We analyze a deterministic cellular automaton σ⋅=(σn:n≥0) corresponding to the zero-temperature case of Domany's stochastic Ising ferromagnet on the hexagonal lattice \documentclass[12pt]{minimal}
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$$\mathbb{N}$$
\end{document}. The state space \documentclass[12pt]{minimal}
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$$\mathcal{S}_\mathbb{H} = \left\{ { - 1, + 1} \right\}^\mathbb{H}$$
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$$\mathbb{H}$$
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$$\sigma ^0 = \left\{ {\sigma _{^x }^0 } \right\}_{x \in \mathbb{H}}$$
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$$\mathbb{H}$$
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$$\mathcal{A}$$
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$$\mathcal{B}$$
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$$\mathcal{A}$$
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$$\mathcal{B}$$
\end{document} and vice versa, and the discrete time dynamics is such that the σ⋅x's with \documentclass[12pt]{minimal}
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$${x \in \mathcal{A}}$$
\end{document} (respectively, \documentclass[12pt]{minimal}
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$$\mathcal{B}$$
\end{document}) are updated simultaneously at odd (resp., even) times, making σ⋅x agree with the majority of its three neighbors. In ref. 1 it was proved that there is a percolation transition at p=1/2 in the percolation models defined by σn, for all times n∈[1,∞]. In this paper, we study the nature of that transition and prove that the critical exponents β, ν, and η of the dependent percolation models defined by σn, n∈[1,∞], have the same values as for standard two-dimensional independent site percolation (on the triangular lattice).
