Self-assembled gold nanoclusters are attractive building blocks for future nanoscale sensors and optical devices due to their exciting catalytic properties. In this work, we report direct bottom-up synthesis of spiral patterns of gold nanoclusters in silicon (100) substrates by Au ion implantation followed by thermal annealing. This unique phenomenon is observed only above a critical threshold implantation dose and annealing temperature. Systematic study by electron microscopy, analytical x-ray diffraction and atomic force microscopy shows the temperature- and time-dependent nucleation, growth of Au nanoclusters and evolution of the spiral patterns. The observed patterns of gold nanoclusters bear a resemblance to the spiral growth prevalent in some directionally solidified eutectic alloys. Based on this systematic study of the growth and morphology of nanoclusters, a tentative model has been proposed for the formation mechanism of this unusual self-assembled pattern in an amorphous Si/Au system. This model shows that melting of the implanted layer is essential and without which no spiral patterns are observed. A better understanding of this self-assembly process will open up new ways to fabricate ordered arrays of gold nanoclusters in silicon substrates for seeding selective growth of one-dimensional nanostructures.