The Sierpinski triangle is one such fractal. It is constructed by taking (surprise!) a triangle, splitting it into four equal parts, and removing the central section. Then, for each smaller triangle, you do the same.
Using a bit of mathematical know-how, it’s possible to prove that the Sierpinski triangle has a dimension of log23 – roughly 1.58. quantum physics books quantum physics equations principles of quantum physics
Now, fractals are all very well in the world of math, where infinite limits and abstract logic can replace the laws of physics, but in the real world, there’s a limit to how small things can get. So the team looked at what would happen if they built a real-life Sierpinski triangle that was fractal all the way down to the level of individual electrons. quantum physics books quantum physics equations principles of quantum physics
First, they constructed a frame made from carbon monoxide particles. Electrons were then placed in this atomic “muffin tin” in the shape of the Sierpinski triangle.