As I understand it, a paradox starts as a fertilized double-yolked egg, and the two fuse early in embryonic life. So it is a case of twins that became one snake. From what I have read, double-yolked eggs tend to run in families, but it is not a trait caused by a single Mendelian gene. And double-yolked eggs are more common in species with large eggs, like ball pythons and Burmese pythons.
I had a bullsnake that produced occassional eggs that I believe were double yolked simply from the size (twice as long and nearly as wide as a normal egg). The babies from those eggs may have been chimeras (with cell lines from each of the two fertilized eggs), but those babies were not paradoxes because they were normals, like both parents. A paradox is a chimera whose cell lines produce different appearances so they can be distinguished.
A paradox male does not produce eggs, so he may pass on a tendency to produce double-yolked eggs to his female offspring, but that doesn't affect his mate. A paradox female may produce another paradox, if she produces a double-yolked egg. And if the color genetics are right in her and her mate.
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