I need help for a school project

[IndyNeerhoff]

I am working on a model that predicts the patterns on a chladni plate for a high school project. I have the following equation: 0=asin(πnx)sin(πmy)+bsin(πmx)sin(πny) where a, b, m and n are all given numbers. I've tried a couple of things like plotting the equation and solving x and y and then plot all the points but im not getting anywhere close to what it should look like. In the link below you can see what result i should be getting. Could anyone pls help me
https://thelig.ht/chladni/

[Gribouillis]

I think you can draw them with a well thought call to matplotlib.pyplot.contour(). It may be a rudimentary method but it can give results with very little code. A more sophisticated approach could use numerical algorithms for differential equations and invoke scipy.integrate.ode() or scipy.integrate.odeint().