A structural wall unit system includes a plurality of wall units having at least one face being a rotational tessellation. The face has at least two irregular sides extending therefrom. Each side of the wall units have at least one spacer or connector configured to engage other wall units. The structural wall unit system also includes a plurality of starter course units, where each starter course unit has a portion of a primary rotational tessellation element having at least one irregularly shaped side that is an image of the first side or the third side. Each irregularly shaped side of the starter course units have at least one spacer or connector configured to engage the wall units, and the starter course units have at least one straight side. The starter course units and the wall units are configured for assembly as a structural wall having a natural, random appearance.