A Feast of Fractiles

A rep-tile is a shape that can be divided into copies of itself. One of the simplest rep-tiles is the equilateral triangle, which can be divided into four copies of itself, like this:

Self-dividing equilateral triangle

If, on the other hand, the triangle is subdivided and then one of the copies is discarded, many interesting fractals can be made from this very simple shape:

Fractal triangle creating Sierpinski gasket

Triangle fractal 2

This sequence illustrates how a more complex fractal is created:

Triangle fractal 3 split image 1

Triangle fractal 3 split image 2

Triangle fractal 3 split image 3

Triangle fractal 3 split image 4

Triangle fractal 3 split image 5

Triangle fractal 3 split image 6

Triangle fractal 3 split image 7

Triangle fractal 3 split image 8

And here is the sequence in a single animated gif:

Triangle fractal 3

Triangle fractal 4

Triangle fractal 5

Triangle fractal 6

Triangle fractal 7

Triangle fractal 8

Triangle fractal 9

Triangle fractal 10

Triangle fractal 11

Triangle fractal 12

Triangle fractal 13

Triangle fractal 15

Triangle fractal 16

Triangle fractal 17

Triangle fractal 18

Triangle fractal 19

Triangle fractal 20

Triangle fractal 21

Triangle fractal 22

Triangle fractal 23

Triangle fractal 24

Triangle fractal 25

Triangle fractal 26

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