z(0) = pixel; z(n + 1) = z(n)² + c
2 parameters: real and imaginary parts of c.
These sets were named for mathematician Gaston Julia, and can be generated by a simple change in the iteration process described for the Mandelbrot Set.
Start with a specified value of C,
"C-real + i * C-imaginary"; use as the initial value of Z "x-coordinate + i * y-coordinate";
and repeat the same iteration,
Z(n+1) = Z(n)² + C.
The relationship between the Mandelbrot
set and Julia set can hold between other sets as well. All these
are generated by equations that are of the form z(k+1) = f[z(k),c],
where the function orbit is the sequence z(0), z(1), ..., and
the variable c is a complex parameter of the equation.
The value c is fixed for "Julia" sets. The initial orbit value z(0) is the complex number corresponding to the screen pixel.