The natural ordering of shapes is not historically used in visualization applications. It could be helpful to show if an order exists among shapes, as this would provide an additional visual channel for presenting ordered bivariate data. Objective—we rigorously evaluate the use of visual entropy allowing us to construct an ordered scale of shape glyphs. Method—we evaluate the visual entropy glyphs in replicated trials online and at two different global locations. Results—an exact binomial analysis of a pair-wise comparison of the glyphs showed a majority of participants (n = 87) ordered the glyphs as predicted by the visual entropy score with large effect size. In a further signal detection experiment participants (n = 15) were able to find glyphs representing uncertainty with high sensitivity and low error rates. Conclusion—Visual entropy predicts shape order and provides a visual channel with the potential to support ordered bivariate data.