A gallery of quasicrystalline quantum states: In nature there is always a competition between order and disorder. This occurs in simple models of solid state systems also, and this has inspired our research into quasicrystals. Quasicrystals are a fundamental form of matter that exists in between perfectly ordered crystals and disordered amorphous materials. This means that they always have a competition between order and disorder built into them. Some of our recent work has focused on the unintuitive physics that arises from this competition, and this physics is often described by quantum states that exhibit this competition clearly. Shown are four example quantum states that show the beauty that emerges from competing order and disorder, from intricate structures, to fractal patterns, and even to states that look like they come from the era of 8-bit video games.