Lovelock proposed a concept, referred to as Gaia, in which feedbacks from the biosphere minimize fluctuation in climatic conditions. A simple model, referred to as daisyworld, was later developed to illustrate the Gaia concept. Daisyworld is defined on a cloudless flat or cylindrical planet with negligible atmospheric greenhouse gases in which bare soil and daisies of different colors interact so as to maintain stable climatic conditions. In the current paper, this daisyworld model is used to study the interaction between biota and their environment in more detail. It is found that periodic, and even chaotic, states can exist when the parameter controlling the feedback between biota and environmental temperature is changed. The existence of periodic and chaotic solutions is verified by their power spectra, fractal dimensions, and Lyapunov exponents. These results show that stable climatic conditions are not always maintained in daisyworld, despite the presence of daisies which supply the required feedback. While daisyworld is a simple model, the mathematical analysis of this model raises questions about the validity of the Gaia hypothesis.