Wilkinson’s polynomial example of p. 23:

Showing that a tiny perturbation can mess things up royally (sensitive dependence on initial conditions).

Wilkinson[z_]:=(∏_(i=1)^20)(z-i)

Roots[Wilkinson[z]==0,z]

WilkinsonHat[z_]:=Wilkinson[z]+10^(-7)z^19

roots=N[Roots[WilkinsonHat[z]==0,z]]

rootsList=Apply[List,roots]

roots=Map[Part[#,2]&,rootsList]
Re[roots]
Im[roots]

ListPlot[Transpose[{Re[roots],Im[roots]}]]