# Fylfy Fractals

An equilateral triangle is a rep-tile, because it can be tiled completely with smaller copies of itself. Here it is as a rep-4 rep-tile, tiled with four smaller copies of itself: Equilateral triangle as rep-4 rep-tile

If you divide and discard one of the sub-copies, then carry on dividing-and-discarding with the sub-copies and sub-sub-copies and sub-sub-sub-copies, you get the fractal seen below. Alas, it’s not a very attractive or interesting fractal:  Stage #2 Stage #3 Stage #4 Stage #5 Stage #6 Stage #7 Stage #8 Stage #9 You can create more attractive and interesting fractals by rotating the sub-triangles clockwise or anticlockwise. Here are some examples:        Now try dividing a square into four right triangles, then turning each of the four triangles into a divide-and-discard fractal. The resulting four-fractal shape is variously called a swastika, a gammadion, a cross cramponnée, a Hakenkreuz and a fylfot. I’m calling it a fylfy fractal: Divide-and-discard fractals in the four triangles of a divided square stage #1 Fylfy fractal #2 Fylfy fractal #3 Fylfy fractal #4 Fylfy fractal #5 Fylfy fractal #6 Fylfy fractal #7 Fylfy fractal #8 Fylfy fractal (animated)

Finally, you can adjust the fylfy fractals so that each point in the square becomes the equivalent point in a circle:                  This site uses Akismet to reduce spam. Learn how your comment data is processed.