To put it in scientific terms:
In this function, z as a complex variable corresponds to a point in the Gaussian plane, c is a complex constant. The recursive calculation of this function results in a series of complex figures which, for certain starting points of c, are directed to infinity or remain beneath a finite limit.
A value of c is an element of the Mandelbrot set if the series of calculations remains limited (»converges«).
Enlargements of peripheral areas of the Mandelbrot set always result in new structures which, however, still resemble the larger original one.
