  The strange attractor represents a complex pattern of behavior in dynamic
systems. This paper introduces a strange attractor for synthetic channels in
polar coding as a result of a geometric property of density evolution that is a
polar code construction technique. First, we define a subset of synthetic
channels that are universally less reliable than the original channel. Here,
the cardinality of the attractor set is (n+2)-th Fibonacci number for the block
length N = 2n. This can be seen as a significantly large number for very long
codes. On the other hand, strange attractor can provide new achievable rates
for the finite block lengths. Secondly, it is known that polar codes can be
constructed with sub-linear complexity by the use of partial orderings. In this
study, we additionally define 1 + log2(log2 N) universal operators to reduce
the complexity. Then, these universal operators can be applied on the attractor
set to increase the number of synthetic channels that are universally less
reliable than the natural channel.
