Feedback in the equations describing the scattering coefficients cause
chaotic behavior in the scattering intensities from a system composed
of a pair of osculating spheres. Unlike other systems which display c
haos as a trajectory in phase space, this system exhibits chaotic beha
vior in a partial summation. As the region of osculation increases, te
ll-tale signs of chaos emerge, and the Lyapunov exponent, a measure of
the system's mean rate of exponential error growth, is shown to be gr
eater than zero in these chaotic regions. We show bifurcation diagrams
which depict regions of transformation from stability to chaos, inclu
ding periodic windows and super-cycles.