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Video abstract for the article 'Qubism: self-similar visualization of many-body wavefunctions ' by Javier Rodríguez-Laguna, Piotr Migdał, Miguel Ibáñez Berganza, Maciej Lewenstein and Germán Sierra (Javier Rodríguez-Laguna et al 2012 New J. Phys. 14 053028) Read the full article in New Journal of Physics at http://iopscience.iop.org/1367-2630/14/5/053028/article. GENERAL SCIENTIFIC SUMMARY Introduction and background. Quantum many-body wavefunctions encode the behaviour of most interesting systems studied by condensed-matter physics or quantum information theory: correlations, entanglement, local or non-local order parameters, etc. They are extremely complex mathematical objects: their number of parameters scales exponentially with the system size. Main results. We introduce a two-dimensional pictorial representation technique for many-qubit wavefunctions, which we have termed 'qubism'. Its main property is recursivity: increasing the number of qubits reflects in an increase in the image resolution. Thus, the plots are typically fractal-like for translationally-invariant states. We examine ground states of commonly used Hamiltonians in condensed matter and cold atom physics, such as the Heisenberg or the Ising model in a transverse field. Many features of the wavefunction, such as magnetization, correlations and criticality, are represented by visual properties of the images. In particular, entanglement can be easily spotted, as a deviation from trivial self-similarity. Wider implications. Visualization of mathematical objects is always a source of insight and new problems. Our techniques allow the researchers in quantum many-body physics to use plots and images as a guide and representation tool. The extension of these techniques to other fields which suffer from combinatorial explosion (DNA analysis, stochastic processes, categorical time series etc) is straightforward.