Thinking it over, I’ve decided that trircle is a much better name than ciangle:

A Sierpiński triangle

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A Sierpiński trircle, or triangle converted into a circle

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A trircle is a triangle converted into a circle; a ciangle is a circle converted into a triangle. Or another regular polygon. The trircle reminded me that circularized fractals are fungible, because the Sierpiński triangle can be converted into another regular polygon like a square or pentagon or hexagon. You can go viâ the trircle, but you don’t have to. The point is that the Sierpiński triangle has a center and points lying at some distance and some angle 0° through 360°, so you can easily adjust the points to fit inside any other regular polygon:

A Sierpiński triangle again

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A Sierpiński trare, or triangle converted into square

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A Sierpiński trentagon

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A Sierpiński trexagon

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A Sierpiński treptagon

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A Sierpiński troctogon

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Here’s an animation of the conversions:

Sierpiński triangle → square, pentagon, hexagon, heptagon, octagon (animated at ezGif)

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A Sierpiński carpet, with points lying at 0° through 360° inside a square, is similarly fungible:

A Sierpiński carpet

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A Sierpiński carpet converted into a circle

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A Sierpiński carpet converted into a triangle

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A Sierpiński carpet again

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A Sierpiński carpet converted into a pentagon

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And an animation of the carpet conversions:

Sierpiński carpet → triangle, pentagon, hexagon, heptagon, octagon (animated at ezGif)

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Finally, and fungibly, the fractal that I call the centered Sierpiński triangle:

A centered Sierpiński triangle

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A centered Sierpiński trircle, or triangle converted into a circle

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And the final animation:

Centered Sierpiński triangle → square, pentagon, hexagon, heptagon, octagon (animated at ezGif)

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