Hox is a turing model not a gradient model like Shh
Hox uses the turing model which forms alternating and repeating patterns using an activator and an inhibitor. The activator turns on itself and the inhibitor that is far away from the activator. Once the inhibitor is on, it turns off the activator as well as itself. These two interact to form a standing wave, showing areas where the activator is on (inhibitor off) and others where the inhibitor is on (activator off) (Bartlett 2017).
Digits form independently from Shh
Scientists found that the formation of fingers used the Turing model rather than the gradient model by removing Shh and Gli3 which both use the gradient model. What they found was that even after removing Shh and Gli3, fingers still formed. During development, Hox works by regulating this Turing model and increases the wavelength. The increase in wavelength allows for correct finger formation. Without this increase in wavelength, the spaces in between the fingers do not form properly and extra fingers can form. The scientists observed this phenomenon by removing Hox genes from developing mice embryos (Fig. 3). The hands with more Hox genes removed had more, thinner fingers with less space in between. After removing all of the Hox genes, they saw that there was only a stump (Sheth et al. 2012).