X inactivation effects. The tortoiseshell gene is on the X chromosome, and has 2 different alleles, one for orange fur and one for black fur.

In a heterozygous "mosaic" female, orange patches are formed by populations of cells in which the X chromosome with the orange allele is active; black patches have cells in which the X chromosome with the black allele is active.

(“Calico” cats also have white areas, which are determined by yet another gene.)