When placed in the magnetic field, the tiny iron particles in the ferrofluid become magnetized themselves, in the same direction as the external field. This actually causes the field strength to increase around each particle, and therefore makes all of the particles slightly attracted to each other. This creates an instability where the areas with more particles become more strongly magnetized, attracting more particles, becoming more strongly magnetized and so on. This goes on until you either max out the field strength the iron can produce, or deplete the surrounding area of iron particles. Either way, this creates alternating areas of low and high iron density, which we see as spikes.
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