Circus Trix

Here’s a trix, or triangle divided into six smaller triangles:

Trix, or triangle divided into six smaller triangles


Now each sub-triangle becomes a trix in its turn:

Trix stage #2


And again:

Trix #3


Trix #4


Trix #5


Trix divisions (animated)


Now try dividing the trix and discarding sub-triangles, then repeating the process. A fractal appears:

Trix fractal #1


Trix fractal #2


Trix fractal #3


Trix fractal #4


Trix fractal #5


Trix fractal #6


Trix fractal #7


Trix fractal (animated)


But what happens if you delay the discarding, first dividing the trix completely into sub-triangles, then dividing completely again? You get a more attractive and symmetrical fractal, like this:

Trix fractal (delayed discard)


And it’s easy to convert the triangle into a circle, creating a fractal like this:

Delayed-discard trix fractal converted into circle


Delayed-discard trix fractal to circular fractal (animated)


Now a trix fractal that looks like a hawk-god:

Trix hawk-god #1


Trix hawk-god #2


Trix hawk-god #3


Trix hawk-god #4


Trix hawk-god #5


Trix hawk-god #6


Trix hawk-god #7


Trix hawk-god (animated)


Trix hawk-god converted to circle


Trix hawk-god to circle (animated)


If you delay the discard, you get this:

Trix hawk-god circle (delayed discard)


And here are more delayed-discard trix fractals:







Various circular trix-fractals (animated)


Post-Performative Post-Scriptum

In Latin, circus means “ring, circle” — the English word “circle” is actually from the Latin diminutive circulus, meaning “little circle”.

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