These are IFSs in which the elements are laid out in the form of a regular hexagon, and the overall attractor approaches a hexagon as the number of elements approach infinity. Each element is rotated by 30° with respect to the overall figure. The first order flowsnake is the cyclohexamermonomer or Peano-Gosper curve. For each n there are cis- and trans- variants. The nth order flowsnake has 3n2 + 3n + 1elements, each of which is rotated by arctan(nsin(60)/(1+1.5n))
Source: All are independently discovered, except that the angle by which the elements of the cis 1st order flowsnake are rotated was derived from an L-system construction given in Scientific American.