The geometric design is based on your email address; change your email and the design will change. If an account doesn't have an email address set, the ip address of the person browsing is used as the basis for the hash instead.
If you have a Gmail account, you can trivially add an alias by adding
+somevalue to your Gmail username. For example, if your address is
email@example.com you can use
firstname.lastname@example.org too and it'll arrive in the same email box. Moreover, Gmail ignores dots in the email address;
email@example.com is seen as the same address as
firstname.lastname@example.org. Use this to your advantage.
This only applies to 'anonymous' gravatars (called identicons), where you have not set your own image on gravatar.com or selected the identicon explicitly in your profile. The other alternative is for you to pick a geometric image you do like and to upload that to gravatar.com or directly to your profile here.
Note that avatars are used to help others distinguish between different posters; the anonymous 'identicons' give us this even for people who have not uploaded an avatar image, here or on gravatar.com. As such we don't want the image to change too often.