search documentation about player who move in a grid

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i'm searching documentation about grid who give the illusion that the player move.

I have found a lot of article about create a grid and move a player in a static grid but not about a "moving grid".

By moving grid : i wonder a grid who delete and add line and column each time the player move in a direction, so it give the illusion that the player move on this grid.

i could do alone but i have an interrogation for how to translate the data grid each time i'm add or delete line or column in my grid. 

second interrogation, i move my player on for example grid[3][5] but in the same time my grid move so grid[3][5] become grid[3][6] (vertical movement) how to make this ? 

thanks for your help.


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