Multipole expansions of electric charge and current distributions and the fields those multipoles create are a fundamental pillar of electromagnetic theory, but explanations and examples are rare beyond a dipole. In this paper we describe a low-cost exploration of magnetic multipoles. Using the field from ideal magnetic dipoles and a simple binomial approximation, we show that each multipole obeys $B propto r^n$, with $n=-3, -4,-5,-6$ for a dipole, quadrupole, sextupole, and octupole, respectively. Using commercially available NdFeB magnets and the magnetic field sensor inside a smartphone, we experimentally verify the power-law dependence of the multipole configurations. Finally, the open-source Python library Magpylib can simulate the magnetic field of arbitrary permanent magnet distributions, which also shows the same power law dependence for the different multipole configurations.
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