Mixing due to cutting-and-shuffling is studied at a fundamental level using 2D mappings known as Piecewise Isometries (PWI) which can create beautiful mixing patterns. The PWI studied here splits a hemispherical shell (HS) into four curved triangular pieces that are rearranged to make a shuffled HS. Applying the PWI repeatedly...
A fractal is created by a Piecewise Isometry (PWI) which cuts a 2D object into pieces and rearranges those pieces to recreate the original object in a scrambled form. The PWI studied here splits a hemispherical shell into four pieces along cutting lines and rearranges them into a shuffled hemisphere....