We study creating and breaking symmetry in digitally generated artificial-life-based visual art. Therefore, an artificial swarm-based pattern-making system is used as a test bed. The patterns are generated algorithmically by emulating the collective feeding behavior of sand-bubbler crabs. Our focus is on analyzing concepts and templates for incorporating symmetry and broken symmetry into the creation process of bioinspired art. All four types of two-dimensional symmetry defined by isometric maps are used to create images. Apart from treating geometric symmetry, we also consider color as an object of symmetric transformations. Color symmetry is realized as a color permutation consistent with the isometric maps. Therefore, color permutation groups have been designed which utilize mappings on a color wheel.