How to make complex bifurcation diagrams

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I am wondering if anyone here can direct me to a method or software resource that can be used for developing high quality bifurcation diagrams. The bifurcation diagram I am trying to develop is very complex, and unfortunately the function that generates it is quite abstract so I do not have some recursive function available to use in developing it. I can give the software both the location of each periodic point on the interval and the parameter values where the system snaps into a different stable periodic orbit.

Would any of you happen to have any ideas? Thanks!