<s>
The	O
Ulam	O
–	O
Warburton	O
cellular	O
automaton	O
(	O
UWCA	O
)	O
is	O
a	O
2-dimensional	O
fractal	B-Application
pattern	O
that	O
grows	O
on	O
a	O
regular	O
grid	O
of	O
cells	O
consisting	O
of	O
squares	O
.	O
</s>
<s>
This	O
surjective	B-Algorithm
property	O
emerges	O
from	O
the	O
simple	O
rule	O
of	O
growth	O
–	O
a	O
new	O
cell	O
is	O
born	O
if	O
it	O
shares	O
only	O
one-edge	O
with	O
an	O
existing	O
ON	O
cell	O
-	O
the	O
process	O
appears	O
disorderly	O
and	O
is	O
modeled	O
by	O
functions	O
involving	O
but	O
within	O
the	O
chaos	O
there	O
is	O
regularity	O
.	O
</s>
<s>
The	O
Hexagonal-Ulam	O
–	O
Warburton	O
cellular	O
automaton	O
(	O
Hex-UWCA	O
)	O
is	O
a	O
2-dimensional	O
fractal	B-Application
pattern	O
that	O
grows	O
on	O
a	O
regular	O
grid	O
of	O
cells	O
consisting	O
of	O
hexagons	O
.	O
</s>
<s>
The	O
resulting	O
structure	O
has	O
a	O
fractal-like	O
appearance	O
.	O
</s>
<s>
A	O
subtraction	O
game	O
called	O
LIM	O
,	O
in	O
which	O
two	O
players	O
alternately	O
modify	O
three	O
piles	O
of	O
tokens	O
by	O
taking	O
an	O
equal	O
amount	O
of	O
tokens	O
from	O
two	O
of	O
the	O
piles	O
and	O
adding	O
the	O
same	O
amount	O
to	O
the	O
third	O
pile	O
,	O
has	O
a	O
set	O
of	O
winning	O
positions	O
that	O
can	O
be	O
described	O
using	O
the	O
Ulam	B-Algorithm
–	I-Algorithm
Warburton	I-Algorithm
automaton	I-Algorithm
.	O
</s>
