On my way to becoming a graphics developer at Wolfram Research, I took detours through degrees in design and architecture. One of my enduring passions is exploring graphic design with programmatic and generative systems. While some aspects of design require the skilled hand of the designer, others can be formalized and explored by computer. For those tasks, Mathematica is an exceptional tool. As starting points for design explorations, corporate logos are ideal. They often distill a single idea into simplified geometric form that is straightforward to parameterize in Mathematica. Once a logo is in Mathematica, exploring its parameter space quickly leads to the discovery of new graphic phenomena, emergent forms, unexpected relationships, and burgeoning lines of inquiry. Mathematica's very high-level programming and interface constructs help your explorations keep pace with your brain as it flings out new ideas left and right. Take a logo as simple as the Mercedes-Benz star. Just three points framed by a circle, its geometry is easily described in a few lines of Mathematica code, with some obvious parameters controlling the number of points on the star, the sharpness of the star's points, the thickness of the outer circle, and the orientation of the star.