Extensive research has been done to show that heart-beats are composed of the interaction of many physiological components operating on different time scales, with nonlinear and self-regulating nature. The more direct, and easily accessible manifestation of the heart-beat is the pulse; however, it has not been studied anywhere near as extensively. In this paper, we establish the relevance of the multifractal formalism for the arterial pulse, which has long been used as a fundamental tool for diagnosis in the Traditional Indian Medicine, (Ayurveda). The finding of power-law correlations through detrended fluctuation analysis indicates presence of scale-invariant, fractal structures in the pulse. These fractal structures are then further established by self-affine cascades of beat-to-beat fluctuations revealed by wavelet decomposition at different time scales. Finally, we investigate how these pulse dynamics change with age, and disorder. The analytic tools we discuss may be used on a wide range of physiological signals. © 2008 IEEE.