Healthy systems in physiology and medicine are remarkable for their structural variability and dynamical complexity. The concept of fractal growth and form offers novel approaches to understanding morphogenesis and function from the level of the gene to the organism. For example, scale-invariance and long-range power-law correlations are features of non-coding DNA sequences as well as of healthy heartbeat dynamics. For cardiac regulation, perturbation of the control mechanisms by disease or aging may lead to a breakdown of these long-range correlations that normally extend over thousands of heartbeats. Quantification of such long-range scaling alterations are providing new approaches to problems ranging from molecular evolution to monitoring patients at high risk of sudden death. We briefly review recent work from our laboratory concerning the application of fractals to two apparently unrelated problems: DNA organization and beat-to-beat heart rate variability. We show how the measurement of long-range power-law correlations may provide new understanding of nucleotide organization as well as of the complex fluctuations of the heartbeat under normal and pathologic conditions.