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The last of four short articles on mirror symmetric tiles. This is another of Ortwin Schenker's ideas.  The sheep's head and anchor are from Bob Nungester's treasure trove of computational shapes.   The anchor is composed of a stopcock and two bowties (below, far right): Arnaud  Chéritat  was the first to find a periodic tiling (below left).  I noticed it could be broken down into a smaller component  comprised of two sheep's heads and one anchor : The example below shows all possible legitimate configurations when combining two of these motifs.  It can be thought of as a single polygon, as it does not use reflections: Many periodic tilings are possible; two examples below: And another with a tree motif: Here are two attempts of a hexagon without any gaps.  The motifs are still intact although less obvious: Some familiar shapes disguised as voids (highlighted in white): These drawings were created using the latest stable version of Arnaud Ché...

Continuing on the theme of symmetric figures, Ortwin Schenker suggested combining a Mystic (two Spectres) with a rotor: both are non-tilers.  Arnaud Chéritat was the first to respond with a periodic tiling.  He used a motif of three Mystics and one rotor.  Gaps are filled with single rotors: A cut-down version of Arnaud's motif can be used to create more complex periodic tilings.  The square unit can be of any size and with different arrangements: There are eight different combinations of the 'chair' tromino: Any one of these can be assembled to produce a nonperiodic tiling using a substitution rule: A beautiful flower motif: This simple motif produces an attractive spiral: These drawings were created using the latest stable version of Arnaud Chéritat's applet: https://www.math.univ-toulouse.fr/~cheritat/AppletsDivers/Monotile/generic/v4.3/