Here’s a simple fractal created by dividing an equilateral triangle into smaller equilateral triangles, then discarding (and rotating) some of those sub-triangles, then doing the same to the sub-triangles:

Fractangle (triangle-fractal) (stage 1)

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Fractangle #2

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Fractangle #3

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Fractangle #4

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Fractangle #5

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Fractangle #6

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Fractangle #7

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Fractangle #8

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Fractangle #9

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Fractangle (animated)

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I’ve used the same fractangle to create this shape, which is variously known as a swastika (from Sanskrit svasti, “good luck, well-being”), a gammadion (four Greek Γs arranged in a circle) or a fylfot (from the shape being used to “fill the foot” of a stained glass window in Christian churches):

Trifylfot

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Because it’s a fylfot created ultimately from a triangle, I’m calling it a trifylfot (TRIFF-ill-fot). Here’s how you make it:

Trifylfot (stage 1)

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Trifylfot #2

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Trifylfot #3

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Trifylfot #4

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Trifylfot #5

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Trifylfot #6

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Trifylfot #7

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Trifylfot #8

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Trifylfot #9

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Trifylfot (animated)

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And here are more trifylfots created from various forms of fractangle:

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Elsewhere other-accessible

• Fractangular Frolics — more on fractals from triangles