Zygote and its Progeny
In his book, ''A New Kind of Science"
(1), Stephen Wolfram describes a new modeling tool, called Cellular Automat
(CA). Simple programs evolve in an unpredicted fashion and become extremely complex.
CA is particularly suitable for illustrating some characteristics of life,
which cannot be modeled with other Artificial Life (AL) tools, e.g., neural
networks (NN), or genetic algorithms (GA).
Life is complex, creative , optimal
, and continually moves (changes). These characteristics will be illustrated here with
CAs . specified by Wolfram. The following examples will apply two totalistic
CAs with the respective rules
, #357, #600. The first image illustrates the structure of a rule #600
CA. It originates in a seed which is always a 1. Each row represents a
state of the CA. The last row is its present state. The picture depicts
a CA trajectory which is also its history.
Rule #357
The picture depicts four
CA histories. The first (marked by a 0), depicts a history of a single CA,
which gradually grows, yet will soon die. The next history depicts two CAs
whose seeds were 5 units apart from each other. After fusing, they became
immortal. The next history depicts two CAs whose seeds were 22 units apart
from each other. Both grow
along each other, and shortly before they die they interact (fertilize)
each other and become immortal. In the last history the two CAs interact,
gain mass (strength), and die.
The picture depicts 5
CA histories. When the distance between two seeds is 30 units, the CAs are
immortal. Yet when the seeds are placed 8 units apart, they die young (annihilation).
The third history (marked by 13) shows that the two CAs fused, thrived for
a while and then died. The following history starts with a single CA. At
time = 30 a second seed is planted at a distance = 8. This interaction (fertilization)
caused the CA to move to the left and establish a new niche where it remained
until the end of time. . A less pronounced movement to the left
is observed also in the fourth history (13). The last CA was fertilized
at t=30. It thrived for a while, gained in mass and then died
CA rules are global and
deterministic. After a seed is planted, its progeny oscillates in a strange
attractor which it never leaves. This bleak fate changes dramatically when
two CAs interact. A mortal #357 CA becomes immortal (5), or accumulates
mass and lives somewhat longer (23). On the other hand an immortal #600 CA becomes mortal. Here fertilization leads
to extinction.
Fertilization may cause
a CA to move and establish a new strange attractor (#600-8). Its fate was
changed when a pollen coming from another dimension hit it. The CA responded creatively and established a new niche.
Time series
Each history (trajectory) is specified by the
following functions, f[rule, x, t]. Actually it is a time series. The interaction
occurring in the last history can be expressed as f[600,50,0] * f[600,58,30]
(* stands for interaction). Although it specifies exactly the CA trajectory,
it cannot predict it. The outcome of two interactions f*f is unpredictable. It may turn two mortals into immortals (#357
distance = 22), or vice versa (#600 distance = 13).
Cause and effect
In the interaction, f[600,50,0] * f[600,58,30], it appears
as if the pollen f[600,58,30], caused a f[600,50,0] displacement. Did it
really cause it? Obviously it is not the same cause which brings about a
displacement of an elastic ball hit by another one.
One tends to describe this phenomenon in terms of triggering, or initiation. Aristotle
said that this type of interaction has four causes:
1. Material cause: CA structure.
2. Formal cause: Its rule
3. Efficient cause: The second CA (here
the pollen)
4. Final cause: The "purpose of the
collision". Better, the benefit of the collision to the CA, which
will be implemented in the future.
Modern physics rejects three
causes and keeps the effective cause, which causes a ball to move when hit
by another one. Yet effective cause is inadequate to describe biological
phenomena. Here all four causes are required.
The same applies to CAs. Hitherto
the final cause was not implemented. Although CAs tend to settle in strange attractors, we are unable to
explain why they choose a special niche. The living organism is governed
by an optimality principle (Wisdom
of the Body (WOB)) which drives it to specific strange attractors
called homeorhesis.
The implementation of the final cause in the CA design may assist us
in this endeavor..
Interaction between
CA with different rules
Please note that in its
new niche, the differentiated CA#357 adhered to its rule, while none other
structure adhered to rule #600
1.
Wolfram S. A New Kind of Science ISBN
1-57955-008-8