Try this: narrow the slit width a and watch the bright band spread wider — closing each slit diffracts light over a larger angle, so more fringes appear under a broader envelope. Switch to a point source to see curved wavefronts reach the slits instead of flat ones.
Real numbers, exaggerated waves. β and its dependence on λ, D, d are exact; the ripples are drawn ~10³× larger than real light so you can see them travel.