It basically using the fact that fractal is self similar. So picking one function (that scales whole triangle to one of the one thirds) and transforming single point on a fractal into a new point also gets you a point on the fractal.
If you repeat this process many times you get a lot of points of the fractal.
You can even start the process at any point and it will "get attracted" to the fractal.
That's why fractals are called strange attractors.
https://en.m.wikipedia.org/wiki/Sierpi%C5%84ski_triangle
It basically using the fact that fractal is self similar. So picking one function (that scales whole triangle to one of the one thirds) and transforming single point on a fractal into a new point also gets you a point on the fractal.
If you repeat this process many times you get a lot of points of the fractal.
You can even start the process at any point and it will "get attracted" to the fractal.
That's why fractals are called strange attractors.