A modified fractal equation is proposed for the irregular profiles obtained from metal fracture surfaces. Experimental results do not conform to the self-similitude postulate of Mandelbrot. Instead a reversed sigmoidal curve is obtained in the fractal plot. A new procedure is developed whereby a linear fractal plot and a constant fractal dimension are obtained. A parallel fractal equation is provided for rough, irregular surfaces. The details of the new analyses are presented in depth, emphasizing the assumptions and advantages underlying the adopted procedure.