I will present some interesting properties of packing dimension spectrum of local dimension for a Bernoulli measure on McMullen carpet. The spectrum turns out to be much different than the Hausdorff spectrum, in particular it needs not to be continuous wrt the parameters. This is not because the packing dimension is a wrong tool for the job - on the opposite, it lets us notice a new phenomenon that was too subtle for the Hausdorff dimension to detect. It is a joint work with Thomas Jordan.