MandelbrotSetIterationCount

MandelbrotSetIterationCount[c] returns the number of iterations of the function f(z) = z² + c, beginning with z₀ = 0, that are needed to determine whether c is in the Mandelbrot set.

Examples

Count iterations for a point:

MandelbrotSetIterationCount[0.3 + 0.5 I]

Point in the set:

MandelbrotSetIterationCount[0]
(* Infinity *)

Create Mandelbrot visualization:

DensityPlot[MandelbrotSetIterationCount[x + I y], 
  {x, -2, 1}, {y, -1.5, 1.5}]

Please visit the official Wolfram Language Reference for more details.