Ah, I see. Yes, I did misunderstand the mechanics of your frog thought experiment. However the math for the classical case still doesn't work out the way you need it to. Setting up the mechanics the way you did, you will not get the probability distribution you mentioned on the frog's radial distance from the wall. Nor will you get many alternating wet and dry spots on the wall, even allowing for frogs to jump through the wall. I encourage you to try the math yourself or to set up a Monte-Carlo simulation to estimate the classical consequences of your jumping rules.

If you're not convinced yet, consider the following:

What happens if Hitachi's experimental setup had only one path for the electron to follow rather than two? You're claiming that the frogs are a good model for Hitachi's setup, so it should be the same result that you claim for the frog model with one door. You're claiming that the frog model with one door produces a pattern of alternating wet and dry. What happens in the lab when you try it with electrons? Electrons following a single path don't produce an alternating pattern; they produce a pattern very close to a Gaussian.

Moreover, here's the really wild part of the experiment. If you let electrons go through either just one path or just the other path, you'll get nice smooth Gaussians from both (translated a bit from each other). But open both paths up, you'll see the distribution dim at places. That's very unexpected! Somehow letting more electrons through has decreased the electrons hitting certain parts of the screen. And if you carefully observe your experiment, you'll see that some other areas of the wall more than double in intensity when you open up both paths. It's pretty clear that you'll never be able to invent mechanical rules for classical frogs that can mirror these experimental results.

> i'm trying to understand where do you see the interference of a particle with itself.

This is a slightly subtly distinction, and it's easy to miss what's going on. You "see" the effect of a particle destructively interfering with itself when there's only a single electron on the screen. You "see" the effect in the probability distribution for where that electron appears, but you can't say with high confidence that this is a real effect until you've seen a statistically significant number of particles. But the effect had to have been there the whole time because destructive interference happens independently and individually on each electron. If you still think there's some effect being transmitted between different electrons, then realize that the fact that all the electrons are showing up on the same screen is just a convenience for the experimenter. You would get exactly the same effects by setting up a statistically significant number of screens all spatially separated from each other and running the experiments without signals being able to be communicated between screens and then overlaying the resultant observed positions.

However, the Mach–Zehnder Interferometer is, I believe, an better physical model to witness a single photon interfering with itself. Young's double-slit experiment was invented first, so for really that reason alone, it's taught first, but because of its continuous nature, it's easier to get bogged down in certain irrelevancies. The Mach–Zehnder Interferometer is really much more plainly impossible in a classical universe, or an ensemble interpretation universe for that matter.