The properties of selected knotted strapwork strands emergent in a Girih decoration of an aperiodic Penrose P2 tiling are quantified. The selected strands are from six families with distinctive shapes and knot topology. Although it is not evident how to predict strand properties a priori, and despite the evolution of fractal structures, many features of these strand families follow quantitative scaling laws arising from the characteristics of Penrose tilings.