We Can Circ It Out

It’s a pretty little problem to convert this triangular fractal…

Sierpiński triangle (Wikipedia)

…into its circular equivalent:

Sierpiński triangle as circle

Sierpiński triangle to circle (animated)

But once you’ve circ’d it out, as it were, you can easily adapt the technique to fractals based on other polygons:

T-square fractal (Wikipedia)

T-square fractal as circle

T-square fractal to circle (animated)

Elsewhere other-accessible…

Dilating the Delta — more on converting polygonic fractals to circles…

Bent Pent

This is a beautiful and interesting shape, reminiscent of a piece of jewellery:

Pentagons in a ring

I came across it in this tricky little word-puzzle:

Word puzzle using pentagon-ring

Here’s a printable version of the puzzle:

Printable puzzle

Let’s try placing some other regular polygons with s sides around regular polygons with s*2 sides:

Hexagonal ring of triangles

Octagonal ring of squares

Decagonal ring of pentagons

Dodecagonal ring of hexagons

Only regular pentagons fit perfectly, edge-to-edge, around a regular decagon. But all these polygonal-rings can be used to create interesting and beautiful fractals, as I hope to show in a future post.