Mandelbrotin
Mandelbrotin is a fictional class of fractal sets used in discussions of complex dynamics and fractal geometry that generalize the Mandelbrot set. In this conception, one studies families of polynomials P_p,c(z) = z^p + c with degree p ≥ 2, where c is a complex parameter. For a fixed p, the Mandelbrotin is defined as the set of complex numbers c for which the orbit of z0 = 0 under iteration z_{n+1} = P_p,c(z_n) remains bounded. When p = 2, this construction yields the classical Mandelbrot set. Varying p changes the shape and topological properties of the resulting set, often producing richer or differently connected boundary structures. Mandelbrotins are typically explored numerically using escape-time coloring to visualize the boundary, and they are used pedagogically to illustrate how degree, nonlinearity, and parameter choices influence fractal geometry and dynamical behavior.
Although not a standard term in rigorous mathematics, Mandelbrotin serves as a conceptual tool in textbooks