and (2) it serves the aim of artificial life research to
discover underlying mechanisms necessary for the
existence of living systems.
This project was primarily inspired by three recent
efforts: Hutton’s artificial chemistry Squirm3 (2002),
Smith, Turney and Ewaschuk’s JohnnyVon (2003), and my
prior work on intercellular signaling (Portegys 2002). Prior
to these, Dittrich et al. (2001) compared a wide range of
artificial chemistry approaches, including assembler
automata (Rasmussen et al. 1990, Ray 1992, Adami and
Brown 1994), Ono and Ikegami’s autocatalytic membrane
formation (1999), and lattice molecular systems (McMullin
and Varela 1997), in which the atoms comprising a
molecule map discretely to cellular space.
Squirm3 is a lattice molecular system in which mobile
molecules self-replicate using available atoms in a 2D
cellular space. Atoms have a fixed type and a variable
state. Chemical reaction rules based on type, state and
proximity determine the states and bonding status of atoms.
Atoms move by jumping from cell to cell through
simulated Brownian motion; however, atoms bound into
molecules are largely immobile. Beginning with a soup of
inert atoms exposed to state-disrupting cosmic rays, self-
replication was shown to spontaneously occur.
In JohnnyVon, by contrast, T-shaped atoms called
codons move through a continuous 2D space and interact
exclusively through force fields; collisions do not occur.
There are two types of codons, distinguished by their field
“colors”. Each codon is an automaton containing a set of
rules governing its field strengths in response to signals
represented by the proximity of other codon fields.
This project uses the intercellular signaling scheme put
forth in my recent work addressing the problem of
allowing cells in a CA to communicate without disturbing
the state of intervening cells. In this project, signals are
chiefly directed toward atoms residing within cells, rather
than the cells themselves.
Description
This system is an artificial chemistry featuring atoms and
molecules moving and colliding in a continuous manner in
a viscous fluid filling a 2D cellular space. A molecule
consists of a bound set of atoms. Chemical reactions are
mappings of discrete cellular configurations to
parameterized actions on atoms. Actions allow atom
creation and destruction, bonding and unbonding to make
and break molecules, orientation, type change, and
propulsion. Time proceeds in discrete steps.
Atoms and molecules
Atoms are elementary particles possessing a type, mass,
radius, charge, orientation, position, and velocity. A
molecule is a set of atoms connected by bonds. The atoms
within a molecule must form a connected set; there must be
a bond path directly or indirectly connecting any pair of
atoms. A bond may be of variable but limited length.
Forces resulting from elastic collisions and chemical
reactions result in continuous velocity and position updates
according to Newtonian physics. For the initial
implementation, rotational momentum is not supported.
The atoms within a molecule respond to forces as a single
unit; so a collision of one of its atoms results in a force
applied to the mass of the entire molecule. An atom is
oriented in one of the eight compass directions. It may also
be in a mirrored state to support symmetric reactions.
Space
The space is a 2D cellular grid filled with a viscous fluid
that impedes the movement of atoms through it. In the
current implementation, the diameter of an atom is equal to
the dimensions of a cell.
Reactions
Reactions arise from the interaction of atoms. At any
moment, the center of an atom resides within a unique cell.
This cell forms the center of a 3x3 Moore neighborhood of
cells. A reaction specifies a configuration of atom types
residing within a neighborhood. Since atoms have an
orientation, their cell neighborhoods are oriented
accordingly, as shown in Figure 1.
Figure 1: Oriented Cell Neighborhoods
A neighborhood cell value is one of {atom type, empty,
occupied, ignore}. The neighborhood evaluation is a
conjunction of all 9 value matches. An empty value
specifies that a cell must not contain any atom. This could
be used for inhibitory control of a reaction. The occupied
value matches any atom type. The ignore value positively
matches any cell condition.
A reaction consists of the following: {neighborhood,
action, target, parameters}. Target is the location of the cell
where the action is directed via a signal. This may reside
outside of the neighborhood. Parameters apply to actions.
These are: {atom type, orientation, strength, tendency,
delay, duration}. The actions are:
• Create and bond atom. Parameters: type and
orientation of created atom.
• Destroy atom. Parameter: target atom type.
• Bond/unbond acting atom to/from atom. Parameter:
target atom type.
• Grapple atom: bond to and move atom to location in
acting atom’s neighborhood. Parameters: target
atom type, orientation relative to neighborhood
center cell.
• Orient atom relative to acting atom’s orientation.
For example, if acting atom is oriented east, and it
orients an atom to its west, the atom will acquire a
north orientation. Parameters: target atom type and
orientation.
• Modify atom type. Parameter: target atom old and
new types.
• Propel atom: apply a propulsion force to a specific
atom (see below).
Propel atom action:
This is a reaction in which atoms apply propulsion forces
to themselves and other atoms, which when combined with
the viscous fluid medium gives the chemistry a more active
and interesting nature, albeit at the expense of real world
fidelity. More natural alternatives would be to employ
charge forces or Brownian motion to achieve coarser and
slower movements and reactions. The parameters for the
propel action are: target atom type, force direction
(orientation), speed (strength), tendency (relative
probability), delay, and duration. Since the atoms within a
molecule move as a unit, the propulsion forces are
combined at a molecular level. Propulsion forces are
accumulated with collision forces to update the positions
and velocities of molecules.
Update cycle
1. Update positions and velocities of molecules based on
accumulated forces.
2. Clear forces.
3. Compute new collision forces.
4. Match reactions to atom neighborhoods and distribute
action signals to target cells.
5. Execute actions.
Results
This section presents a demonstration of the capabilities of
the framework. Both Squirm3 and JohnnyVon solved the
challenge of self-replication. For the sake of variety, a
different problem is ventured here that I propose is of
comparable complexity. The problem involves an
orchestration of cooperating reactions that allows a
particular molecule to randomly encounter and
systematically destroy atoms of a particular type. The
overall impression is one of “foraging”, a metaphor that
will be used in the following description.
The molecule, called “Maxwell” (for whimsical reasons)
is shown in Figure 2.
Figure 2: The Maxwell Molecule
This molecule is a ring of bonded atoms. Its atoms are
labeled with ‘M’ in order to distinguish atoms “belonging”
to Maxwell from others. However, the corner atoms are of
a different type than the side atoms. In addition, the
orientations of all the atoms point directly away from the
center, so for example the top center atom is oriented north,
the top right atom northeast, etc. This allows the same
reaction rules to work regardless of the molecule’s relative
position to external atoms. One set of reactions is
structured to allow the Maxwell molecule to destroy “food”
atoms by “ingesting” them. In doing so, a variety of
reaction types are brought into play.
Figure 3: Beginning Ingestion Reaction
Figure 3 show the beginning of the ingestion reaction
sequence as Maxwell approaches a food atom.
Figure 4: Ingestion Reaction Continued
Figure 4 show the next three steps. Proceeding from left to
right: the lower right corner atom grapples the food atom,
moving it counterclockwise over the side atom; the side
atom has destroyed itself to create a pathway into the
center, and the other nearby corner atom has bonded to the
food atom; the food atom is grappled into the center.
Figure 5: Ingestion Reaction Completion
The reaction completes in Figure 5 with the restoration of
the side atom and rebonding of the molecule. The process
is facilitated by a type change to the center food atom
before it is destroyed. There are 21 reactions involved in
the entire process.
Maxwell will systematically ingest food atoms it comes
into contact with. The propel reaction type allows it to
move about, or “forage”, in a space that is stocked with
variable-sized patches of food atoms.
Figure 6: Foraging Reaction
Figure 6 shows Maxwell ingesting a food patch it has come
into contact with. In the “programmed” version of
foraging, it will move in a spiral counter-clockwise pattern
around the perimeter of the patch, usually resulting in the
complete ingestion of it. Figure 7 shows the finale of the
process.
Figure 7: Foraging Reaction Finale
Figure 8: Foraging Reaction Neighborhoods
Three propel reactions are involved in foraging. The left
portion of Figure 8 shows the neighborhood of the first
propel reaction that produces movement in free space (no
food present). The neighborhood specifies a corner atom
with an empty cell directly “north” of it. Table 1 shows the
other attributes of this reaction. The direction and strength
values translate to a fairly high rate of speed moving the
entire molecule in a northeast direction. The tendency
value indicates that, in the absence of other propel
reactions, there is a 10% probability of this reaction
occurring. This is important considering that this reaction
applies to all four corners of the molecule. If all “fired” at
every step, the propulsions would cancel and the molecule
would not move. As it is, the result is a random Brownian-
type motion with fairly long legs.
Attribute
Value
target type
corner
displacement
0,0
direction
north
strength
2.0
tendency
0.1
delay
0
duration
1
Table 1: First Foraging Reaction
The neighborhood in the right portion of Figure 8 applies
to the second and third reactions. The second reaction
attribute values are given in Table 2. This reaction moves a
corner atom east when a food atom is north of it, which
results in the molecule moving along the side of a food
patch. The strength value causes it to move slowly, lest the
food be knocked away by impact.
Attribute
Value
target type
corner
displacement
0,0
direction
east
strength
0.1
tendency
5.0
delay
0
duration
20
Table 2: Second Foraging Reaction
The tendency and duration of this reaction causes it to
heavily outweigh and outlast the first reaction, so that an
intermittent exposure to free space will not result in the
molecule darting away from the food patch.
Attribute
Value
target type
corner
displacement
0,0
direction
north
strength
0.1
tendency
3.0
delay
20
duration
50
Table 3: Third Foraging Reaction
The third reaction is given in Table 3. The purpose of this
reaction is to steer the molecule around food patch corners.
The delay and duration values allow this reaction to remain
in effect for a relatively long time after running off the
edge of the patch. It will subsequently cause the atom to
move north, resulting in the corner atom counter-clockwise
from it to “engage” the next edge using the second
reaction.
Evolving the chemistry
In the previous discussion, the foraging reactions were
programmed to perform suitably. Two additional
experiments were done using a genetic algorithm to evolve
the three reactions pertaining to foraging. For the evolution
procedure, a population member consisted of a set of
foraging reactions. The population size was twenty, with
the ten fittest members selected out of each generation as
measured by foraging success. Foraging success is defined
by the number of food atoms ingested times a value of ten
each. A set of eight randomly selected fit members were
mutated, the nature of which depended on the experiment
(see below). An additional two fit members were selected
for mating. Mating involved randomly selecting one
reaction from each of the three parental pairs of foraging
reactions.
In the first experiment (hill-climb), the action,
neighborhood, target type, and displacement attributes of
the reactions were fixed at the programmed values, while
the direction, strength, delay, and duration attributes were
set to minimum values and subjected to a simple hill-
climbing mutation procedure. The aim of this experiment
was to “tune” the propulsion parameters.
In the second experiment (random), the reactions were
initially rendered inert by clearing them to minimum values
and setting the action to a null value. Mutation consisted of
randomly setting the various attributes to values within set
tolerances. The exception to this was that when the action
was mutated, the rest of the attributes were again cleared.
0
200
400
600
800
1000
1200
50
100
150
200
250
300
350
400
450
500
Generation
Foraging success
Programmed
Hill-climb
Random
Figure 9: Foraging Evolution
Figure 9 shows the results of the experiments. The
programmed (unevolved) version was run for the same
number of generations and is shown as a control. The hill-
climbing experiment proved to be an immediate success.
Upon closer examination of the fittest members, it became
obvious that the programmed foraging speed was too slow,
especially the reactions controlling speed in the presence of
food atoms. The random experiment quickly produced a
functional set of reactions, but failed to improve
dramatically after that. An inspection of the reactions of the
fittest members revealed a basic propel reaction triggered
by the presence of free space. Surprisingly, this was
enough to approach the performance of the programmed
version. Conclusions
One of the aims of this project was to find a way to acquire
some of the benefits of a continuous physical medium,
such as that in which organic chemistry takes place, and
also retain the computability benefits of a cellular
automaton as a chemistry framework. The Maxwell
molecule was designed to showcase some of the
capabilities of this approach. The framework is easily
extensible: new reaction types can be plugged in with few
code changes.
This model has some obvious similarities and differences
with Squirm3 and JohnnyVon; the former is CA based, and
latter is based on continuous fields and movements. At this
point it would be premature to attempt more definitive
comparisons, since all are in early stages of development.
Besides further applications, such replicating molecules
and semi-permeable membranes, there are a number of
relatively easy enhancements that can be made to make the
model more realistic, such as going to 3D (the physics code
already supports this), adding rotation/angular momentum
effects, and introducing charge as a source of attraction and
repulsion force.
The open source C++ code is available at
www.itk.ilstu.edu/faculty/portegys/research.html
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