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So, have a seat. Put your feet up. This may take some time. Can I get you some tea? Earl Grey? You got it.
Okay. How do I want to do this? He did so much. It’s hard to just dive in. You know? You pick a spot to go from, but soon you have to back up and and go over this or that item, and you get done with that only to see that you have to back up some more. So if you feel like I’m off to the side of the tale half the time, well, this is why. Just bear with me, and we’ll get to the end in good time. Okay?
Okay. Let’s see….
Source: Short Words to Explain Relativity
Constructing the Sierpinski triangle
Throughout my years playing around with fractals, the Sierpinski triangle has been a consistent staple. The triangle is named after Wacław Sierpiński 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 sub triangles: