The fact that the first image has a random distribution, shows that each electron interferes with itself and strikes a point on on the screen which would be dictated by the probability function.
What a) tells us is that a single electron was fired at two slits and was deflected to a point at an angle from a straight projections from the slits. The same would happen if one threw a billiard ball at two slits with the analogous sizes to the diameter of the ball.
b) and c) tells us that the shooter kept mostly hitting edges.
It is d) that shows a clear interference pattern in a distribution that answers to the question "what is the probability if I throw electrons against a double slit of appropriate dimensions that it will hit (x,y) on the screen."
The conclusion is that an electron does not behave like a billiard ball, i.e. classical mechanics, it does not have the behavior of a classical billiard ball when scattered.
This behavior is described accurately by solutions of the quantum mechanical equation with the boundary problem "electron scattering off two slits". The square of these solutions, called wave functions, give us the probability distribution .
The statement "each electron interferes with itself" is misleading/confusing as far as the behavior of matter in dimensions where quantum mechanics prevails ( i.e. commensurate with h_bar). "The wave function describing the electron has interference terms passing the boundary of the two slits" is more correct. It is not a mass wave, nor an energy wave.