this post was submitted on 17 Sep 2024
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The rule is 3x +2
The first isn’t 5x, it still follows the same rule.
I never said they did, I was explaining how the rule would apply to anything, the first iteration is never 5x…
What a fucked up way to explain a simple thing, while making yourself wrong at the same time… while attempting to call someone else out… yikes…
Here, maybe some pictures will get it through your thick skull.
One triangle:
Five triangles:
A triangle made into a tri-force equals five times as many triangles.
From there, it becomes x3+2 (Ie: what my original comment, which you failed to read, said.)
1 -> 5 -> 17
If the first is only 1 triangle, I can't see how the second would be anything but 3 triangles.
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
If you're counting black triangles, the first is 3.