Here’s a simple pattern of three triangles:

Three-Triangle Pattern

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

Replacing triangles

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)

Trigonal Fractal stage #4

Trigonal Fractal stage #5

Trigonal Fractal #6

Trigonal Fractal #7

Trigonal Fractal #8

Trigonal Fractal (animated) (click for larger)

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:

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

Trigonal fractal (animated)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Trigonal fractal (anim)

Note: The title of this incendiary intervention is of course a paranomasia 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).