Theoretically, can mathematical equations be used to graph any picture imaginable?

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I know that quadratic formulas make parabolas, linear makes straight lines and sin, cos and tan make cool curves but after messing around with WolframAlpha and online equation graphing tools I can make really varied and weird shapes with just the right type of equation. Is it possible that there is an equation to graph a picture of the Mona Lisa? Is this how computers show draw things perhaps?

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It is technically possible, but it's very hard to create complex images like this. And you can only create linearts with this method, except if you use some type of coloring.

No, computers draw pictures on your screen, by changing the pixels on your monitor. The closest to this are vector graphics, but they still aren't the same.