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Some triangle-induced equivalence relations

**Figure 1.5:** Each triangle defines a unique successor in at least four different ways, depending on vertex-contact. Here two tree families are partially sketched for evolution from a random initial configuration.
$\begin{figure}\centering\begin{picture}(320,380) \put(0,0){\epsfysize = 380pt \epsffile{treeb.eps}} \end{picture}\end{figure}$

**Figure 1.6:** Here tree families are sketched for a particular regular lattice.
$\begin{figure}\centering\begin{picture}(320,380) \put(0,0){\epsfysize = 380pt \epsffile{treea.eps}} \end{picture}\end{figure}$

Jose Manuel Gomez Soto 2002-01-31