Several measures from information theory are used to describe the stru
ctural complexity of the Sceloporus graciosus push-up display signal s
ystem and to compare this complexity to that of other animal communica
tion systems. Data from focal animal observations of both male and fem
ale animals in the field are used to describe the push-up display as a
simultaneous combination of three components: display body postures (
e.g., lateral flattening, arched back), the number of legs extended du
ring the display (0, 2, or 4), and the number, type, and sequence of h
ead-bobs. Various grammatical rules are described that govern the comb
ination of these components into push up displays. Body postures are s
hown to be discrete signals, whereas the number of legs extended and t
he pattern of head-bobs serve as graded signals. The three structural
components are related to each other such that more head bobs are comb
ined with more legs being extended and a greater likelihood that displ
ay body postures are used. Males use more head-bobs, extend more legs,
and use display body postures more often than do females; and sexual
dimorphism is greater during the mating season than after mating has e
nded. Finally, the push up display is ''open'' or ''generative'' such
that new forms of the signal system will be encountered with an increa
sing number of displays observed. Overall, the push up display system
is shown to contain most of the types of complexity observed in the co
mmunicative displays of birds and mammals.