One of the most striking signatures of self-organization is spontaneous pattern formation. Among the morphologies observed, stripes are intrinsically fascinating and have potential for technological applications including nanolithography and nanoelectricity. Examples of materials featuring stripe patterns include Langmuir monolayers, magnetic films, lipid monolayers, liquid crystals and polymer films. Stripe formation is generally attributed to the competition between short-range attractive forces and long-range repulsion arising from dipole interactions. Here we show that stripe phases may result from a different mechanism based on a purely repulsive isotropic short-range pair potential with two characteristic length scales. We consider a two-dimensional (2D) assembly of particles consisting of a hard core surrounded by a soft corona and find that at densities where the hard-and-soft core radii compete with each other, decreasing the temperature induces a transition from a disordered state to an orientationally ordered phase characterized by stripe patterns.