It is as if every photon that went through the slit is somehow aware of all other photons that did so too so each photon can choose the (random) position where it hits on the wall behind the slit such that together they look like as if a WAWE went through the slit.
That is (one reason) why they call it "Quantum Weirdness". God is playing dice with us
Why isn't it just that there's a probability density function that describes the aggregate outcomes of a large number of samples from a random process? Why is "memory" involved?
There's no photon multiplication, and no "all other photons" changing their path.
There is some inter-photon interaction because they are bosons. But it's not significant enough to impact the multi-slit experiment. And the experiment works exactly the same way if you send only one photon at a time.
There is no photon multiplication happening on the double slit.