Folding and horseshoes are found in two dimensional maps computed from simulations of the driven, damped pendulum. A simple model illustrates how horseshoes produce fractal boundaries of the basins of attraction for separate steady state solutions. Fractal basin boundaries result in noise amplification through extrinsic intermittency, and in long transients when the dimension of the boundary approaches that of the phase space. Folding of the phase space beyond a crisis, in which chaotic attractors collide with the boundary that separates their basins of attraction, produces complex, intermittent dynamical behavior. Both noise and crisis induced intermittency can produce power spectra S(ω) ∝ 1 ω α , with α ≅ 1, over several decades in frequency ω.