"All patterns, whether drawn by artists, calculated by mathematicians, or produced by natural forces are shaped by the same spatial environment. All are subject to the tyranny of space. Synthetic patterns of lines and dots are engaging in their own right but, more importantly, they speak eloquently of the order that all things inevitably share." (Peter B Stevens, "Patterns in Nature", 1974)
"Although we expect to find eddies in turbulent flow, we do not know when any specific eddy will come into being or die away . We cannot yet predict how eddies interact. Similarly, we know as a general rule that any particle within a turbulent flow gets knocked about in an aimless fashion by the swirls, so that it describes an erratic meandering path, but at any given moment we cannot predict the precise location or velocity of the particle." (Peter B Stevens, "Patterns in Nature", 1974)
"But even if we cannot predict all the details, we can predict something about the average case. We can consider the unpredictable local velocities and pressures as chance or random occurrences and then, with the aid of probability theory, take the mean of those occurrences and obtain mathematical descriptions of average motions in average flows." (Peter B Stevens, "Patterns in Nature", 1974)
"In order to describe meanders, then, we can invoke a model involving scour and centrifugal force, a model that describes the uniform expenditure of energy, or a model based on probability theory. All three models describe the same phenomenon. As far as meanders are concerned, all three models happen to be interrelated - but not out of any fundamental necessity. That is to say, the cross circulation induced by centrifugal force need not necessarily result in a uniform distribution of effort or produce a path that is especially probable. In a world of limited patterns, however, the meander answers several entirely different sets of specifications, so that scour, uniform effort, and probability produce the same design." (Peter B Stevens, "Patterns in Nature", 1974)
"The analysis of turbulence in terms of probability reveals several interesting things about eddies. For instance, the average eddy moves a distance about equal to its own diameter before it generates small eddies that move, more often than not, in the opposite direction. Those smaller eddies generate still smaller eddies and the process continues until all the energy dissipates as heat through molecular motion." (Peter B Stevens, "Patterns in Nature", 1974)
"Of all constraints of nature, the most far-reaching are imposed by space. For space itself has a structure that influences the shape of every existing thing." (Peter B Stevens, "Patterns in Nature", 1974)
"The effect of magnitude or absolute size as a determinant of form shows again how space shapes the things around us. In studying polyhedrons we are unconcerned with magnitude. We assume that a cube is a cube no matter what its size. We find, however, that the geometric relations that arise from a difference in size affect structural behavior, and that a large cube is relatively weaker than a small cube. We also find, as a corollary, that in order to maintain the same structural characteristics a difference in size must be accompanied by a difference in shape." (Peter B Stevens, "Patterns in Nature", 1974)
"The spiral is beautifully uniform; it curves around on itself in a perfectly regular manner. It can fill all of two-dimensional space, being capable of infinite expansion, and it is also quite short. But [...], as measured by the mean of distances to its center, the spiral is extremely indirect." (Peter B Stevens, "Patterns in Nature", 1974)
"Turbulence forms the primordial pattern, the chaos that was 'in the beginning'." (Peter B Stevens, "Patterns in Nature", 1974)
"We might note in passing that the lines and circles adopted by natural forms are never perfect. Neither the stream nor the meteor runs perfectly straight, nor is the pond or orbital trajectory a perfect circle. Straight lines and circles are only the pure forms. They occur under only the simplest conditions. In nature, however, conditions are never entirely simple, and any 'elementary' or 'isolated' part is embedded in a larger system that operates in turn within other still larger systems. To some extent, then, the part is acted upon by the whole - by the totality of all the systems - and it never exactly fits an easily definable pattern. The warning is clear: nature never conforms precisely to our simple models; she introduces modifications as dictated by her lawful response to a multiplicity of demands." (Peter B Stevens, "Patterns in Nature", 1974)
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