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Metamorphosis and Artificial Development:
An Abstract Approach to Functionality
Gunnar Tufte
The Norwegian University of Science and Technology
Department of Computer and Information Science
Sem Selandsvei 7-9, 7491 Trondheim, Norway
[email protected]
Abstract. An artificial developmental process may reflect the principle
of a process starting with a zygote which develops to a multicellular
organism. An organism goes through an interwoven process of shaping
the form and behaviour. Metamorphosis is a stage in the development of
many species, e.g. insects, which include a large variation of phenotypic
shape and behaviour in the life-time of the organism. Here principles
from metamorphosis are included as a developmental stage that can be
exploited by evolution to produce artificial organisms with variation in
behaviour at different developmental stages. The target developmental
system is a cellular system close to a non-uniform cellular automaton.
As such, Darwin’s discovery is exploited for evolving genomes for the
construction (development) of von Neumann’s cellular machines, Darwin
meets von Neumann.
1
Introduction
Artificial developmental systems include system with some kind of mapping process that produce a phenotype out of the genotypic information by some kind
of indirect iterative mapping process. The input information to the developmental process may include information from the adaptive process of evolution (the
genome), environmental information (the conditions in which the organism develops) and intermediate phenotypic properties (cues provided by the emerging
phenotype), —See [1].
In nature the developmental process is cellular, a process starting from a zygoth developing to an adult (multicellular) phenotype. A cellular process refer
to communication, inter– and intracellular, autonomous processing of information in each cell, and that the cell is both the constructor and construct of the
phenotype. The developmental process, the process of constructing the phenotype, may consists of stages, e.g. zygote, blastula, embryo, nymphs, larva, pupa,
juvenile and adult, depending on the strategy adapted by the species, —See[2,3].
In living organisms functionality may be viewed as the purpose, i.e. reproduction, and the behaviour as the means of achieving the functionality. As such, the
complexity of the organism, i.e. the behaviour, is given by the need to obtain an
organism with a complexity necessary to achieve the purpose. In the artificial
G. Kampis, I. Karsai, and E. Szathmáry (Eds.): ECAL 2009, Part I, LNCS 5777, pp. 83–90, 2011.
c Springer-Verlag Berlin Heidelberg 2011
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counter part a machine have a purpose and hence a functionality. The behaviour
of the machine fulfils the purpose. The complexity of the machine most be at a
level that makes the machine work, —See[4].
Taking the view of machines at a complexity level that makes them work into
artificial development raises the question of what is needed to make (develop) a
machine that work. Here this question is used as inspiration to look into, and
trying to, include, inspiration from insect metamorphosis. Metamorphosis is an
evolved biological adaptation implying stages. Stages in metamorphosis separate
resources to deal with specialised tasks. The different tasks enables a kind of
resource ”optimisation” as resources can be aimed at obtaining intermediate
organism properties on the developmental path to a reproductive adult [5].
Herein metamorphosis is taken as inspiration to reduce the resources usage in
artificial development [6] and to enable artifacts with different behavioar given
by life phases and/or external infuence. The stage vice development, including
different phenotypic properties, is taken into the mapping process as stage where
the resources used is relieved of functional requirements, i.e. fitness. The experimental approach shows how evolution and development (EvoDevo [7,3]) can
exploit this stage’s relive in pressure to be exploited for generating the general
form of the ”adult” phenotype from the non/different functional early phenotypic form.
2
Metamorphosis: Form and Function
As stated the process of development is an iterative process of creating and forming of the phenotypic structure. This implies an alteration of the phenotype during development, e.g. by growth, cell division and differentiation. The phenotype
includes an inherent plasticity. This may be divided in two. Individual plasticity,
i.e. phenotypic plasticity [8], an ability to adapt form and function of the developing phenotype depending on environmental conditions. As such, phenotypic
form and function of artificial organisms can depend on environmental conditions as to be robust to environmental changes [9]. A second form of plasticity
relates to the change of phenotypic form during development, i.e. developmental plasticity [10]. Metamorphosis is an evolved developmental plasticity [5] that
enables development of phenotypes that include intermediate phenotypes with
form and function that largely deviate from the adult (reproductive) phenotype.
In the view of evolution the origin of metamorphosis possible relates to exploitation of available resources by introducing a stage to transform one phenotypic form/function capable of exploiting available resources to a form for the
actual function (purpose) of reproduction. The pupa stage in this transformation
include an extreme expression of plasticity hence also a increased activation of
genes. However, at this stage the functionality (or purpose) is not reproduction
but the transformation to a functional (reproductive) phenotype.
By introducing stages in artificial development that is relieved of an actual
functionality requirement, except for the emergence of a functional phenotype
at a later stage in development, this intermediate stage can as in insect metamorphosis be concentrated on producing a form for a functional phenotype.
Metamorphosis and Artificial Development
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Introducing such a stage hopefully reduces the resources needed to develop a
functional phenotype. This reduction in resources is here given as a time slot in
development where there is no requirement of functionality. As such, this time
slot in developmental time is exploitable (by evolution) to transform an early
phenotypic form, e.g. larva, to an functional adult form.
3
EvoDevo: Darwin Meets von Neumann
In this work the structures targeted are developing structures capable of computation. The computational architecture is based on Cellular Automata (CA)
originating from von Neumann [11]. von Neumann’s Self-Reproducing Automata
is in itself close to artificial development [12], cells with a finite number of
states that can self-replicate, i.e. an expanding cellular structure. Herein the
developmental phenotypes is based on a cellular computational machine [13]. A
non-uniform CA is developed, i.e. the structure/form, emerges out of a set of
developmental rules capable of cellular growth, differentiation and cell death.
The developmental rules are evolved using a Genetic Algorithm (GA), a principle inspired by Darwin [14].
As stressed in Section 1 organisms have a functionality (purpose). The functionality here is the output of the non-uniform CA phenotype, i.e. an emerging
behaviour given by running the CA.
Fig. 1 is an example of development of a cellular machine and it’s behaviour.
The phenotype is an emerging non-uniform Cellular Automata (top). Development of the structure goes through steps, Development Steps (DS), where the
structure is formed by growth (expanding the number of cells) and differentiation (changing the rule of a given cell). The different colours in the emerging
phenotype represent what CA rule the cell contains. White cells are considered
Fig. 1. Snapshot of the development of phenotypic structure (top) and the corresponding emergent behaviour (bottom) shown as space-time pattern
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empty. The dashed lines indicate that there exists events that are not shown in
the figure, e.g. the phenotypic structure between DS 8 and DS 98 are not shown.
The behaviour of the system in Fig. 1 (bottom) is the state space produced from
an initial state executed by the developing non-uniform CA. The space time
plots for the behaviour consists of 100 State Steps (SS) for each development
step. This implies that there exists 10 000 space time plots describing the behaviour of the system. It is important to note that in this system a behaviour
exists from the first cell throughout the life-time of the organism. This opens for
a adaptive system that can respond to externally enforced changes.
The evolution of a developing cellular machine in such a system exploits Darwin’s discovery for evolving genomes for the construction (development) of von
Neumann’s cellular machines, Darwin meets von Neumann [15].
4
The EvoDevo System
The system as a whole is close to an Evolutionary Developmental (EvoDevo)
approach —see e.g. [3,7]. This implies a developmental system with a possibility to include information from the environment, intermediate structures and
behaviour in addition to the genetic information carried in the genome. The details of the system are only discussed in brief. For a complete description of the
system —see [9] (developmental model) and [16] (evolutionary algorithm).
The development model is based on cellular development. This implies that
the genome is present and processed autonomously in every cell. In the model,
the cell also contains the functional building blocks. Fig 2(a) illustrates the
developmental system — the cell. The cell is divided into three parts: the genome,
development process and the functional component of the cell.
The genome consists of a set of rules. Rules are restricted to expressions
consisting of the type and state of the target cell and the types and state of the
cells in its von Neumann neighbourhood. There are two types of rules i.e. change
and growth rules. Cell growth is a mechanism to expand the organism.
Result
Active?
Action
Condition
Active?
Type
state
Active?
Type
state
Active?
Type
state
Active?
Type
state
Active?
Type
state
N
W
C
E
S
(a) Components of the cell.
(b) Gene regulation for a single rule.
Fig. 2. The basic cell and a rule showing the gene regulation
Metamorphosis and Artificial Development
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Differentiation changes a cell’s type i.e. its functionality. The result part of a
change rule give the cell the target cell is going to be changed into. Cell death
is a result of a change rule changing a cell type into empty whilst the state
information is keept. As such, a cell can be killed off, but the state information
in the cell is still avilable to neighbouring cells.
Each rule, shown in Fig. 2(b), consists of a result and a condition. The conditional part provides information about the cell itself (type and state) and each of
the neighbouring cells. State information provides a way to include information
relating to the functionality of the organism at a given point in time as well as
information about the external environment — the empty cells in the environment also have state information. As such, a cell is represented in the condition
of a rule by two genes representing its type and its state. However, a target cell
is only represented by one gene: it’s type for change rules or growth direction
for growth rules. The state of cell may be 0, 1 or Don’t Care (DC).
The functional components of the cell consists of a look-up table (LUT) defining functionality and a flip-flop as a memory element. The output value is synchronously updated and sent to all its four neighbours and as a feedback to itself.
Available cell types were based on Sippers universal non-uniform CA [13] and
threshold elements [17]. For further details on LUT definitions see [9].
One update of the cell’s type under the execution of the development process
is termed a development step (DS). A development step is thus a synchronous
update of all cells in the cellular array. The update of the cell’s functional components i.e. one clock pulse on the flip-flop, is termed a state step (SS). A development step is thus made up of a number of state steps. An example of execution
of developmental and state steps for the model can be seen in Fig. 1.
5
Experiment: Metamorphosis Enforced
In the previous section the principles of a EvoDevo system was described. In
order to target the system to an abstract approach the metamorphic stage in
the process of development was introduced by defining a portion of the available
developmental steps differently and enforcing a portion of the cells to output a
logical ”1”, a square three cell wide frame of 176 cells. As such, there is no internal
regulation controlling developmental stages, rather defined enforced changes that
can be exploited by evolution.
In the experiment the main behaviour (or functionality of the adult) is a
sequential counter. Counting is based on the state information of the entire
cellular space and the sequential operation of the functional components of the
cells, i.e. the look-up table and flip-flop. A counting sequence is defined in the
cellular array as the number of logical ”1” in the cellular array increasing by one
for each state step.
An organism witch goes through metamorphosis can in the early stage optimise its resources to reach an intermediate phenotype. Here this is represented as
an entry in the fitness function counting the number of cell expressing a logical
”1”, i.e. a static pattern. In the metamorphic process there is no requirement
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(a) DS 0
(b) DS 49
(c) DS 99
(d) DS 199
Fig. 3. The developing phenotypic structure at different development steps
800
40
1000
one
count
30
500
400
300
25
600
20
400
15
200
10
200
100
Count sequence length
35
800
600
Number of one
Number of active rules
700
5
0
0
50
100
Development step
150
200
(a) Number of cells expressing a active
rule.
0
0
0
50
100
Development step
150
200
(b) Counter sequence and cells outputting a logical ”1”.
Fig. 4. Gene activation and lifetime behaviour
for functionality. The adult stage, the final targeted functionality, targets the
counting behaviour described. As such, the organism goes through an initial
developmental phase (larva) producing a static bit patter, the next step is the
metamorphic transformation from bit patter generator to a functional counter
behaviour. In the last phase (adult) the organism perform it’s counter to the
end of the apportioned number of development steps.
As stated, there is no functional requirement in the metamorphic stage. To
further differentiate this stage to be exploitable by evolution each development
step is here set to include zero state steps. As such, the change in state information between development steps is not present. This implies that the resources
for a trajectory in the state space are reduced from 100 to 1 node for each
development step.
The experiments was done using a genome consisting of 32 rules evolved for a
maximum of 100 000 generations. As such, herein the target is to evolve developmental rules that can exploit the different stages as to produce a functional
adult phenotype in the apportionated 200 DS, the functionality is given by 100
SS on each DS. The size of the cellular array was set to a maximum of 32 x
32 cells. In the experiment the state information of all empty cells ,except the
initial zygote, was set to a logic ’1’.
Metamorphosis and Artificial Development
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Fig. 3 shows an example of how the phenotypic structure develops. The initial
configuration of the first single cell at DS 0 is shown in Fig. 3(a). The intermediate phenotypic form and function (bit pattern) for the first stage of development
is shown in Fig. 3(b). This stage is the final development step targeting a bit
pattern functionality. From DS 49 the organism goes through metamorphosis to
a new phenotypic form shown in Fig 3(c). Between DS 49 and DS 99 there is
no functional requirement to the developing organism. The phenotype shown in
Fig 3(d) is the final phenotypic form considered.
The gene activation plot for the development of the organism in Fig. 3 is shown
in Fig 4(a). The plot show the gene activation level, i.e. number of expressed rules
in the organism, There are active rules, i.e. changes expressed in the phenotypic
structure in the initial stage of development, DS 0 to DS 49. In this phase the
structure shown in Fig. 3(b) is the outcome of development.
In the Metamorphic stage, DS 49 to DS 99, the gene activity is at its peek
before decreasing when the metamorphic stage end. In the plot shown there is
gene activity early in the adult stage finalizing the phenotypic structure and
behavioar.
In Fig. 4(b) the counter sequence behaviour is plotted for the life-time of an individual together with the total number of cells outputing a logical ”1”. Here the
metamorphosis is at its most prominent. At the early stage there are hardly any
stable counter behaviour but the number of cells outputting a logical ”1” encreases.
This stage was not intended to include counter behaviour, it targets to maximize
the number of logical ”1” in the array. When the metamorphic stage is reached
there are no counting behaviour at all, as the number of state steps for this stage is
set to one. The absence of state steps provide a reduction in resources (state steps)
and a more stable ”environment” caused by an preservation of the regulatory input
from the functional components of the cells. At DS 99 - 100 the effect of the metamorphosis emerges as the adult behaviour emerges, a counter sequence of length
33. As such, if the behaviour is considered, it shows how the development creates
a functional adult emerging at the end of the metamorphic stage.
6
Conclusion
In this work it is shown that metamorphosis can be included by defining a part
of the available life-time of the organism as a specialised developmental stage.
The introduction of such a stage can be exploited to create a phenotypic form
that can produced functionality that may change during the life-time of the
organism. Here the experiment shows example of how different functionalities
can be targeted at different stages of development. In the example shown the
metamorphic effect was clearly shown in form of gene activation and the change
in behaviour throughout the life-time of the organism. In ongoing work the
abstract approach are extended to evolve organisms that are sensible to external
environmental variations as to produce different targeted functions. As such, the
metamorphic stage is exploited as a transition phase for reshaping the phenotype
to express different functionalities.
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