Thermal convection in a self-gravitating rotating fluid shell is modeled using a hemispherical fluid shell that can be rotated about its axis of symmetry. In this apparatus, a teriary convective state begins to exist at a Rayleigh number approximately equal to 2.1 times the critical value for the onset of convection (RC1). This state is characterized by the coexistence of three waves. In this tertiary state noise is always present. At a slightly higher Rayleigh number, a strong interaction was observed to develop. Frequency locking takes place at 2.4 RC1. Later, the flow exhibits chaotic behavior as shown by the broad band Fourier spectra of the temperature records. Planetary implications of these findings are discussed. ¿ American Geophysical Union 1993