Flowsnake or Gosper Teardrops

There are 6 distinct attractors (with the 6 possible orientations of the central element) with all 6 elements of the outer ring of a flowsnake packed into a single position. However only two of these are connected.

The IFSs are

{ p → ap; p → ap + 1; p → e^iπ/3ap + 1; p → e^2iπ/3ap + 1; p → e^3iπ/3ap + 1; p → e^4iπ/3ap + 1;p → e^5iπ/3ap + 1}

{ p → e^5iπ/3ap; p → ap + 1; p → e^iπ/3ap + 1; p → e^2iπ/3ap + 1; p → e^3iπ/3ap + 1; p → e^4iπ/3ap + 1;p → e^5iπ/3ap + 1}

There are also equivalent trans-heptahextals, with IFSs

{ p → ap; p → ap + 1; p → e^iπ/3ap + 1; p → e^2iπ/3ap + 1; p → e^3iπ/3ap + 1; p → e^4iπ/3ap + 1;p → e^5iπ/3ap + 1}

{ p → e^5iπ/3ap; p → ap + 1; p → e^iπ/3ap + 1; p → e^2iπ/3ap + 1; p → e^3iπ/3ap + 1; p → e^4iπ/3ap + 1;p → e^5iπ/3ap + 1}

They both tile with plane with six copies in the unit cell, with the tiling vectors as for the parent flowsnakes.

For each of these there 7 order 13 partial postcomposition derivatives, but only three or four of each set are connected. These tile the plane with 12 copies in the unit cell.

Source: Indepedent discovery (William Gosper and myself discovered teardrops as a class at about the same time).

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