  Quadrature amplitude modulation (QAM), deployed in billions of communication
devises, exhibits a shaping-loss of $\pi \mathrm{e}/6$ ($\approx 1.53$ dB)
compared to the Shannon-Hartley theorem. With inspiration gained from special
(leaf, flower petal, and seed) packing arrangements (so called spiral
phyllotaxis) found among plants, we have designed a shape-versatile, circular
symmetric, modulation scheme, \textit{the Golden angle modulation (GAM)}.
Geometric- and probabilistic-shaping-based GAM schemes are designed that
practically overcome the shaping-loss of 1.53 dB. Specifically, we consider
mutual information (MI)-optimized geometric-, probabilistic-, and joint
geometric-and-probabilistic-GAM, under SNR-equality, and PAPR-inequality,
constraints. Out of those, the joint scheme yields the highest MI-performance,
and then comes the probabilistic schemes. This study finds that GAM could be an
interesting candidate for future communication systems. Transmitter resource
limited links, such as space probe-to-earth, satellite, and
mobile-to-basestation, are scenarios where capacity achieving GAM could be of
particular value.
