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A branch that produces less photosynthate than it uses becomes a liability and is shed by the tree. The shedding of branches has an important impact on the structure and visual 21 Figure 19: A modi cation of the tree model by Borchert and Slade 7 . The branches that produce less photosynthate than they use are shed by the tree. For clarity, leaves are not shown. presentation of older trees bottom row of Figure 19. In the above model, the shedding had only a limited e ect on the development of the remaining parts of the tree.

Knuth. Semantics of context-free languages. Mathematical Systems Theory, 22:191 220, 1968. 34 A. J. Koch and H. Meinhardt. Biological pattern formation: from basic mechanisms to complex structures. Manuscript, Max-Planck-Institut fur Entwicklungsbiologie, Tubingen, 1993. 35 P. M. Lewis II, D. J. Rosenkrantz, and R. E. Stearns. Compiler design theory. AddisonWesley, Reading, 1978. 36 A. Lindenmayer. Mathematical models for cellular interaction in development, Parts I and II. Journal of Theoretical Biology, 18:280 315, 1968.

P x; y. According to production p1, this branch develops in the same manner as the main axis. When its apex extends beyond the clipping box, it is removed by production p2, and signal S is generated again. This process may continue until all dormant buds have been activated. Selected phases of the described developmental sequence are illustrated in Figure 23. In derivation step 6 the apex of the main axis grows out of the clipping box. In step 7 this apex and the last internode are removed from the structure, and the bud-activating signal S is generated.

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