A countably infinite series of 2 dimensional IFS attractors is obtained by laying out n elements in two rows of (n+1)/2 and (n-1)/2 elements respectively, with the elements rotated by 90° with respect to the overall figure. When the rows are aligned parallel to the X-axis the interval between x-coordinates is a constant, which may be set to 1, and the distance in the y-coordinates of the two rows is sqrt(n) times this.
A second countably infinite series is obtained by applying the trans technique to the first.
In both cases the attractor converges on a rectangle as the number of elements tends to infinity.
These are IFSs in which the elements are rotated by 90 degrees with respect to the overall figure, and which are laid out in a zigzag pattern. The attractor approaches a rectangle as the number of elements approaches infinity. The interval, parallel to the the long axis, between elements is constant, and the ratio of the distance between the parallel rows to this is sqrt(n):1.
The first (n=3) members are the cis-fudgeflake and tran-fudgeflake, which are also encountered, inter alia, from constructions based on elements placed on a circle, and on the edges of an alternating n,n-1 sided hexagon.
Source: All are independently discovered, although I have since found copies of the 1st order cis-fudgeflake on the web. The construction was discovered while investigating polylineopolymers (still to be written up).