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submitted 4 days ago* (last edited 4 days ago) by [email protected] to c/[email protected]
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[-] [email protected] 2 points 4 days ago

If the first is only 1 triangle, I can't see how the second would be anything but 3 triangles.

[-] [email protected] 2 points 4 days ago

Three small white triangles, one black triangle and one large multicoloured triangle, I think.

[-] [email protected] 1 points 4 days ago

The second triangle is 5 on account of the black triangle on the inside and the compound triangle made up of all three smaller triangles and the fourth negative space triangle. I believe the formula for how many triangles is linear because each iteration of the fractal can be represented as scooping more negative space triangles from the existing set of triangles. Each iteration you scoop out the same number of black triangles as you had white triangles the previous iteration, creating two more white triangles for every white triangle you had before, and adding one more compound triangle.

The numbers we see though from each early iteration are as follows:

1 -> 5 -> 17 -> 53 -> 161

Which happens to conform with 3(n-1)+2

[-] [email protected] 2 points 3 days ago

If you're counting black triangles, the first is 3.

this post was submitted on 17 Sep 2024
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