Using time series of US patents per million inhabitants, knowledge-generating cycles can be distinguished. These cycles partly coincide with Kondratieff long waves. The changes in the slopes between them indicate discontinuities in the knowledge-generating paradigms. The knowledge-generating paradigms can be modeled in terms of interacting dimensions (for example, in university-industry-government relations) that set limits to the maximal efficiency of innovation systems. The maximum values of the parameters in the model are of the same order as the regression coefficients of the empirical waves. The mechanism of the increase in the dimensionality is specified as self-organization which leads to the breaking of existing relations into the more diversified structure of a fractal-like network. This breaking can be modeled in analogy to 2D and 3D (Koch) snowflakes. The boost of knowledge generation leads to newly emerging technologies that can be expected to be more diversified and show shorter life cycles than before. Time spans of the knowledge-generating cycles can also be analyzed in terms of Fibonacci numbers. This perspective allows for forecasting expected dates of future possible paradigm changes. In terms of policy implications, this suggests a shift in focus from the manufacturing technologies to developing new organizational technologies and formats of human interactions
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