A plain JavaScript ESM implementation:
Try it out: https://josdejong.github.io/mandelbrot-explorer/
Explanation from Wikipedia:
The Mandelbrot set is the set of values of c in the complex plane for which the orbit of the critical point z=0 under iteration of the quadratic map
zn+1 = zn2 + c
remains bounded. Thus, a complex number c is a member of the Mandelbrot set if, when starting with z0=0 and applying the iteration repeatedly, the absolute value of zn remains bounded for all n>0.