Icicles that have grown from slightly impure water develop ripples around their circumference. The ripples have a near-universal wavelength and are thought to be the result of a morphological instability. Using laboratory-grown icicles and various species of impurities, including fluorescent dye, we show that a certain fraction of the impurities remain trapped inside the icicle, forming inclusions within the ice. The inclusions are organized into chevron patterns aligned with the peaks of the ripples. Within the chevrons, a substructure of crescent-shaped structures is observed. We also examine the crystal grain structure of laboratory icicles with and without impurities. We present the first detailed study of these growth patterns in the interior of icicles and discuss their implications for the mechanism of the ripple-forming instability.