The main differece between Julia and Mandelbroth sets is that Julia set is confined by the complex number C in the function Z = Z^2 + C as it is always constant throughout the iteration of the complex plane. The Julia set is sometimes refferred to as Mandelbrot's dust, since locking down to a specific coordinate of the complex plane will determine the complex number C, therefore producing a slice in time of Julia set. It could also be looked at as an extra dimension of Mandelbrot set.
To run simply download Processing - https://processing.org/download/ and run the .pde file
I've written this with the help of https://www.youtube.com/channel/UCvjgXvBlbQiydffZU7m1_aw (The Coding Train). Go check out his channel, this guy is awesome.