One of the characteristic features of complex adaptive systems is fractal structures and self-similarity. This means that certain features repeat themselves at different scales both in temporal and spatial dimensions. The mechanism that creates these fractal, self-similar structures is often a simple, local construction or growth rule. There exist a number of computer algorithms -many of them in the area of artificial live- that illustrate that principle of recurrent spatial branching like in trees or river beds. In the temporal domain self-similar structures are often related to the phenomenon of deterministic chaos. The dynamical system behaves quite regularly over long stretches of time but occasionally excursions to unpredictable types of behavior occur. These intermittent transitions are spaced in time at a wide range of intervals. The frequency and magnitude of the transition often follows a 1/f-distribution, which implies that small transitions occur at much higher frequency and large transitions. This apparently universal phenomenon also seems to apply to the magnitude and frequency of innovations. Fundamental innovations are typically of by a sequence of innovations that constitute improvements of the original concept up to the point of only marginal improvements or the next fundamental innovation.