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A Calculus of Number Based on Spatial Forms - University of ...

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24<br />

Involuti<strong>on</strong>: ([A]) =A : =[(A)]<br />

:<br />

Equivalent Expressi<strong>on</strong>s Template Replacement<br />

([])<br />

<br />

A = <br />

( ([][]) )<br />

(([([][])]))<br />

A = ([][])<br />

[ ()([() ()])]<br />

[ () () () ] A = ()()<br />

[([() ()])() ] A = ()()<br />

( [][([] [])])<br />

( [] [] [] ) A = [][]<br />

([([] [])][] ) A = [][]<br />

([] )<br />

([][]) A =<br />

(([[()]][]))<br />

(([ ][])) A = <br />

(( [])) A =<br />

( ) A = <br />

Figure 4.1: Examples <str<strong>on</strong>g>of</str<strong>on</strong>g> Involuti<strong>on</strong>.

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