Mexican-hat (Ricker) surface

Equation: z = (1 - (x^2 + y^2)/8) * exp(-(x^2 + y^2)/8)

The Mexican hat is the Laplacian of a Gaussian up to a constant. A positive center is ringed by a negative trough, then fades to 0.

It is used in computer vision (blob detection) and seismology (the Ricker wavelet).

Related surfaces

• Decaying exponentialz = 10 * exp(-(x^2 + y^2)/10)
• Breathing Mexican hatz = (1 - (x^2 + y^2)/8) * exp(-(x^2 + y^2)/8) * cos(t)
• Cone (upper half)z = sqrt(x^2 + y^2)