On Routine Evolution
of Complex
Cellular Automata
Michal Bidlo
[email protected]
Humies 2016
Presentation outline
This entry is based on the paper:
M. Bidlo: On Routine Evolution of Complex Cellular
Automata. In: IEEE Transactions on Evolutionary
Computation, PP(99), 2016 (in print)

Research overview & challenges

Reasons for human competitiveness

Why should this paper win
Topic overview
Uniform cellular automata (CA) represent a class of
complex systems in which the behavior emerges from
local interactions between cells.
The design of transition functions for CA becomes very
difficult with the increasing number of cell states,
Input:
i.e. the aim is to automate this process.
X=4
An efficient encoding of transition functions
is needed in order to solve a given application
(which was a subject of the proposed paper).
Some existing CA benchmarks:
Output: Y=X2
Langton's self-replicating loop
Codd's construction arm
Wolfram's generic
squaring CA
Why is the CA design hard?
The design of transition rules for CA is not intuitive.
A need to explore huge spaces of potential solutions, e.g.
for 1D CA, 8 states, 3-cell neighborhood there are over
2.4x10462 transition functions,

the 2D CA, 6 states, 5-cell neighborhood induces more
than 8.0x106050 transition functions.

Sometimes it is even not known whether a solution exists,
so the evolution is a real discovery.
In our case: given some input and expected output,
the EA should find both the CA behavior leading to
the output and the transition rules determining
how to achieve it.
Common approach
CA have been designed and studied analytically, for example:
Langton's
loop
Byl's loop
The loop of
Chou-Reggia
Conway's Game of Life
universal computing
self-replicating loops
Wolfram's prime
number generator
These were usually designed by means of well-established
engineering methods.
Can evolution bring us something more?
YES, IT CAN!
The proposed evolutionary approach
Instead of using extensive chromosomes:
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5
we introduced a special encoding using conditions:
=0 ≤1 ≥2 ≠0 ≥0 1 ≤4 =0 ≥3 ≠0 ≥0 4 =0 =0 ≤3 =0 ≥1 5 ≥0 ≤2 =0 ≥0 ≥1 1 ≥0 =0 ≤1 ≥0 ≠0 4 ≥0 =0 ≤1 ≥0 ≠0 2 ≤2 =0 ≥0
≠0 ≥0 0 =0 ≤5 =0 ≥4 ≠0 1 ≤0 =0 ≥5 =0 ≠0 0 =0 ≤0 =0 ≥0 ≠0 4 ≤3 =0 ≥0 ≠0 ≥0 0 =0 ≤4 ≥2 =0 ≠0 3 ≥0 ≤2 =0 ≥3 ≠0 0
≤2 =0 ≥1 =0 ≠0 1 =0 ≤1 ≥2 ≠0 =0 0 ≥0 ≤5 =0 ≥1 =0 3 =0 ≤0 =0 ≥4 ≠0 4 ≤2 =0 ≥5 =0 ≠0 4 =0 ≤3 =0 ≥2 ≠0 0 =0≤2
=0 ≥1 ≠0 5
This allowed us to discover processes in CA, which have
never been observed before.
For example: a replicating loop grown from a seed
Why are our results human competitive?
Our evolved replication schemes (in 2D CA) and generic
square calculations (in 1D CA) are equal to or better than a
result that was accepted as a new scientific result at the time
when it was published in a peer-reviewed scientific journal.
(satisfying criterion B)
Our best replication scheme
Bidlo, 2016
IEEE Trans. On Evol.
Computation (in print)
Byl, 1989
Physica D: Nonlinear
Phenomena, vol. 34,
no. 1-2, pp. 295-299
Why are our results human competitive?
Our evolved replication schemes (in 2D CA) and generic square
calculations (in 1D CA) are equal to or better than a result
that was accepted as a new scientific result at the time when
it was published in a peer-reviewed scientific journal.
(satisfying criterion B)
Our best generic squaring CA
Wolfram, 2002
New Kind of Science (book),
p. 638
some of our solutions for x=5
Bidlo, 2016
IEEE Trans. On Evol.
Computation (in print)
Why are our results human competitive?
Our outcomes are publishable in its own right as a new
scientific results independently of the fact that they were
mechanically created because completely new algorithms
were discovered using our method for the problems
mentioned above, which exhibit better properties compared
to existing solutions.
(satisfying criterion D)
Published in:
http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=
&arnumber=7377086&isnumber=4358751
Why are our results human competitive?
In the author's opinion the proposed method solves a problem
of indisputable difficulty in its field (i.e. automatic evolutionary
design of multi-state cellular automata) because no
similar results have yet been published using the existing
approaches.
(satisfying criterion G)
Our experiments performed evolution of CA with up to 12 cell
states, which theoretically allows more than 6.7 x 10268 534
transition functions. Example of an evolved moving GECCO
label:
Why should this work win
We believe that the proposed method, that provided human
competitive results, can be generally applicable.
Various benchmarks we have successfully solved:
Generic squaring problem (1D)

Replicating structures (2D CA)

Pattern development problem
the Czech flag (2D CA)

Complex moving structures

Why should this work win
We believe that the proposed method, that provided
human competitive results, can be generally applicable.
Examples of other benchmarks we have solved:
A stable pattern development from a seed: the French flag

A moving surname of the author
developed from a 3-cell zygote

CA is a platform potentially suitable
for future technologies.
Thank you for your attention!