Dimensions of fractals related to languages defined by tagged strings in complete genomes

摘要

A representation of frequency of strings of length K in complete genomes ofmany organisms in a square has led to seemingly self-similar patterns when Kincreases. These patterns are caused by under-represented strings with acertain "tag"-string and they define some fractals when K tends to infinite.The Box and Hausdorff dimensions of the limit set are discussed. Although themethod proposed by Mauldin and Williams to calculate Box and Hausdorffdimension is valid in our case, a different and simpler method is proposed inthis paper.