Final answer:
The inheritance of coat color in cats involves a sex-linked trait on the X chromosome, with females potentially displaying a tortoiseshell pattern due to random X inactivation. Male cats can't exhibit this pattern because they have only one X chromosome. In calico cats, codominance results in the expression of both alleles in the form of different fur color patches.
Step-by-step explanation:
The inheritance of coat color in cats is a fascinating example of how genetics determines physical traits. The gene for coat color in cats is located on the X chromosome, which means it is a sex-linked trait. In female cats, during embryonic development, one of the two X chromosomes is randomly inactivated in each cell. This process, known as X inactivation, can result in the distinctive tortoiseshell pattern in cats that have two different alleles (versions) of the coat color gene. As each cell inactivates one of the X chromosomes, patches of color corresponding to the active X chromosome's gene expression appear across the cat's body.
Male cats, on the other hand, have only one X chromosome. This means they can never exhibit a tortoiseshell pattern because they cannot have two different alleles for coat color that would result in varied patches. In terms of types of inheritance, cat coat color can display complete dominance if one allele completely masks the presence of another, but in the case of calico or tortoiseshell patterns, codominance is observed where both alleles' traits are visible in separate patches of fur.