Damped circular wave e^{−αr} sin(r − 4t)

Equation: z = exp(-0.12 * sqrt(x^2 + y^2)) * sin(sqrt(x^2 + y^2) - t * 4)

Compared with a pure sin(r − ct) drop, the factor e^{−αr} mimics geometric or frictional decay.

α = 0.12 leaves a few visible rings before the surface flattens at the domain edge.

Related surfaces

• Water dropz = sin(sqrt(x^2 + y^2) - t * 3)
• Concentric ripplesz = sin(sqrt(x^2 + y^2))
• Decaying exponentialz = 10 * exp(-(x^2 + y^2)/10)