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# User:Jon Awbrey/Figures and Tables 17

## Peirce Duality as Group Symmetry

### Index Order

#### PNG

 ${\displaystyle {\text{Peirce Duality as Group Symmetry}}}$

#### WIKI + JPG

 ${\displaystyle f}$ ${\displaystyle \gamma }$ ${\displaystyle 1\gamma }$ ${\displaystyle t\gamma }$ ${\displaystyle {\begin{matrix}f_{0}\\[10pt]{\text{false}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{1}\\[10pt]{\text{neither}}~x~{\text{nor}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{2}\\[10pt]y~{\text{and not}}~x\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{3}\\[10pt]{\text{not}}~x\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{4}\\[10pt]x~{\text{and not}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{5}\\[10pt]{\text{not}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{6}\\[10pt]x~{\text{not equal to}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{7}\\[10pt]{\text{not both}}~x~{\text{and}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{8}\\[10pt]x~{\text{and}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{9}\\[10pt]x~{\text{equal to}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{10}\\[10pt]y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{11}\\[10pt]{\text{if}}~x~{\text{then}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{12}\\[10pt]x\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{13}\\[10pt]{\text{if}}~y~{\text{then}}~x\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{14}\\[10pt]x~{\text{or}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{15}\\[10pt]{\text{true}}\end{matrix}}}$ ${\displaystyle {\text{Fixed Point Total}}}$ ${\displaystyle 16}$ ${\displaystyle 4}$

### Orbit Order

#### PNG

 ${\displaystyle {\text{Peirce Duality as Group Symmetry}}~{\stackrel {_{\bullet }}{}}~{\text{Orbit Order}}}$

#### WIKI + JPG

 ${\displaystyle f}$ ${\displaystyle \gamma }$ ${\displaystyle 1\gamma }$ ${\displaystyle t\gamma }$ ${\displaystyle {\begin{matrix}f_{12}\\[10pt]x\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{10}\\[10pt]y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{3}\\[10pt]{\text{not}}~x\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{5}\\[10pt]{\text{not}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{15}\\[10pt]{\text{true}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{0}\\[10pt]{\text{false}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{7}\\[10pt]{\text{not both}}~x~{\text{and}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{1}\\[10pt]{\text{neither}}~x~{\text{nor}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{2}\\[10pt]y~{\text{and not}}~x\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{11}\\[10pt]{\text{if}}~x~{\text{then}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{4}\\[10pt]x~{\text{and not}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{13}\\[10pt]{\text{if}}~y~{\text{then}}~x\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{8}\\[10pt]x~{\text{and}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{14}\\[10pt]x~{\text{or}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{6}\\[10pt]x~{\text{not equal to}}~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{9}\\[10pt]x~{\text{equal to}}~y\end{matrix}}}$ ${\displaystyle {\text{Fixed Point Total}}}$ ${\displaystyle 16}$ ${\displaystyle 4}$

## HTML + JPG

### Ex → En

${\displaystyle {\text{Boolean Functions, Existential Graphs, Entitative Graphs}}}$
${\displaystyle {\text{Boolean Function}}}$ ${\displaystyle {\text{Existential Graph}}}$ ${\displaystyle {\text{Entitative Graph}}}$
${\displaystyle f_{0}}$
${\displaystyle f_{1}}$
${\displaystyle f_{2}}$
${\displaystyle f_{3}}$
${\displaystyle f_{4}}$
${\displaystyle f_{5}}$
${\displaystyle f_{6}}$
${\displaystyle f_{7}}$
${\displaystyle f_{8}}$
${\displaystyle f_{9}}$
${\displaystyle f_{10}}$
${\displaystyle f_{11}}$
${\displaystyle f_{12}}$
${\displaystyle f_{13}}$
${\displaystyle f_{14}}$
${\displaystyle f_{15}}$

### En → Ex

${\displaystyle {\text{Boolean Functions on Two Variables}}}$
${\displaystyle {\text{Boolean Function}}}$ ${\displaystyle {\text{Entitative Graph}}}$ ${\displaystyle {\text{Existential Graph}}}$
${\displaystyle f_{0}}$

${\displaystyle {\text{false}}}$

${\displaystyle {\text{false}}}$

${\displaystyle {\text{false}}}$
${\displaystyle f_{1}}$

${\displaystyle {\text{neither}}~x~{\text{nor}}~y}$

${\displaystyle \lnot (x\lor y)}$

${\displaystyle \lnot x\land \lnot y}$
${\displaystyle f_{2}}$

${\displaystyle y~{\text{and not}}~x}$

${\displaystyle \lnot x\land y}$

${\displaystyle \lnot x\land y}$
${\displaystyle f_{3}}$

${\displaystyle {\text{not}}~x}$

${\displaystyle \lnot x}$

${\displaystyle \lnot x}$
${\displaystyle f_{4}}$

${\displaystyle x~{\text{and not}}~y}$

${\displaystyle x\land \lnot y}$

${\displaystyle x\land \lnot y}$
${\displaystyle f_{5}}$

${\displaystyle {\text{not}}~y}$

${\displaystyle \lnot y}$

${\displaystyle \lnot y}$
${\displaystyle f_{6}}$

${\displaystyle x~{\text{not equal to}}~y}$

${\displaystyle x\neq y}$

${\displaystyle x\neq y}$
${\displaystyle f_{7}}$

${\displaystyle {\text{not both}}~x~{\text{and}}~y}$

${\displaystyle \lnot x\lor \lnot y}$

${\displaystyle \lnot (x\land y)}$
${\displaystyle f_{8}}$

${\displaystyle x~{\text{and}}~y}$

${\displaystyle x\land y}$

${\displaystyle x\land y}$
${\displaystyle f_{9}}$

${\displaystyle x~{\text{equal to}}~y}$

${\displaystyle x=y}$

${\displaystyle x=y}$
${\displaystyle f_{10}}$

${\displaystyle y}$

${\displaystyle y}$

${\displaystyle y}$
${\displaystyle f_{11}}$

${\displaystyle {\text{if}}~x~{\text{then}}~y}$

${\displaystyle x\Rightarrow y}$

${\displaystyle x\Rightarrow y}$
${\displaystyle f_{12}}$

${\displaystyle x}$

${\displaystyle x}$

${\displaystyle x}$
${\displaystyle f_{13}}$

${\displaystyle {\text{if}}~y~{\text{then}}~x}$

${\displaystyle x\Leftarrow y}$

${\displaystyle x\Leftarrow y}$
${\displaystyle f_{14}}$

${\displaystyle x~{\text{or}}~y}$

${\displaystyle x\lor y}$

${\displaystyle x\lor y}$
${\displaystyle f_{15}}$

${\displaystyle {\text{true}}}$

${\displaystyle {\text{true}}}$

${\displaystyle {\text{true}}}$

## Table A3. Ef Expanded Over Differential Features

 ${\displaystyle f}$ ${\displaystyle {\begin{matrix}\mathrm {T} _{11}f\\\mathrm {E} f|_{\mathrm {d} x~\mathrm {d} y}\end{matrix}}}$ ${\displaystyle {\begin{matrix}\mathrm {T} _{10}f\\\mathrm {E} f|_{\mathrm {d} x{\texttt {(}}\mathrm {d} y{\texttt {)}}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}\mathrm {T} _{01}f\\\mathrm {E} f|_{{\texttt {(}}\mathrm {d} x{\texttt {)}}\mathrm {d} y}\end{matrix}}}$ ${\displaystyle {\begin{matrix}\mathrm {T} _{00}f\\\mathrm {E} f|_{{\texttt {(}}\mathrm {d} x{\texttt {)(}}\mathrm {d} y{\texttt {)}}}\end{matrix}}}$ ${\displaystyle f_{0}}$ ${\displaystyle 0}$ ${\displaystyle 0}$ ${\displaystyle 0}$ ${\displaystyle 0}$ ${\displaystyle 0}$ ${\displaystyle {\begin{matrix}f_{1}\\f_{2}\\f_{4}\\f_{8}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}x{\texttt {)(}}y{\texttt {)}}\\{\texttt {(}}x{\texttt {)}}~~y~~\\~~x~~{\texttt {(}}y{\texttt {)}}\\x~~~~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}x~~~~y\\~~x~~{\texttt {(}}y{\texttt {)}}\\{\texttt {(}}x{\texttt {)}}~~y~~\\{\texttt {(}}x{\texttt {)(}}y{\texttt {)}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}~~x~~{\texttt {(}}y{\texttt {)}}\\x~~~~y\\{\texttt {(}}x{\texttt {)(}}y{\texttt {)}}\\{\texttt {(}}x{\texttt {)}}~~y~~\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}x{\texttt {)}}~~y~~\\{\texttt {(}}x{\texttt {)(}}y{\texttt {)}}\\x~~~~y\\~~x~~{\texttt {(}}y{\texttt {)}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}x{\texttt {)(}}y{\texttt {)}}\\{\texttt {(}}x{\texttt {)}}~~y~~\\~~x~~{\texttt {(}}y{\texttt {)}}\\x~~~~y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{3}\\f_{12}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}x{\texttt {)}}\\x\end{matrix}}}$ ${\displaystyle {\begin{matrix}x\\{\texttt {(}}x{\texttt {)}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}x\\{\texttt {(}}x{\texttt {)}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}x{\texttt {)}}\\x\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}x{\texttt {)}}\\x\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{6}\\f_{9}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}x{\texttt {,}}~~y{\texttt {)}}\\{\texttt {((}}x{\texttt {,}}~~y{\texttt {))}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}x{\texttt {,}}~~y{\texttt {)}}\\{\texttt {((}}x{\texttt {,}}~~y{\texttt {))}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {((}}x{\texttt {,}}~~y{\texttt {))}}\\{\texttt {(}}x{\texttt {,}}~~y{\texttt {)}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {((}}x{\texttt {,}}~~y{\texttt {))}}\\{\texttt {(}}x{\texttt {,}}~~y{\texttt {)}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}x{\texttt {,}}~~y{\texttt {)}}\\{\texttt {((}}x{\texttt {,}}~~y{\texttt {))}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{5}\\f_{10}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}y{\texttt {)}}\\y\end{matrix}}}$ ${\displaystyle {\begin{matrix}y\\{\texttt {(}}y{\texttt {)}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}y{\texttt {)}}\\y\end{matrix}}}$ ${\displaystyle {\begin{matrix}y\\{\texttt {(}}y{\texttt {)}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}y{\texttt {)}}\\y\end{matrix}}}$ ${\displaystyle {\begin{matrix}f_{7}\\f_{11}\\f_{13}\\f_{14}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}~~x~~~~y~~{\texttt {)}}\\{\texttt {(}}~~x~~{\texttt {(}}y{\texttt {))}}\\{\texttt {((}}x{\texttt {)}}~~y~~{\texttt {)}}\\{\texttt {((}}x{\texttt {)(}}y{\texttt {))}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {((}}x{\texttt {)(}}y{\texttt {))}}\\{\texttt {((}}x{\texttt {)}}~~y~~{\texttt {)}}\\{\texttt {(}}~~x~~{\texttt {(}}y{\texttt {))}}\\{\texttt {(}}~~x~~~~y~~{\texttt {)}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {((}}x{\texttt {)}}~~y~~{\texttt {)}}\\{\texttt {((}}x{\texttt {)(}}y{\texttt {))}}\\{\texttt {(}}~~x~~~~y~~{\texttt {)}}\\{\texttt {(}}~~x~~{\texttt {(}}y{\texttt {))}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}~~x~~{\texttt {(}}y{\texttt {))}}\\{\texttt {(}}~~x~~~~y~~{\texttt {)}}\\{\texttt {((}}x{\texttt {)(}}y{\texttt {))}}\\{\texttt {((}}x{\texttt {)}}~~y~~{\texttt {)}}\end{matrix}}}$ ${\displaystyle {\begin{matrix}{\texttt {(}}~~x~~~~y~~{\texttt {)}}\\{\texttt {(}}~~x~~{\texttt {(}}y{\texttt {))}}\\{\texttt {((}}x{\texttt {)}}~~y~~{\texttt {)}}\\{\texttt {((}}x{\texttt {)(}}y{\texttt {))}}\end{matrix}}}$ ${\displaystyle f_{15}}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle 1}$ ${\displaystyle {\text{Fixed Point Total}}}$ ${\displaystyle 4}$ ${\displaystyle 4}$ ${\displaystyle 4}$ ${\displaystyle 16}$