154 The Phenomena of Morphogenesis 



ference, one going to the right (clockwise) and the other to the left 

 (counterclockwise). The effect is something like that of a spinning pin- 

 wheel, or rather of two spinning in opposite directions. The inner mem- 

 bers of each spiral are progressively smaller since they were formed later. 

 We are looking down, in effect, on the top of a growing system, even 

 though growth may have stopped. These spirals are logarithmic ones, 

 since the radial distance to each successive unit on them increases geo- 

 metrically and not arithmetically. The spirals are termed parastichies, 

 or sometimes contact parastichies since each unit is usually somewhat 

 flattened against its inner and outer neighbors in the spiral, a fact which 



Fig. 7-2. A pine cone seen from below. The scales are in two sets of parastichies, 8 

 counterclockwise and 13 clockwise. 



makes the spiral easy to trace ( Fig. 7-2 ) . The spirals intersect each other 

 at an angle which is near to 90°. 



In a bud or meristematic tip that will give rise to a shoot with a rela- 

 tively low phyllotactic fraction ( % or % ) , the units are fewer than in 

 large structures like a cone. In a cross section of such a bud (Fig. 7-3) it 

 is possible to distinguish by the relative sizes of the leaf primordia the 

 order in which they were produced. The genetic spiral can thus be traced, 

 compact and almost two-dimensional here although later it will be pulled 

 out like a telescope when the shoot elongates. In a bud like this one can 

 confirm the observation of Church, that orthostichies do not exist. Were 

 they here, they would appear as radial rows made by every fifth, or 



