TREES: TWO-DIMENSIONAL ENGINES THAT FINESSE THE RIGORS OF THREE-DIMENSIONALITY
by Bob WulkowiczTrees are both simple and complex creatures that continue to challenge our many professional assumptions and understandings of their biological functions, mechanisms, and chemistry.
In recent years, many long-held beliefs about trees have been corrected or discarded, and contemporary literature is now filled with innovative research and explorations. The author discusses a new and much different perspective about trees that may help explain some of the evolutionary successes of forests and landscapes. This same perspective also strongly recommends a number of significant changes in future research and tree care practices.
We now easily explore the fascinating underlying mathematics of trees in the newly emerging sciences of fractals and chaos which allow us to mimic the shapes and structures of plants that are immediately recognizable by the biologically inclined. Computer images from math and algorithms give us existing leaf patterns, trace different branching characteristics, and even paint realistic landscapes of full pine and aspen forests. Rather than dismissing these results as mechanical imitations of nature, we are obligated to examine whether nature has more likely always been building from those mathematical rules that are just as fundamental as any familiar law of chemistry or physics.
The author proposes that the evolution of trees has been enhanced by a subtle, but critical, use of a unique and previously unexamined mathematically-defined dynamic. Certain vascular plants such as trees possess a growth template that remains clearly two-dimensional, yet generates a resultant three-dimensional physical structure.
By that stratagem, those vascular plants have taken a remarkable evolutionary path by manipulating simple mathematical principles. The deft shaping of physical placements and orderly division mechanisms in cambial layers provides a significant advantage to their growth potential and survival that is simply not enjoyed by other creatures.
Cambium structures built as two-dimensional templates allow a frugality and disciplined volumetric growth that has engendered more than two hundred million years of replication and progressive continuity. There are few better examples than trees as measures of evolutionary success, and it is proposed here that an important contributory element in that evolution has been a unique and seemingly paradoxical "dimensional duality" of cambial configurations.
It is my statement that trees grow and operate primarily as two-dimensional or sheet creatures leaving a residue of three-dimensional material without assuming many of the mathematical or physical "responsibilities or liabilities" of a volumetric structure.
What has not been discussed or posited previously in the literature is a mathematical magnification made possible by the cambium's linear control over non-linear gain. This paper offers an inquiry into that numerical nature and the remarkable productivity of cambial dynamics, the underlying mathematics, and the evasion of complexities of scale, along with an expanded re-examination of certain existing and established literature in what has been previously considered unrelated areas.
© Bob Wulkowicz, 1996
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