Thinking it over, I’ve decided that trircle is a much better name than ciangle:
↓
A Sierpiński trircle, or triangle converted into a circle
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
↓
A Sierpiński trare, or triangle converted into square
↓
A Sierpiński trentagon
↓
A Sierpiński trexagon
↓
A Sierpiński treptagon
↓
A Sierpiński troctogon
Here’s an animation of the conversions:
Sierpiński triangle → square, pentagon, hexagon, heptagon, octagon (animated at ezGif)
A Sierpiński carpet, with points lying at 0° through 360° inside a square, is similarly fungible:
↓
A Sierpiński carpet converted into a circle
↓
A Sierpiński carpet converted into a triangle
↓
A Sierpiński carpet again
↓
A Sierpiński carpet converted into a pentagon
↓
↓
↓
And an animation of the carpet conversions:
Sierpiński carpet → triangle, pentagon, hexagon, heptagon, octagon (animated at ezGif)
Finally, and fungibly, the fractal that I call the centered Sierpiński triangle:
A centered Sierpiński triangle
↓
A centered Sierpiński trircle, or triangle converted into a circle
↓
↓
↓
↓
↓
And the final animation:
Centered Sierpiński triangle → square, pentagon, hexagon, heptagon, octagon (animated at ezGif)
