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this post was submitted on 14 Sep 2024
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Exactly three times as many? Do you count all surfaces that form triangles or only the white ones?
If I understand where this us going, the additional triangles will all be of the small white variety to hit the target of 3x triangle increase. If we consider negative space triangles and composite triangles, the next phase of the fractal will probably have more than 3x the triangles but that math is hard and I don't have a notebook
Current shape x3, start with triangle > Triforce > Triforce of Triforces and so on
Looking at the image from here in my bed, it looks like with each iteration, you get 3x as many white triangles, and 3x+1 as many black triangles between white triangles as there were before. At iteration 1, you have 1 white triangle and 0 black triangles.
I'm too lazy to double check.