Sir Pinski Rides Again

The iterative procedure of removing “almost everything” from a triangle ultimately leading to the Sierpinski's gasket S is well-known. But what is in fact left when almost everything has been taken out? Using the Sir Pinski's game described by Schroeder [4], we identify two dual sets of invariant points in this exquisite game, and from these we identify points left over in Sierpinski gasket. Our discussion also shows that the chaos game does not generate the Sierpinski gasket. It generates an approximation or, at most, a subset of S