the Sierpinski triangle is a fractal image, which is self similar: Meaning that any small portion of it will look the same as a larger portion down to the microscopic level.
I have had a soft spot for fractals all my life, since my first research project was using mangelbrot fractals to model wire roughness. Fractals are used a lot by Scientists and Mathematicians to model different natural phenomena as so many, from broccoli to lightning to blood vessels can be described by the principle.
So, I decided that the Sierpinsky triangle is a beautiful fractal for introducing to kids, because it can be easily scaled up and scaled down. After a couple of iterations, Anjali caught on and did it all by herself, marking and measuring the triangles.