A famous subgenus of the genus  Complex Quadratic polynomial dynamical laws  is :
Z_n+1 = Z_n² + C,  where Z is a so-called complex variable, and that means that the value of Z (and thus of  Z_n ,  Z_n+1 ,  Z_n+2 ,  Z_n+3 ,  etc.) does not need to be chosen only from the set of real numbers (that is, numbers that can be written by means of decimal expansions) but also from the set of complex numbers (of which the real numbers constitute a subset, that is, a special case. Complex numbers are numbers having the form  a + bi,  where  a  and  b  are real numbers, and where  i  is equal to the square root of minus one).
This dynamical law results in one of the most complicated mathematical patterns (visible on the computer screen as a very complicated and moreover esthetically appealing figure of shapes and colors) ever encountered. The pattern, generated by this law, is called the MANDELBROT landscape. It is widely known. The next Figure illustrates this landscape.