Weierstrass–Mandelbrot function

Not to be confused with the Weierstrass function (continuous but nowhere differentiable) or the Mandelbrot set.

The Weierstrass–Mandelbrot function (often abbreviated W-M function and sometimes referred to as Weierstrass–Mandelbrot Noise) is a generalization of the classical Weierstrass function, extended to higher dimensions to model natural fractal phenomena. It is frequently used in terrain generation, particularly in simulated environments for robotics and autonomous vehicle testing. Unlike its 1D counterpart, the W-M function in multiple dimensions displays directionality, anisotropy, and multifractality, making it suitable for simulations of physically realistic surfaces.

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