How would I go about creating shapes on a graph?

Question

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I've been building shapes using piece wise functions however, for more complexed shapes and curves, I've been told to use parametric equations or multivariable equations. I want to know how to create certain unique curves as well as easy methods for creating polygons on a graph. I want to understand easier methods for creating say, shapes like the batman symbol without having to use tedious piece wise functions and instead find a way to create a single equation like this image here.

Answer 1

wow! I would love to know how interesting shapes can be created on graph, but I used to know that plotting $(x^2+y^2-1)^3 = x^2y^3$ gives us a love shape. for something that looks much as atom but when zoomed out looks like whatsapp default chat wallpaper plot $sin(x^2+y^2) = cos(xy)$.
but I feel that plotting specific interesting shapes like the Batman symbols would give rough polynomial or complex parametric stuff