can every object be represented mathematically?

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I was just wondering if all 2D/3D objects/images/shapes could be represented by equations. For example, SpongeBob 2D curve and many more. How should I approach, as in, some theories that already exist? Perhaps, It would be of a great help if I get to hear your incredibly usable points of view!

The REAL QUESTION is:

how can I develop equation all descriptions of some pictures I have in mind?