Video feedback mathematical model

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There are several video demonstrations for video feedback leading chaos such as [1], [2], [3], [3].

My question is how to model it?

If I have such a color matrix of

struct Color
{
    unsigned char r,g,b;
};

Color screen[1280][720];

at time $t$, then how can I calculate screen at time $t+\Delta t$?

I am looking for a model with zooming the camera enough so chaos happens.