CHAPTER ONE: THE BASIS OF DESIGN IN NATURE

FOR the purpose of the present work, it will be sufficient to deal only with the conclusions obtained by the study of the bases of design in nature. There are so many fascinating aspects of natural form, so many tempting by-paths, that it would be easy to wander far from the subject now under consideration. Moreover, the morphological field has received attention from many explorers more gifted and better equipped to examine and interpret the phenomena of shape from a scientific point of view than the writer, whose training has been, and disposition is, merely that of a practical artist.⁴ His working hypothesis, responsible for the material here presented, was formulated upon the assumption that the same curve persists in vegetable and shell growth. This curve is known mathematically as the constant angle or logarithmic spiral. This curiously fascinating curve has received much attention.⁵ As a curve form, its use for purposes of design is limited, but it possesses a property by which it may readily be transformed into a rectangular spiral. The spiral in nature is the result of a process of continued proportional growth. This will be clear if we consider a series of cells produced during a period of time, the first cell growing according to a definite ratio as new cells are added to the system. (See Figs. 1 and 2.) The shell is but a cone rolled up. Fig. 1 represents the cone of such an aggregate, while Fig. 2 shows the system coiled.

Two side-by-side diagrams illustrating biological growth principles. Fig. 1 shows a vertical stack of seven circles decreasing in size from bottom to top, representing an "aggregate cone" of growth. Fig. 2 shows a series of circles of varying sizes arranged in a spiral pattern within a larger circle, representing the system in its "coiled" state.

Fig. 1.                                       Fig. 2. <-

The curve of the coil is a logarithmic spiral in which the law of proportion is inherent. A distinctive feature of this curve is that when any three radii vectors are drawn, equi-angular distance apart, the middle one is a mean proportional between the other two; in other words, the three vectors, or the three lines drawn from the center or pole to the circumference, equi-angular distance apart, form three terms of a simple proportion; A is to B, as B is to C, and according to the "rule of three" the product of the extremes, A and C, is equal to the square of the mean. A multiplied by C equals B multiplied by itself. The early