In this paper the concept of local languages is extended to infinite triangular arrays and ωω local languages are defined. ωω-recognizable languages of infinite triangular arrays accepted by two direction online tesselation automata are considered. Properties of these languages are studied.

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A new subclass of infinite triangular arrays called hrl-local infinite triangular arrays is introduced. We introduce infinite triangular domino systems to recognize the infinite triangular picture language. Also we introduce strictly domino testable ωω-triangular array languages.