Here is where you can find a continually growing block of zeros

Yes, you found it. A continually, albeit slowly, growing block of zeros. 

What’s the value of a continually growing block of zeros? Pretty small. But if you need it, here we are.

So you invented a random-number algorithm which can usefully use a large block of an occasionally-changing number of contiguous zeros? Have at it. Copy and paste these zeros freely, without even mentioning where they came from if you want. They're yours, you can have them. 

Each visit to the Zero Generator adds another zero before sending back a page full of zeroes.