Quadrature amplitude modulation (QAM) exhibits a shaping-loss of πe/6, (≈1.53 dB) compared to the AWGN Shannon capacity. With inspiration gained from special (leaf, flower petal, and seed) packing arrangements (spiral phyllotaxis) found among plants, a novel, shape-versatile, circular symmetric, modulation scheme, the Golden Angle Modulation (GAM) is introduced. Disc-shaped, and complex Gaussian approximating bell-shaped, GAM-signal constellations are considered. For bell-GAM, a high-rate approximation, and a mutual information optimization formulation, are developed. Bell-GAM overcomes the asymptotic shaping-loss seen in QAM, and offers Shannon capacity approaching performance. Transmitter resource limited links, such as space probe-to-earth, and mobile-to-basestation, are cases where GAM could be particularly valuable.