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I want to generate a simulator for behavior that is displayed via charts.

The end result will be a behavior that follows some formula like

f = sin(x)

which will output a sin behavior.

However, I want to create my own "handmade" graphs to simulate different scenarios. Is there a tool online where I can draw a graph and it will output its formula (in whatever complexity or approximation)

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Yes and no.

There are tools which allow you to design so-called free-form curves obtained by (polynomial or piecewise polynomial) interpolation or by approximation. These will be defined on a finite domain.

https://www.ibiblio.org/e-notes/Splines/Intro.htm

But if you want special features like vertical tangents, cornerpoints, periodicity, specific asymptotic behavior... polynomials won't suffice.

For a better answer, you need to be more specific.

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