Abstract: In our report, the method of generating fractals based on the matrix iteration of Kronecker product was discussed. Different from the fractals generated by iterated function systems, the fractals generated by the matrix iteration of Kronecker product might be related to the choice of the initial set. If the initial set was square, the fractals were the McMullen set; The definite proportion and separated points were used to construct a bi Lipschitz map among convex quadrilateral, sector ring and square, and it was proved that if the initial set was changed from the square to an arbitrary convex quadrilateral or sector ring which central angle less than 180°，the fractals would be Lipschitz equivalent with McMullen set.