Sierpinski Relative Frieze Demonstrations

My cross-stitch embroidery "Sierpinski Relative Friezes" was part of the Mathematical Art Exhibit at the January 2024 Joint Mathematics Meeting in San Francisco, California. This piece was inspired by Tara Taylor's Bridges 2018 article that demonstrated how the convex hulls of symmetric Sierpinski relative fractals can be tiled together to form frieze patterns.

The following videos illustrate the various symmetries found in each of the four frieze patterns: translations (T), rotations by 180° (R), vertical reflections (V), and glide reflections (G).

TRVG in a frieze pattern constructed using Sierpinski Relative 111.

 

TV in a frieze pattern constructed using Sierpinski Relative 214.

 

TRVG in a frieze pattern constructed using Sierpinski Relative 412.

 

TV in a frieze pattern constructed using Sierpinski Relative 313.

 

Credits: Videos made using Manim Community Edition