  Topological entropy has been one of the most difficult to implement of all
the entropy-theoretic notions. This is primarily due to finite sample effects
and high-dimensionality problems. In particular, topological entropy has been
implemented in previous literature to conclude that entropy of exons is higher
than of introns, thus implying that exons are more "random" than introns. We
define a new approximation to topological entropy free from the aforementioned
difficulties. We compute its expected value and apply this definition to the
intron and exon regions of the human genome to observe that as expected, the
entropy of introns are significantly higher than that of exons. Though we
surprisingly find that introns are less random than expected: their entropy is
lower than the computed expected value. We observe the perplexing phenomena
that chromosome Y has atypically low and bi-modal entropy, possibly
corresponding to random sequences (high entropy) and sequences that posses
hidden structure or function (low entropy).
