A method and corresponding apparatus are configured to generate a mipmap are configured to allocate a mipmap status register of a mipmap level generated with respect to a texture, receive a request for the texture, and calculate a mipmap level with respect to the texture. The method and corresponding apparatus are also configured to determine whether a mipmap of the calculated mipmap level exists using the mipmap status register and outputting a result indicative thereof, and determine whether to generate the mipmap of the mipmap level based on the result.