Here’s a simple pattern of three triangles:

Three-Triangle Pattern

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Now replace each triangle in the pattern with the same pattern at a smaller scale:

Replacing triangles

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If you keep on doing this, you create what I’ll call a trigonal fractal (trigon is Greek for “triangle”):

Trigonal Fractal stage #3 (click for larger)

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Trigonal Fractal stage #4

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Trigonal Fractal stage #5

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Trigonal Fractal #6

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Trigonal Fractal #7

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Trigonal Fractal #8

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Trigonal Fractal (animated) (click for larger)

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You can use the same pattern to create different fractals by rotating the replacement patterns in different ways. I call this “rigging the trigging” and here are some of the results:

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You can also use a different seed-pattern to create the fractals:

Trigonal fractal (animated)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Trigonal fractal (anim)

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Note: The title of this incendiary intervention is of course a paronomasia on the song “Frigging in the Rigging”, also known as “Good Ship Venus” and performed by the Sex Pistols on The Great Rock ’n’ Roll Swindle (1979).