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Abstract :

With my study I want to advance a hypothesis that Phyllotaxis is caused by a lattice of Ice-Crystals or large Water Clusters which are stablized (coated) by certain proteins, e.g. special Ice-binding- or Water-Cluster-binding-proteins.

The microscopic Image of the remains of an evaporated water droplet shows a phyllotactic pattern that formed during the evaporation of the water droplet on a silicon wafer.

This image is a proof that Water itself must be the main contributor which causes Phyllotaxis !

The pysical process Evaporation, and electric charge and coloumb forces caused by evaporation also seem to play a role in the pattern formation and in the precise orientation and positioning of the water clusters in the pattern.

Important for the formation of a phyllotactic Fibonacci pattern seems to be a large central Water Cluster, that may have icosahedral MacKay-geometry, consisting of large icosahedral Sub-Clusters

formed by the stable icosahedral water clusters (H2O)100 or (H2O)280.

Typical cluster numbers of Mackay-Clusters are 13 and 55 which are Fibonacci Numbers ! Additional proof comes from SEM-Images of the Sunflower Capitulum.

These images indicate that new primordia are caused by rhombic crystals, which seem to be either ice-crystals or large water cluster crystals that formed with the help of ice-binding proteins or similar.

Proof for a physical cause of Phyllotaxis is also provided by a study about variations in the Fibonacci-spiral patterns of twigs of the three “Pinus Mugo“,

which shows that the Fibonacci-pattern variation depends on altitude and temperature- / radiation- conditions.

With the results of this study I developed an infinite Fibonacci-Number-Sequences-Table that contains all existing Fibonacci-Sequences and all natural numbers.

Finally I present a mathematical discovery regarding constant Phi. All natural numbers and their square roots, as well as constant Pi (π), can be expressed by only using constant Phi (1.618…) and the base unit 1.

Part III of the book “Symmetry in Plants“ emphasizes the thesis that the resolution of an important part of the mystery of Phyllotaxis can be found in the basic laws of nature responsible for the homologies of structure,

and that a global and synthetic view on nature can give important keys for the understanding of Phyllotaxis.