If the modifications of the grouped element technique are applied to one of the order 5 asymmetric metasymmetric tiles, even though it has no symmetries, a set of 32 attractors, including the original one, is found, all of which have a similarity dimension of 2. 8 of these generate 6 partial postcomposition derivatives of the symmetric and demisymmetric tiles, and one is disconnected, leaving 23 novel tiles.
Eight of these tiles have a fairly compact appearance, but 4 of them are partial postcomposition derivatives of the demisymmetric tiles. The remaining 4 are shown below.
Four copies of these tiles combine to make a symmetric tile, so tilings of these tiles have a multiple of four copies in the unit cell. (Dissecting one of the four copies replaces one copy by five, so dissection doesn't result in exceptions to this rule.)
© 2015, 2016 Stewart R. Hinsley