In Java we can use the iterate method of the Stream class to create an unbounded stream based on function invocations. We pass to the iterate method an initial value and a function that can be applied to the value. The first element in the unbounded stream is the initial value, the next element is the result of the function invocation with as argument the value from the previous element and this continues for each new element. Suppose we have a function expressed as lambda expression i → i + 2. When we use this lambda expression with the iterate method and a initial value of 1 we get a stream of 1, 1 → 1 + 2, 3 → 3 + 2, …​.

In Java we can use the generate method of the Stream class to create an infinite stream of values. The values are coming from a Supplier instance we pass as argument to the generate method. The Supplier instance usually will be a lambda expression. To give back a fixed value we simply implement a Supplier that returns the value. We can also have different values when we use a method that returns a different value on each invocation, for example the randomUUID method of the UUID class. When we use such a method we can create the Supplier as method reference: UUID::randomUUID.