  Shannon information (SI) and its special case, divergence, are defined for a
DNA sequence in terms of probabilities of chemical words in the sequence and
are computed for a set of complete genomes highly diverse in length and
composition. We find the following: SI (but not divergence) is inversely
proportional to sequence length for a random sequence but is length-independent
for genomes; the genomic SI is always greater and, for shorter words and longer
sequences, hundreds to thousands times greater than the SI in a random sequence
whose length and composition match those of the genome; genomic SIs appear to
have word-length dependent universal values. The universality is inferred to be
an evolution footprint of a universal mode for genome growth.
