The magnetic field surrounding a bar-magnet (for example) is continuous. The lines that are drawn to depict the strength and direction of the field don't actually exist. They are akin to drawing contours on an OS map, are they not? What therefore explains the behaviour of iron filings when they are scattered in the magnetic field of a bar magnet? Why do the arrange themselves along distinct 'lines', creating a pattern of peaks and troughs in the field? Does continuum or statistical mechanics offer an explanation the observed behaviour?