  Through experimentation, we have discovered that with the changing of driving
conditions, the Faraday waves undergo two abrupt transitions in spatiotemporal
order: onset and instability. The driving amplitudes and frequencies
corresponding to these two transition points exhibit power-law relationships.
The power-law exponent of the onset can be used to categorize different liquids
into two distinct classes, which primarily reflects the differential
contribution of surface tension and viscous forces in the surface wave
dispersion relation. Meanwhile, the power-law exponent of the instability
serves as an indicator of the non-Newtonian properties of the liquid. Based on
our experimental data, we have developed a phenomenological theoretical model
that offers a unified understanding of the Faraday pattern properties.
