Sir Pinski Rides Again
M. Ivette Gomes, Dínis Pestana, Pedro Pestaña · Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT) · 2011
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.