Il triangolo di Sierpinski

Tutto, ma proprio tutto quello che avreste sempre voluto sapere sul triangolo di Sierpinski. Il frattale descritto nel 1915 da Waclaw Sierpinski esempio base di insieme auto-similare, cioè matematicamente generato da un pattern che si ripete allo stesso modo su scale diverse.

Throughout my years playing around with fractals, the Sierpinski triangle has been a consistent staple. The triangle is named after Waclaw Sierpinski and as fractals are wont the pattern appears in many places, so there are many different ways of constructing the triangle on a computer.

All of the methods are fundamentally iterative. The most obvious method is probably the triangle-in-triangle approach. We start with one triangle, and at every step we replace each triangle with 3 subtriangles.