As an example of repetition of ancestors, there is a famous pedigree that begins having significant repetition within the first few generations:  that of outlaw, Jesse JAMES.  There is even more pronounced repetition in his wife's pedigree, so the repetition is further compounded for their children:

When repetition happens in the near generations, we call it "inbreeding."  It happens so often among southerners, like Jesse & Zerelda, that it's become a cultural cliché, as in the movie,  Deliverance.

For those of you being autosomal-DNA tested (e.g., FTDNA's FamilyFinder test, 23andMe, and the Ancestry-DNA test), an examination of this table makes it very clear why At-DNA is most useful within five generations, with it's use diminishing rapidly with each additional generation.  Even at five generations, you are likely to have only 3.125% of each ancestor's genes, and by seven generation, you are likely to have less than one percent.  This is the reason my genealogical goal is not to go deeply into my ancestry — though I inadvertently have on some lines — my goal is to get all lines back eight generations.  I'll know more about myself that way, than I do by the fact that I've bumped into a connection to Charlemagne (la de dah).

The greatly diminishing percentage of one ancestor's genes in your personal genome as you go back in your pedigree is just one reason why it's so biologically insignificant to have distant illustrious ancestors.  Socially, culturally, and historically it may be very significant to you, personally, but not because you are any kind of genetic "image" of your ancestor.  It's also a cautionary as to why it's foolish to think you live on in your children.  Your genetic contribution to your descendants diminishes so rapidly, the idea that bearing children gives you "continuence" is absurd.  You do share 99.9% of your genetic endowment with other human beings; the variable part we study amounts to less than one percent of our genetic endowment.  Be more concerned that the human genome has continuence.

The table below is based on an average generation time of 30 years and uses a person born in 1950 as an example.