  The generator matrices of polar codes and Reed-Muller codes are obtained by
selecting rows from the Kronecker product of a lower-triangular binary square
matrix. For polar codes, the selection is based on the Bhattacharyya parameter
of the row, which is closely related to the error probability of the
corresponding input bit under sequential decoding. For Reed-Muller codes, the
selection is based on the Hamming weight of the row. This work investigates the
properties of the index sets pointing to those rows in the infinite blocklength
limit. In particular, the Lebesgue measure, the Hausdorff dimension, and the
self-similarity of these sets will be discussed. It is shown that these index
sets have several properties that are common to fractals.
