"Mandelbrot sets" for different polynomials

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What is the correct term for a set defined analogously to the Mandelbrot set, but for different $1$-parametric polynomial families?

I've found multibrot sets, but they are still defined only for specific families.

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the connectedness locus is a subset of the parameter space of rational functions, which consists of those parameters for which the corresponding Julia set is connected. A bifurcation locus is the boundary of the Mandelbrot set.