Two-dimensional repetitive symmetry patterns

(This is a work in progess...) 

The Four Fundamental Features

  • wonders:  repeated without reflection. not explained by gyrations, mirrors or miracles
  • gyrations: rotational symmetry
  • kaleidoscopes:  mirror lines
  • miracles: mirrorless crossing

Conway Cost$

\large\color{blue}{\bf{\circ}}: 2
\large\color{blue}{\bf{N}}: \frac{N-1}{N}
\large\color{blue}{\bf{\infty}}: 1
\large\color{red}{\bf{\ast}}: 1
\large\color{red}{\bf{\times}}: 1
\large\color{red}{\bf{N}}: \frac{N-1}{2N}
\large\color{red}{\bf{\infty}}: \frac{1}{2}

Total cost of a plane (repeating) symmetry pattern is 2

17 planar symmetry possibilities:

                                       \large{\begin{array}{cccccc}\color{red}{632}&\color{red}{442}&\color{red}{333}&\color{red}{2222}&\color{red}{*} \\&&&\color{blue}{2}\color{red}{*22}&\\&&&&\color{red}{\ast\times}\\&\color{blue}{4}\color{red}{*2}&\color{blue}{3}\color{red}{*3}&\color{blue}{22}\color{red}{*}&\\&&&&\color{red}{\times\times}\\&&&\color{blue}{22}\color{red}{\times}&\\\color{blue}{632}&\color{blue}{442}&\color{blue}{333}&\color{blue}{2222}&\color{blue}{\circ}\end{array}}

\color{red}{*632}

\color{red}{*442}


\color{red}{*333}

\color{red}{*2222}

\color{red}{**}

\color{blue}{2}\color{red}{*22}

\color{blue}{4}\color{red}{*2}

\color{blue}{3}\color{red}{*3}

\color{blue}{22}\color{red}{*}

\color{red}{\ast\times}

\color{red}{\times\times}

\color{blue}{22}\color{red}{\times}

\color{blue}{632}

\color{blue}{442}

\color{blue}{333}

\color{blue}{2222}

\color{blue}{o}

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