Selfsimilar structures incorporate in their geometrical design the noble numbers, i.e. numbers which are functions of the golden mean and are characterized by fivefold symmetry of the pentagon and dodecahedron. The golden mean is the most irrational number in the sense that rational approximations converge very slowly to as compared to other irrational numbers.
Irrational numbers are numbers such as which has an infinite number of non-periodic decimals.
The golden mean had a special significance in ancient cultures. The association of noble numbers with growth of selfsimilar patterns has been established quantitatively in plant phyllotaxis in botany. A summary of documented evidence collected over a period of more than 150 years is given below and will help understand the association between noble numbers and selfsimilar patterns in the plant kingdom. Phyllotaxis is the study of the arrangement of all plant elements which originate as primordia on the shoot apex. The botanical elements which constitute plants are branches, leaves, petals, stamens, sepals, florets, etc.