Java random numbers using a seed

If you're giving the same seed, that's normal. That's an important feature allowing tests.

Check this to understand pseudo random generation and seeds:

Pseudorandom number generator

A pseudorandom number generator (PRNG), also known as a deterministic random bit generator DRBG, is an algorithm for generating a sequence of numbers that approximates the properties of random numbers. The sequence is not truly random in that it is completely determined by a relatively small set of initial values, called the PRNG's state, which includes a truly random seed.

If you want to have different sequences (the usual case when not tuning or debugging the algorithm), you should call the zero argument constructor which uses the nanoTime to try to get a different seed every time. This Random instance should of course be kept outside of your method.

Your code should probably be like this:

private Random generator = new Random();
double randomGenerator() {
    return generator.nextDouble()*0.5;
}

The easy way is to use:

Random rand = new Random(System.currentTimeMillis());

This is the best way to generate Random numbers.

You shouldn't be creating a new Random in method scope. Make it a class member:

public class Foo {
   private Random random 

   public Foo() {
       this(System.currentTimeMillis());
   }

   public Foo(long seed) {
       this.random = new Random(seed);
   }

   public synchronized double getNext() {
        return generator.nextDouble();
   }
}

This is only an example. I don't think wrapping Random this way adds any value. Put it in a class of yours that is using it.

That's the principle of a Pseudo-RNG. The numbers are not really random. They are generated using a deterministic algorithm, but depending on the seed, the sequence of generated numbers vary. Since you always use the same seed, you always get the same sequence.