Tests whether a complex number is in the Mandelbrot set (exact cardioid/bulb tests plus escape iteration with MaxIterations option)
MandelbrotSetMemberQ[z]
MandelbrotSetMemberQ[{0 , 1, I / 2, I + 1}]
→ {True, False, True, False}Quiet[MandelbrotSetMemberQ[{0, -2, -1.979, -2.9`2, 1 / 4, 0.26, I, 1 + I, -1 / Pi, N[1 / Pi, 200]}]]
→ {True, True, True, False, True, False, True, False, True, False}{MandelbrotSetMemberQ[25001 / 100000, WorkingPrecision -> 5], MandelbrotSetMemberQ[25001 / 100000, WorkingPrecision -> 6]}
→ {False, False}- MaxIterations — default 1000
- WorkingPrecision — default Automatic