Here is an equilateral triangle divided into nine smaller equilateral triangles:

Rep-9 equilateral triangle

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The triangle is a rep-tile — it’s tiled with repeating copies of itself. In this case, it’s a rep-9 triangle. Each of the nine smaller triangles can obviously be divided in their turn:

Rep-81 equilateral triangle

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Rep-729 equilateral triangle

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Rep-729 equilateral triangle again

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Rep-6561 equilateral triangle

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Rep-9 triangle repeatedly subdividing (animated)

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How try trimming the original rep-9 triangle, picking one of the trimmings, and repeating in finer detail. If you choose six triangles in this pattern, you can create a symmetrical braided fractal:

Triangular fractal stage 1

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Triangular fractal #2

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Triangular fractal #3

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Triangular fractal #3 (cleaning up)

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Triangular fractal #3 (cleaning up more)

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Triangular fractal #4

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Triangular fractal #5

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Triangular fractal #6

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Triangular fractal (animated)

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But this fractal using a three-triangle trim-picking isn’t symmetrical:

Trim-picking #1

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Trim-picking #2

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Trim-picking #3

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Trim-picking #4

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Trim-picking #5

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To make it symmetric, you have to delay the trim, using the full rep-9 trim for the first stage:

Delayed trim-picking #1

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Delayed trim-picking #2

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Delayed trim-picking #3

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Delayed trim-picking #4

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Delayed trim-picking #5

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Delayed trim-picking #6 (with first two stages as rep-9)

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Delayed trim-picking (animated)

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Here are some more delayed trim-pickings used to created symmetrical patterns:

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