There are IFSs with c3-symmetry, in which the elements are laid out in the form of a modified hexagon. The overall attractor approaches a hexagon as the number of elements approaches infinity.
These can be constructing by taking the corresponding flowsnake, and placing elements at the vertices and centres of the elements of the flowsnake. However they are more conveniently constructing by taking rectangular section, of 3n+3 × 2n+3 units, and therefore consisting of alternating rows of 3n+3 and 3n+2 elements, of a hexagonal grid, and to add additional rows above and below this rectangle, each row being 3 elements shorter than the preceding.
For each n there are 0°- and 60°- variants. The nth order starflake has 9n2 + 15n + 7elements. Each element is rotated by arctan(sin(60)/(2.5+3n)).
Source: Independently discovered. No other source known.