# 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:

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