A method of machining a surface of a workpiece is accomplished by bringing a cutting tool into contact with the surface of the workpiece and for at least one cutting pass, i, causing relative movement between the cutting tool and the surface of the workpiece along a path in the surface of the workpiece. The path is in the nature of a mathematical function defined over a segment, C, of a coordinate system and characterized by a set of nonrandom, random or pseudorandom parameters selected from the group consisting of amplitude, phase and period or frequency. Relative movement between the cutting tool and the surface of the workpiece may be accomplished by bandpass filtering a noise signal; providing the bandpass filtered signal to a function generator; generating a randomly modulated mathematical function from the function generator; and in response to the randomly modulated function, directing the relative movement between the cutting tool and the surface of the workpiece along the path in the surface of the workpiece.